├── .gitignore ├── .texpadtmp ├── 475.aux ├── 475.log ├── 475.synctex.gz ├── 475.toc ├── calculus.aux ├── calculus.log ├── calculus.out ├── calculus.synctex.gz ├── calculus.toc ├── comp551.aux ├── comp551.log ├── comp551.out ├── comp551.synctex.gz ├── comp551.toc ├── m247.aux ├── m247.log ├── m247.out ├── m247.synctex.gz ├── m247.toc ├── m254.aux ├── m254.log ├── m254.out ├── m254.synctex.gz ├── m254.toc ├── m357.aux ├── m357.log ├── m357.out ├── m357.synctex.gz ├── m357.toc ├── m454.aux ├── m454.log ├── m454.synctex.gz ├── m458.aux ├── m458.log ├── m458.out ├── m458.synctex.gz ├── m458.toc ├── m475.aux ├── m475.log ├── m475.synctex.gz ├── m475.toc ├── math455ch11.aux ├── math455ch11.log ├── math455ch11.synctex.gz ├── math455ch8.aux ├── math455ch8.log ├── math455ch8.synctex.gz ├── math455ch9.aux ├── math455ch9.log ├── math455ch9.synctex.gz ├── mechanics.aux ├── mechanics.log └── mechanics.synctex.gz ├── README.md ├── calculus-and-analysis ├── calculus.pdf ├── math-141.pdf ├── math-222.pdf ├── math-254.pdf ├── math-454.pdf ├── math-455-final.pdf ├── math-455-midterm.pdf └── math-475.pdf ├── geometry └── math-458.pdf ├── linear-algebra ├── math-133.pdf └── math-247.pdf ├── physics ├── Math-470.pdf └── phys-514.pdf ├── prob-and-stats ├── math-357.pdf ├── math-587.pdf └── math-589.pdf ├── reports ├── ergodictheory1.pdf ├── lie-groups-and-PDE.pdf └── lorentzian-causality-theory.pdf ├── source-code ├── calculus.tex ├── finalsummary.tex ├── m247.tex ├── m254.tex ├── m357.tex ├── m454.tex ├── m458.tex ├── p514.tex └── parallel-transport.png └── teaching ├── calculus ├── math314-meeting-1-suggested-exercises.pdf └── math314-meeting-1.pdf └── linear-algebra └── math133-midterm1-fact-sheet-fall-2021.pdf /.gitignore: -------------------------------------------------------------------------------- 1 | .DS_Store 2 | -------------------------------------------------------------------------------- /.texpadtmp/475.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \providecommand*\new@tpo@label[2]{} 3 | \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}\protected@file@percent } 4 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Domains and Boundary Conditions}{2}\protected@file@percent } 5 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.1}What are the main boundary conditions?}{2}\protected@file@percent } 6 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Classification of PDEs}{3}\protected@file@percent } 7 | \global\@namedef{scr@dte@section@lastmaxnumwidth}{10.84047pt} 8 | \global\@namedef{scr@dte@subsection@lastmaxnumwidth}{18.37163pt} 9 | \global\@namedef{scr@dte@subsubsection@lastmaxnumwidth}{26.8883pt} 10 | -------------------------------------------------------------------------------- /.texpadtmp/475.log: -------------------------------------------------------------------------------- 1 | This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex 2019.7.26) 15 FEB 2020 14:49 2 | entering extended mode 3 | restricted \write18 enabled. 4 | file:line:error style messages enabled. 5 | %&-line parsing enabled. 6 | **475.tex 7 | (./475.tex 8 | LaTeX2e <2018-12-01> 9 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrartcl.cls 10 | Document Class: scrartcl 2019/02/01 v3.26b KOMA-Script document class (article) 11 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrkbase.sty 12 | Package: scrkbase 2019/02/01 v3.26b KOMA-Script package (KOMA-Script-dependent basics and keyval usage) 13 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrbase.sty 14 | Package: scrbase 2019/02/01 v3.26b KOMA-Script package (KOMA-Script-independent basics and keyval usage) 15 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics/keyval.sty 16 | Package: keyval 2014/10/28 v1.15 key=value parser (DPC) 17 | \KV@toks@=\toks14 18 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrlfile.sty 19 | Package: scrlfile 2019/02/01 v3.26b KOMA-Script package (loading files) 20 | ))) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/tocbasic.sty 21 | Package: tocbasic 2019/02/01 v3.26b KOMA-Script package (handling toc-files) 22 | \scr@dte@tocline@numberwidth=\skip41 23 | \scr@dte@tocline@numbox=\box27 24 | ) 25 | Package tocbasic Info: omitting babel extension for `toc' 26 | (tocbasic) because of feature `nobabel' available 27 | (tocbasic) for `toc' on input line 134. 28 | Package scrartcl Info: You've used standard option `11pt'. 29 | (scrartcl) This is correct! 30 | (scrartcl) Internally I'm using `fontsize=11pt'. 31 | (scrartcl) If you'd like to set the option with \KOMAoptions, 32 | (scrartcl) you'd have to use `fontsize=11pt' there 33 | (scrartcl) instead of `11pt', too. 34 | Class scrartcl Info: File `scrsize11pt.clo' used to setup font sizes on input line 2162. 35 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrsize11pt.clo 36 | File: scrsize11pt.clo 2019/02/01 v3.26b KOMA-Script font size class option (11pt) 37 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/typearea.sty 38 | Package: typearea 2019/02/01 v3.26b KOMA-Script package (type area) 39 | \ta@bcor=\skip42 40 | \ta@div=\count80 41 | \ta@hblk=\skip43 42 | \ta@vblk=\skip44 43 | \ta@temp=\skip45 44 | \footheight=\skip46 45 | Package typearea Info: These are the values describing the layout: 46 | (typearea) DIV = 10 47 | (typearea) BCOR = 0.0pt 48 | (typearea) \paperwidth = 597.50793pt 49 | (typearea) \textwidth = 418.25555pt 50 | (typearea) DIV departure = -6% 51 | (typearea) \evensidemargin = 17.3562pt 52 | (typearea) \oddsidemargin = 17.3562pt 53 | (typearea) \paperheight = 845.04694pt 54 | (typearea) \textheight = 595.80026pt 55 | (typearea) \topmargin = -25.16531pt 56 | (typearea) \headheight = 17.0pt 57 | (typearea) \headsep = 20.40001pt 58 | (typearea) \topskip = 11.0pt 59 | (typearea) \footskip = 47.6pt 60 | (typearea) \baselineskip = 13.6pt 61 | (typearea) on input line 1715. 62 | ) 63 | \c@part=\count81 64 | \c@section=\count82 65 | \c@subsection=\count83 66 | \c@subsubsection=\count84 67 | \c@paragraph=\count85 68 | \c@subparagraph=\count86 69 | \scr@dte@section@maxnumwidth=\skip47 70 | Class scrartcl Info: using compatibility default `runin=bysign' 71 | (scrartcl) for `\section on input line 4489. 72 | Class scrartcl Info: using compatibility default `afterindent=bysign' 73 | (scrartcl) for `\section on input line 4489. 74 | \scr@dte@part@maxnumwidth=\skip48 75 | Class scrartcl Info: using compatibility default `afterindent=false' 76 | (scrartcl) for `\part on input line 4497. 77 | \scr@dte@subsection@maxnumwidth=\skip49 78 | Class scrartcl Info: using compatibility default `runin=bysign' 79 | (scrartcl) for `\subsection on input line 4507. 80 | Class scrartcl Info: using compatibility default `afterindent=bysign' 81 | (scrartcl) for `\subsection on input line 4507. 82 | \scr@dte@subsubsection@maxnumwidth=\skip50 83 | Class scrartcl Info: using compatibility default `runin=bysign' 84 | (scrartcl) for `\subsubsection on input line 4517. 85 | Class scrartcl Info: using compatibility default `afterindent=bysign' 86 | (scrartcl) for `\subsubsection on input line 4517. 87 | \scr@dte@paragraph@maxnumwidth=\skip51 88 | Class scrartcl Info: using compatibility default `runin=bysign' 89 | (scrartcl) for `\paragraph on input line 4527. 90 | Class scrartcl Info: using compatibility default `afterindent=bysign' 91 | (scrartcl) for `\paragraph on input line 4527. 92 | \scr@dte@subparagraph@maxnumwidth=\skip52 93 | Class scrartcl Info: using compatibility default `runin=bysign' 94 | (scrartcl) for `\subparagraph on input line 4537. 95 | Class scrartcl Info: using compatibility default `afterindent=bysign' 96 | (scrartcl) for `\subparagraph on input line 4537. 97 | \abovecaptionskip=\skip53 98 | \belowcaptionskip=\skip54 99 | \c@pti@nb@sid@b@x=\box28 100 | Package tocbasic Info: omitting babel extension for `lof' 101 | (tocbasic) because of feature `nobabel' available 102 | (tocbasic) for `lof' on input line 5781. 103 | \scr@dte@figure@maxnumwidth=\skip55 104 | \c@figure=\count87 105 | Package tocbasic Info: omitting babel extension for `lot' 106 | (tocbasic) because of feature `nobabel' available 107 | (tocbasic) for `lot' on input line 5793. 108 | \scr@dte@table@maxnumwidth=\skip56 109 | \c@table=\count88 110 | Class scrartcl Info: Redefining `\numberline' on input line 5957. 111 | \bibindent=\dimen102 112 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/geometry/geometry.sty 113 | Package: geometry 2018/04/16 v5.8 Page Geometry 114 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ifpdf.sty 115 | Package: ifpdf 2018/09/07 v3.3 Provides the ifpdf switch 116 | ) (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ifvtex.sty 117 | Package: ifvtex 2016/05/16 v1.6 Detect VTeX and its facilities (HO) 118 | Package ifvtex Info: VTeX not detected. 119 | ) (/usr/local/texlive/2019/texmf-dist/tex/generic/ifxetex/ifxetex.sty 120 | Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional 121 | ) 122 | \Gm@cnth=\count89 123 | \Gm@cntv=\count90 124 | \c@Gm@tempcnt=\count91 125 | \Gm@bindingoffset=\dimen103 126 | \Gm@wd@mp=\dimen104 127 | \Gm@odd@mp=\dimen105 128 | \Gm@even@mp=\dimen106 129 | \Gm@layoutwidth=\dimen107 130 | \Gm@layoutheight=\dimen108 131 | \Gm@layouthoffset=\dimen109 132 | \Gm@layoutvoffset=\dimen110 133 | \Gm@dimlist=\toks15 134 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsmath.sty 135 | Package: amsmath 2018/12/01 v2.17b AMS math features 136 | \@mathmargin=\skip57 137 | 138 | For additional information on amsmath, use the `?' option. 139 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amstext.sty 140 | Package: amstext 2000/06/29 v2.01 AMS text 141 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsgen.sty 142 | File: amsgen.sty 1999/11/30 v2.0 generic functions 143 | \@emptytoks=\toks16 144 | \ex@=\dimen111 145 | )) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsbsy.sty 146 | Package: amsbsy 1999/11/29 v1.2d Bold Symbols 147 | \pmbraise@=\dimen112 148 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsopn.sty 149 | Package: amsopn 2016/03/08 v2.02 operator names 150 | ) 151 | \inf@bad=\count92 152 | LaTeX Info: Redefining \frac on input line 223. 153 | \uproot@=\count93 154 | \leftroot@=\count94 155 | LaTeX Info: Redefining \overline on input line 385. 156 | \classnum@=\count95 157 | \DOTSCASE@=\count96 158 | LaTeX Info: Redefining \ldots on input line 482. 159 | LaTeX Info: Redefining \dots on input line 485. 160 | LaTeX Info: Redefining \cdots on input line 606. 161 | \Mathstrutbox@=\box29 162 | \strutbox@=\box30 163 | \big@size=\dimen113 164 | LaTeX Font Info: Redeclaring font encoding OML on input line 729. 165 | LaTeX Font Info: Redeclaring font encoding OMS on input line 730. 166 | \macc@depth=\count97 167 | \c@MaxMatrixCols=\count98 168 | \dotsspace@=\muskip10 169 | \c@parentequation=\count99 170 | \dspbrk@lvl=\count100 171 | \tag@help=\toks17 172 | \row@=\count101 173 | \column@=\count102 174 | \maxfields@=\count103 175 | \andhelp@=\toks18 176 | \eqnshift@=\dimen114 177 | \alignsep@=\dimen115 178 | \tagshift@=\dimen116 179 | \tagwidth@=\dimen117 180 | \totwidth@=\dimen118 181 | \lineht@=\dimen119 182 | \@envbody=\toks19 183 | \multlinegap=\skip58 184 | \multlinetaggap=\skip59 185 | \mathdisplay@stack=\toks20 186 | LaTeX Info: Redefining \[ on input line 2844. 187 | LaTeX Info: Redefining \] on input line 2845. 188 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/amsfonts.sty 189 | Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support 190 | \symAMSa=\mathgroup4 191 | \symAMSb=\mathgroup5 192 | LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' 193 | (Font) U/euf/m/n --> U/euf/b/n on input line 106. 194 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/amssymb.sty 195 | Package: amssymb 2013/01/14 v3.01 AMS font symbols 196 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amscls/amsthm.sty 197 | Package: amsthm 2017/10/31 v2.20.4 198 | \thm@style=\toks21 199 | \thm@bodyfont=\toks22 200 | \thm@headfont=\toks23 201 | \thm@notefont=\toks24 202 | \thm@headpunct=\toks25 203 | \thm@preskip=\skip60 204 | \thm@postskip=\skip61 205 | \thm@headsep=\skip62 206 | \dth@everypar=\toks26 207 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/xcolor/xcolor.sty 208 | Package: xcolor 2016/05/11 v2.12 LaTeX color extensions (UK) 209 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics-cfg/color.cfg 210 | File: color.cfg 2016/01/02 v1.6 sample color configuration 211 | ) 212 | Package xcolor Info: Driver file: pdftex.def on input line 225. 213 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics-def/pdftex.def 214 | File: pdftex.def 2018/01/08 v1.0l Graphics/color driver for pdftex 215 | ) 216 | Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1348. 217 | Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1352. 218 | Package xcolor Info: Model `RGB' extended on input line 1364. 219 | Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1366. 220 | Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1367. 221 | Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1368. 222 | Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1369. 223 | Package xcolor Info: Model `Gray' substituted by `gray' on input line 1370. 224 | Package xcolor Info: Model `wave' substituted by `hsb' on input line 1371. 225 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/enumitem/enumitem.sty 226 | Package: enumitem 2019/02/04 v3.8 Customized lists 227 | \labelindent=\skip63 228 | \enit@outerparindent=\dimen120 229 | \enit@toks=\toks27 230 | \enit@inbox=\box31 231 | \enit@count@id=\count104 232 | \enitdp@description=\count105 233 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/inputenc.sty 234 | Package: inputenc 2018/08/11 v1.3c Input encoding file 235 | \inpenc@prehook=\toks28 236 | \inpenc@posthook=\toks29 237 | ) 238 | \c@theorem=\count106 239 | \c@corollary=\count107 240 | \c@definition=\count108 241 | \c@prop=\count109 242 | \c@ex=\count110 243 | (/Users/shereenelaidi/Desktop/University/School /U2/MATH 455 Analysis 4/mathnotes/.texpadtmp/475.aux) 244 | \openout1 = `475.aux'. 245 | 246 | LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 52. 247 | LaTeX Font Info: ... okay on input line 52. 248 | LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 52. 249 | LaTeX Font Info: ... okay on input line 52. 250 | LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 52. 251 | LaTeX Font Info: ... okay on input line 52. 252 | LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 52. 253 | LaTeX Font Info: ... okay on input line 52. 254 | LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 52. 255 | LaTeX Font Info: ... okay on input line 52. 256 | LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 52. 257 | LaTeX Font Info: ... okay on input line 52. 258 | 259 | *geometry* driver: auto-detecting 260 | *geometry* detected driver: pdftex 261 | *geometry* verbose mode - [ preamble ] result: 262 | * driver: pdftex 263 | * paper: 264 | * layout: 265 | * layoutoffset:(h,v)=(0.0pt,0.0pt) 266 | * modes: 267 | * h-part:(L,W,R)=(56.9055pt, 483.69693pt, 56.9055pt) 268 | * v-part:(T,H,B)=(56.9055pt, 731.23593pt, 56.9055pt) 269 | * \paperwidth=597.50793pt 270 | * \paperheight=845.04694pt 271 | * \textwidth=483.69693pt 272 | * \textheight=731.23593pt 273 | * \oddsidemargin=-15.36449pt 274 | * \evensidemargin=-15.36449pt 275 | * \topmargin=-52.7645pt 276 | * \headheight=17.0pt 277 | * \headsep=20.40001pt 278 | * \topskip=11.0pt 279 | * \footskip=47.6pt 280 | * \marginparwidth=59.7508pt 281 | * \marginparsep=12.8401pt 282 | * \columnsep=10.0pt 283 | * \skip\footins=10.0pt plus 4.0pt minus 2.0pt 284 | * \hoffset=0.0pt 285 | * \voffset=0.0pt 286 | * \mag=1000 287 | * \@twocolumnfalse 288 | * \@twosidefalse 289 | * \@mparswitchfalse 290 | * \@reversemarginfalse 291 | * (1in=72.27pt=25.4mm, 1cm=28.453pt) 292 | 293 | (/usr/local/texlive/2019/texmf-dist/tex/context/base/mkii/supp-pdf.mkii 294 | [Loading MPS to PDF converter (version 2006.09.02).] 295 | \scratchcounter=\count111 296 | \scratchdimen=\dimen121 297 | \scratchbox=\box32 298 | \nofMPsegments=\count112 299 | \nofMParguments=\count113 300 | \everyMPshowfont=\toks30 301 | \MPscratchCnt=\count114 302 | \MPscratchDim=\dimen122 303 | \MPnumerator=\count115 304 | \makeMPintoPDFobject=\count116 305 | \everyMPtoPDFconversion=\toks31 306 | ) 307 | LaTeX Font Info: Try loading font information for U+msa on input line 55. 308 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/umsa.fd 309 | File: umsa.fd 2013/01/14 v3.01 AMS symbols A 310 | ) 311 | LaTeX Font Info: Try loading font information for U+msb on input line 55. 312 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/umsb.fd 313 | File: umsb.fd 2013/01/14 v3.01 AMS symbols B 314 | ) 315 | 316 | LaTeX Font Warning: Font shape `OT1/cmr/bx/sc' undefined 317 | (Font) using `OT1/cmr/bx/n' instead on input line 55. 318 | 319 | (/Users/shereenelaidi/Desktop/University/School /U2/MATH 455 Analysis 4/mathnotes/.texpadtmp/475.toc) 320 | \tf@toc=\write3 321 | \openout3 = `475.toc'. 322 | 323 | 324 | Underfull \hbox (badness 10000) in paragraph at lines 59--63 325 | 326 | [] 327 | 328 | [1 329 | 330 | 331 | {/usr/local/texlive/2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2] [3] (/Users/shereenelaidi/Desktop/University/School /U2/MATH 455 Analysis 4/mathnotes/.texpadtmp/475.aux) 332 | 333 | LaTeX Font Warning: Some font shapes were not available, defaults substituted. 334 | 335 | ) 336 | Here is how much of TeX's memory you used: 337 | 5117 strings out of 492616 338 | 82908 string characters out of 6129481 339 | 270674 words of memory out of 5000000 340 | 9007 multiletter control sequences out of 15000+600000 341 | 13950 words of font info for 53 fonts, out of 8000000 for 9000 342 | 1141 hyphenation exceptions out of 8191 343 | 41i,10n,51p,9115b,358s stack positions out of 5000i,500n,10000p,200000b,80000s 344 | 345 | Output written on "/Users/shereenelaidi/Desktop/University/School /U2/MATH 455 Analysis 4/mathnotes/.texpadtmp/475.pdf" (3 pages, 152426 bytes). 346 | PDF statistics: 347 | 70 PDF objects out of 1000 (max. 8388607) 348 | 50 compressed objects within 1 object stream 349 | 0 named destinations out of 1000 (max. 500000) 350 | 1 words of extra memory for PDF output out of 10000 (max. 10000000) 351 | 352 | -------------------------------------------------------------------------------- /.texpadtmp/475.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/475.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/475.toc: -------------------------------------------------------------------------------- 1 | \contentsline {section}{\numberline {1}Introduction}{1}% 2 | \contentsline {subsection}{\numberline {1.1}Domains and Boundary Conditions}{2}% 3 | \contentsline {subsubsection}{\numberline {1.1.1}What are the main boundary conditions?}{2}% 4 | \contentsline {subsection}{\numberline {1.2}Classification of PDEs}{3}% 5 | -------------------------------------------------------------------------------- /.texpadtmp/calculus.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \providecommand\hyper@newdestlabel[2]{} 3 | \providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} 4 | \HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined 5 | \global\let\oldcontentsline\contentsline 6 | \gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} 7 | \global\let\oldnewlabel\newlabel 8 | \gdef\newlabel#1#2{\newlabelxx{#1}#2} 9 | \gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} 10 | \AtEndDocument{\ifx\hyper@anchor\@undefined 11 | \let\contentsline\oldcontentsline 12 | \let\newlabel\oldnewlabel 13 | \fi} 14 | \fi} 15 | \global\let\hyper@last\relax 16 | \gdef\HyperFirstAtBeginDocument#1{#1} 17 | \providecommand\HyField@AuxAddToFields[1]{} 18 | \providecommand\HyField@AuxAddToCoFields[2]{} 19 | \providecommand \oddpage@label [2]{} 20 | \@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Single Variable Calculus}}{1}{section.1}\protected@file@percent } 21 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.1}{Limits and Derivatives}}{1}{subsection.1.1}\protected@file@percent } 22 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.2}{Differentiation Rules}}{2}{subsection.1.2}\protected@file@percent } 23 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.3}{Applications of Differentiation}}{3}{subsection.1.3}\protected@file@percent } 24 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.4}{Integrals}}{4}{subsection.1.4}\protected@file@percent } 25 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.5}{Applications of Integration}}{5}{subsection.1.5}\protected@file@percent } 26 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.6}{Integration Techniques}}{5}{subsection.1.6}\protected@file@percent } 27 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.7}{Further Applications of Integration}}{7}{subsection.1.7}\protected@file@percent } 28 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.8}{Parameter Equations and Polar Coordinates}}{7}{subsection.1.8}\protected@file@percent } 29 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.9}{Infinite Sequences and Series}}{8}{subsection.1.9}\protected@file@percent } 30 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.10}{Strategy for Testing Series}}{9}{subsection.1.10}\protected@file@percent } 31 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.11}{Power Series}}{10}{subsection.1.11}\protected@file@percent } 32 | \@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Multi Variable Calculus}}{11}{section.2}\protected@file@percent } 33 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.1}{Vectors and Geometry of Space}}{11}{subsection.2.1}\protected@file@percent } 34 | \newlabel{accdecomp}{{87}{13}{Vectors and Geometry of Space}{equation.2.87}{}} 35 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.2}{Partial Derivatives}}{14}{subsection.2.2}\protected@file@percent } 36 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.3}{Multiple Integrals}}{15}{subsection.2.3}\protected@file@percent } 37 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.4}{Triple Integrals}}{17}{subsection.2.4}\protected@file@percent } 38 | \@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Vector Calculus}}{17}{section.3}\protected@file@percent } 39 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{Vector Fields}}{17}{subsection.3.1}\protected@file@percent } 40 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{Line Integrals}}{18}{subsection.3.2}\protected@file@percent } 41 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.3}{Green's Theorem}}{19}{subsection.3.3}\protected@file@percent } 42 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.4}{Curl and Divergence}}{19}{subsection.3.4}\protected@file@percent } 43 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.5}{Parametric Surfaces and their Areas}}{20}{subsection.3.5}\protected@file@percent } 44 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.6}{Surface Integrals}}{20}{subsection.3.6}\protected@file@percent } 45 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.7}{Oriented Surface}}{20}{subsection.3.7}\protected@file@percent } 46 | \newlabel{tocindent-1}{0pt} 47 | \newlabel{tocindent0}{0pt} 48 | \newlabel{tocindent1}{19.4667pt} 49 | \newlabel{tocindent2}{38.47682pt} 50 | \newlabel{tocindent3}{0pt} 51 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.8}{Surface Integrals over Vector Fields}}{21}{subsection.3.8}\protected@file@percent } 52 | \@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{3.8.1}{Physical Interpretations: Electric Flux and Heat Flow}}{21}{subsubsection.3.8.1}\protected@file@percent } 53 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.9}{Stokes' Theorem}}{21}{subsection.3.9}\protected@file@percent } 54 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.10}{Divergence Theorem}}{21}{subsection.3.10}\protected@file@percent } 55 | -------------------------------------------------------------------------------- /.texpadtmp/calculus.out: -------------------------------------------------------------------------------- 1 | \BOOKMARK [1][-]{section.1}{1. Single Variable Calculus}{}% 1 2 | \BOOKMARK [2][-]{subsection.1.1}{1.1. Limits and Derivatives}{section.1}% 2 3 | \BOOKMARK [2][-]{subsection.1.2}{1.2. Differentiation Rules}{section.1}% 3 4 | \BOOKMARK [2][-]{subsection.1.3}{1.3. Applications of Differentiation}{section.1}% 4 5 | \BOOKMARK [2][-]{subsection.1.4}{1.4. Integrals}{section.1}% 5 6 | \BOOKMARK [2][-]{subsection.1.5}{1.5. Applications of Integration}{section.1}% 6 7 | \BOOKMARK [2][-]{subsection.1.6}{1.6. Integration Techniques}{section.1}% 7 8 | \BOOKMARK [2][-]{subsection.1.7}{1.7. Further Applications of Integration}{section.1}% 8 9 | \BOOKMARK [2][-]{subsection.1.8}{1.8. Parameter Equations and Polar Coordinates}{section.1}% 9 10 | \BOOKMARK [2][-]{subsection.1.9}{1.9. Infinite Sequences and Series}{section.1}% 10 11 | \BOOKMARK [2][-]{subsection.1.10}{1.10. Strategy for Testing Series}{section.1}% 11 12 | \BOOKMARK [2][-]{subsection.1.11}{1.11. Power Series}{section.1}% 12 13 | \BOOKMARK [1][-]{section.2}{2. Multi Variable Calculus}{}% 13 14 | \BOOKMARK [2][-]{subsection.2.1}{2.1. Vectors and Geometry of Space}{section.2}% 14 15 | \BOOKMARK [2][-]{subsection.2.2}{2.2. Partial Derivatives}{section.2}% 15 16 | \BOOKMARK [2][-]{subsection.2.3}{2.3. Multiple Integrals}{section.2}% 16 17 | \BOOKMARK [2][-]{subsection.2.4}{2.4. Triple Integrals}{section.2}% 17 18 | \BOOKMARK [1][-]{section.3}{3. Vector Calculus}{}% 18 19 | \BOOKMARK [2][-]{subsection.3.1}{3.1. Vector Fields}{section.3}% 19 20 | \BOOKMARK [2][-]{subsection.3.2}{3.2. Line Integrals}{section.3}% 20 21 | \BOOKMARK [2][-]{subsection.3.3}{3.3. Green's Theorem}{section.3}% 21 22 | \BOOKMARK [2][-]{subsection.3.4}{3.4. Curl and Divergence}{section.3}% 22 23 | \BOOKMARK [2][-]{subsection.3.5}{3.5. Parametric Surfaces and their Areas}{section.3}% 23 24 | \BOOKMARK [2][-]{subsection.3.6}{3.6. Surface Integrals}{section.3}% 24 25 | \BOOKMARK [2][-]{subsection.3.7}{3.7. Oriented Surface}{section.3}% 25 26 | \BOOKMARK [2][-]{subsection.3.8}{3.8. Surface Integrals over Vector Fields}{section.3}% 26 27 | \BOOKMARK [2][-]{subsection.3.9}{3.9. Stokes' Theorem}{section.3}% 27 28 | \BOOKMARK [2][-]{subsection.3.10}{3.10. Divergence Theorem}{section.3}% 28 29 | -------------------------------------------------------------------------------- /.texpadtmp/calculus.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/calculus.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/calculus.toc: -------------------------------------------------------------------------------- 1 | \contentsline {section}{\tocsection {}{1}{Single Variable Calculus}}{1}{section.1}% 2 | \contentsline {subsection}{\tocsubsection {}{1.1}{Limits and Derivatives}}{1}{subsection.1.1}% 3 | \contentsline {subsection}{\tocsubsection {}{1.2}{Differentiation Rules}}{2}{subsection.1.2}% 4 | \contentsline {subsection}{\tocsubsection {}{1.3}{Applications of Differentiation}}{3}{subsection.1.3}% 5 | \contentsline {subsection}{\tocsubsection {}{1.4}{Integrals}}{4}{subsection.1.4}% 6 | \contentsline {subsection}{\tocsubsection {}{1.5}{Applications of Integration}}{5}{subsection.1.5}% 7 | \contentsline {subsection}{\tocsubsection {}{1.6}{Integration Techniques}}{5}{subsection.1.6}% 8 | \contentsline {subsection}{\tocsubsection {}{1.7}{Further Applications of Integration}}{7}{subsection.1.7}% 9 | \contentsline {subsection}{\tocsubsection {}{1.8}{Parameter Equations and Polar Coordinates}}{7}{subsection.1.8}% 10 | \contentsline {subsection}{\tocsubsection {}{1.9}{Infinite Sequences and Series}}{8}{subsection.1.9}% 11 | \contentsline {subsection}{\tocsubsection {}{1.10}{Strategy for Testing Series}}{9}{subsection.1.10}% 12 | \contentsline {subsection}{\tocsubsection {}{1.11}{Power Series}}{10}{subsection.1.11}% 13 | \contentsline {section}{\tocsection {}{2}{Multi Variable Calculus}}{11}{section.2}% 14 | \contentsline {subsection}{\tocsubsection {}{2.1}{Vectors and Geometry of Space}}{11}{subsection.2.1}% 15 | \contentsline {subsection}{\tocsubsection {}{2.2}{Partial Derivatives}}{14}{subsection.2.2}% 16 | \contentsline {subsection}{\tocsubsection {}{2.3}{Multiple Integrals}}{15}{subsection.2.3}% 17 | \contentsline {subsection}{\tocsubsection {}{2.4}{Triple Integrals}}{17}{subsection.2.4}% 18 | \contentsline {section}{\tocsection {}{3}{Vector Calculus}}{17}{section.3}% 19 | \contentsline {subsection}{\tocsubsection {}{3.1}{Vector Fields}}{17}{subsection.3.1}% 20 | \contentsline {subsection}{\tocsubsection {}{3.2}{Line Integrals}}{18}{subsection.3.2}% 21 | \contentsline {subsection}{\tocsubsection {}{3.3}{Green's Theorem}}{19}{subsection.3.3}% 22 | \contentsline {subsection}{\tocsubsection {}{3.4}{Curl and Divergence}}{19}{subsection.3.4}% 23 | \contentsline {subsection}{\tocsubsection {}{3.5}{Parametric Surfaces and their Areas}}{20}{subsection.3.5}% 24 | \contentsline {subsection}{\tocsubsection {}{3.6}{Surface Integrals}}{20}{subsection.3.6}% 25 | \contentsline {subsection}{\tocsubsection {}{3.7}{Oriented Surface}}{20}{subsection.3.7}% 26 | \contentsline {subsection}{\tocsubsection {}{3.8}{Surface Integrals over Vector Fields}}{21}{subsection.3.8}% 27 | \contentsline {subsubsection}{\tocsubsubsection {}{3.8.1}{Physical Interpretations: Electric Flux and Heat Flow}}{21}{subsubsection.3.8.1}% 28 | \contentsline {subsection}{\tocsubsection {}{3.9}{Stokes' Theorem}}{21}{subsection.3.9}% 29 | \contentsline {subsection}{\tocsubsection {}{3.10}{Divergence Theorem}}{21}{subsection.3.10}% 30 | -------------------------------------------------------------------------------- /.texpadtmp/comp551.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \providecommand\hyper@newdestlabel[2]{} 3 | \providecommand*\new@tpo@label[2]{} 4 | \providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} 5 | \HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined 6 | \global\let\oldcontentsline\contentsline 7 | \gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} 8 | \global\let\oldnewlabel\newlabel 9 | \gdef\newlabel#1#2{\newlabelxx{#1}#2} 10 | \gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} 11 | \AtEndDocument{\ifx\hyper@anchor\@undefined 12 | \let\contentsline\oldcontentsline 13 | \let\newlabel\oldnewlabel 14 | \fi} 15 | \fi} 16 | \global\let\hyper@last\relax 17 | \gdef\HyperFirstAtBeginDocument#1{#1} 18 | \providecommand\HyField@AuxAddToFields[1]{} 19 | \providecommand\HyField@AuxAddToCoFields[2]{} 20 | \providecommand\BKM@entry[2]{} 21 | \BKM@entry{id=1,dest={73656374696F6E2E31},srcline={70}}{5765656B2031} 22 | \BKM@entry{id=2,dest={73756273656374696F6E2E312E31},srcline={71}}{4C6561726E696E67204F626A65637469766573} 23 | \providecommand \oddpage@label [2]{} 24 | \@writefile{toc}{\contentsline {section}{\numberline {1}Week 1}{1}{section.1}\protected@file@percent } 25 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Learning Objectives}{1}{subsection.1.1}\protected@file@percent } 26 | \BKM@entry{id=3,dest={73756273656374696F6E2E312E32},srcline={83}}{57686174206973204D616368696E65204C6561726E696E673F} 27 | \BKM@entry{id=4,dest={73756273756273656374696F6E2E312E322E31},srcline={88}}{506C6163696E67204D4C3A204F7665726C617070696E67204669656C6473} 28 | \BKM@entry{id=5,dest={73756273656374696F6E2E312E33},srcline={127}}{412055736566756C205065727370656374697665206F6E204D4C} 29 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}What is Machine Learning?}{2}{subsection.1.2}\protected@file@percent } 30 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {1.2.1}Placing ML: Overlapping Fields}{2}{subsubsection.1.2.1}\protected@file@percent } 31 | \BKM@entry{id=6,dest={73756273656374696F6E2E312E34},srcline={141}}{4B2D4E656172657374204E65696768626F7572} 32 | \BKM@entry{id=7,dest={73656374696F6E2E32},srcline={144}}{5765656B2032} 33 | \BKM@entry{id=8,dest={73756273656374696F6E2E322E31},srcline={145}}{4C6561726E696E67204F626A65637469766573} 34 | \BKM@entry{id=9,dest={73756273656374696F6E2E322E32},srcline={164}}{4C696E6561722052656772657373696F6E} 35 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.3}A Useful Perspective on ML}{3}{subsection.1.3}\protected@file@percent } 36 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.4}K-Nearest Neighbour}{3}{subsection.1.4}\protected@file@percent } 37 | \@writefile{toc}{\contentsline {section}{\numberline {2}Week 2}{3}{section.2}\protected@file@percent } 38 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Learning Objectives}{3}{subsection.2.1}\protected@file@percent } 39 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Linear Regression}{3}{subsection.2.2}\protected@file@percent } 40 | \BKM@entry{id=10,dest={73756273756273656374696F6E2E322E322E31},srcline={197}}{4661696C757265204D6F6465205C30343320313A2041766F6964696E672053696E67756C61726974696573} 41 | \BKM@entry{id=11,dest={73756273756273656374696F6E2E322E322E32},srcline={212}}{4661696C757265204D6F6465205C30343320323A204C696E6561722046756E6374696F6E20697320612042616420466974} 42 | \BKM@entry{id=12,dest={73756273656374696F6E2E322E33},srcline={221}}{496E70757420466561747572657320666F72204C696E6561722052656772657373696F6E205C323035204665617475726520456E67696E656572696E67} 43 | \newlabel{reg:closed}{{2}{4}{Linear Regression}{equation.2.2}{}} 44 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.1}Failure Mode \# 1: Avoiding Singularities}{4}{subsubsection.2.2.1}\protected@file@percent } 45 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.2}Failure Mode \# 2: Linear Function is a Bad Fit}{4}{subsubsection.2.2.2}\protected@file@percent } 46 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Input Features for Linear Regression -- Feature Engineering}{4}{subsection.2.3}\protected@file@percent } 47 | \BKM@entry{id=13,dest={73756273656374696F6E2E322E34},srcline={240}}{4F76657266697474696E67205C3034362047656E6572616C69736174696F6E} 48 | \BKM@entry{id=14,dest={73756273756273656374696F6E2E322E342E31},srcline={267}}{4B2D466F6C642043726F73732056616C69646174696F6E} 49 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Overfitting \& Generalisation}{5}{subsection.2.4}\protected@file@percent } 50 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.1}K-Fold Cross Validation}{5}{subsubsection.2.4.1}\protected@file@percent } 51 | \BKM@entry{id=15,dest={73656374696F6E2E33},srcline={275}}{5765656B2033} 52 | \BKM@entry{id=16,dest={73756273656374696F6E2E332E31},srcline={277}}{4C6561726E696E67204F626A65637469766573} 53 | \BKM@entry{id=17,dest={73656374696F6E2E34},srcline={287}}{5765656B2034} 54 | \BKM@entry{id=18,dest={73756273656374696F6E2E342E31},srcline={289}}{4C6561726E696E67204F626A65637473} 55 | \BKM@entry{id=19,dest={73656374696F6E2E35},srcline={301}}{5765656B2035} 56 | \BKM@entry{id=20,dest={73756273656374696F6E2E352E31},srcline={302}}{4C6561726E696E67204F626A65637469766573} 57 | \BKM@entry{id=21,dest={73656374696F6E2E36},srcline={319}}{5765656B2036} 58 | \BKM@entry{id=22,dest={73756273656374696F6E2E362E31},srcline={322}}{4C6561726E696E67204F626A65637469766573} 59 | \@writefile{toc}{\contentsline {section}{\numberline {3}Week 3}{6}{section.3}\protected@file@percent } 60 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Learning Objectives}{6}{subsection.3.1}\protected@file@percent } 61 | \@writefile{toc}{\contentsline {section}{\numberline {4}Week 4}{6}{section.4}\protected@file@percent } 62 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Learning Objects}{6}{subsection.4.1}\protected@file@percent } 63 | \@writefile{toc}{\contentsline {section}{\numberline {5}Week 5}{6}{section.5}\protected@file@percent } 64 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Learning Objectives}{6}{subsection.5.1}\protected@file@percent } 65 | \@writefile{toc}{\contentsline {section}{\numberline {6}Week 6}{6}{section.6}\protected@file@percent } 66 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Learning Objectives}{6}{subsection.6.1}\protected@file@percent } 67 | \BKM@entry{id=23,dest={73756273656374696F6E2E362E32},srcline={338}}{50657263657074726F6E} 68 | \BKM@entry{id=24,dest={73756273756273656374696F6E2E362E322E31},srcline={349}}{486F772063616E2077652066696E6420746865206879706572706C616E653F} 69 | \BKM@entry{id=25,dest={73756273756273656374696F6E2E362E322E32},srcline={382}}{54686520416C676F726974686D} 70 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Perceptron}{7}{subsection.6.2}\protected@file@percent } 71 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.1}How can we find the hyperplane?}{7}{subsubsection.6.2.1}\protected@file@percent } 72 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.2}The Algorithm}{8}{subsubsection.6.2.2}\protected@file@percent } 73 | \@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces Perceptron Algorithm}}{8}{algocf.1}\protected@file@percent } 74 | \global\@namedef{scr@dte@section@lastmaxnumwidth}{10.84047pt} 75 | \global\@namedef{scr@dte@subsection@lastmaxnumwidth}{18.37163pt} 76 | \global\@namedef{scr@dte@subsubsection@lastmaxnumwidth}{26.8883pt} 77 | -------------------------------------------------------------------------------- /.texpadtmp/comp551.log: -------------------------------------------------------------------------------- 1 | This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex 2019.7.26) 3 MAR 2020 11:11 2 | entering extended mode 3 | restricted \write18 enabled. 4 | file:line:error style messages enabled. 5 | %&-line parsing enabled. 6 | **comp551.tex 7 | (./comp551.tex 8 | LaTeX2e <2018-12-01> 9 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrartcl.cls 10 | Document Class: scrartcl 2019/02/01 v3.26b KOMA-Script document class (article) 11 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrkbase.sty 12 | Package: scrkbase 2019/02/01 v3.26b KOMA-Script package (KOMA-Script-dependent basics and keyval usage) 13 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrbase.sty 14 | Package: scrbase 2019/02/01 v3.26b KOMA-Script package (KOMA-Script-independent basics and keyval usage) 15 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics/keyval.sty 16 | Package: keyval 2014/10/28 v1.15 key=value parser (DPC) 17 | \KV@toks@=\toks14 18 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrlfile.sty 19 | Package: scrlfile 2019/02/01 v3.26b KOMA-Script package (loading files) 20 | ))) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/tocbasic.sty 21 | Package: tocbasic 2019/02/01 v3.26b KOMA-Script package (handling toc-files) 22 | \scr@dte@tocline@numberwidth=\skip41 23 | \scr@dte@tocline@numbox=\box27 24 | ) 25 | Package tocbasic Info: omitting babel extension for `toc' 26 | (tocbasic) because of feature `nobabel' available 27 | (tocbasic) for `toc' on input line 134. 28 | Package scrartcl Info: You've used standard option `11pt'. 29 | (scrartcl) This is correct! 30 | (scrartcl) Internally I'm using `fontsize=11pt'. 31 | (scrartcl) If you'd like to set the option with \KOMAoptions, 32 | (scrartcl) you'd have to use `fontsize=11pt' there 33 | (scrartcl) instead of `11pt', too. 34 | Class scrartcl Info: File `scrsize11pt.clo' used to setup font sizes on input line 2162. 35 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrsize11pt.clo 36 | File: scrsize11pt.clo 2019/02/01 v3.26b KOMA-Script font size class option (11pt) 37 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/typearea.sty 38 | Package: typearea 2019/02/01 v3.26b KOMA-Script package (type area) 39 | \ta@bcor=\skip42 40 | \ta@div=\count80 41 | \ta@hblk=\skip43 42 | \ta@vblk=\skip44 43 | \ta@temp=\skip45 44 | \footheight=\skip46 45 | Package typearea Info: These are the values describing the layout: 46 | (typearea) DIV = 10 47 | (typearea) BCOR = 0.0pt 48 | (typearea) \paperwidth = 597.50793pt 49 | (typearea) \textwidth = 418.25555pt 50 | (typearea) DIV departure = -6% 51 | (typearea) \evensidemargin = 17.3562pt 52 | (typearea) \oddsidemargin = 17.3562pt 53 | (typearea) \paperheight = 845.04694pt 54 | (typearea) \textheight = 595.80026pt 55 | (typearea) \topmargin = -25.16531pt 56 | (typearea) \headheight = 17.0pt 57 | (typearea) \headsep = 20.40001pt 58 | (typearea) \topskip = 11.0pt 59 | (typearea) \footskip = 47.6pt 60 | (typearea) \baselineskip = 13.6pt 61 | (typearea) on input line 1715. 62 | ) 63 | \c@part=\count81 64 | \c@section=\count82 65 | \c@subsection=\count83 66 | \c@subsubsection=\count84 67 | \c@paragraph=\count85 68 | \c@subparagraph=\count86 69 | \scr@dte@section@maxnumwidth=\skip47 70 | Class scrartcl Info: using compatibility default `runin=bysign' 71 | (scrartcl) for `\section on input line 4489. 72 | Class scrartcl Info: using compatibility default `afterindent=bysign' 73 | (scrartcl) for `\section on input line 4489. 74 | \scr@dte@part@maxnumwidth=\skip48 75 | Class scrartcl Info: using compatibility default `afterindent=false' 76 | (scrartcl) for `\part on input line 4497. 77 | \scr@dte@subsection@maxnumwidth=\skip49 78 | Class scrartcl Info: using compatibility default `runin=bysign' 79 | (scrartcl) for `\subsection on input line 4507. 80 | Class scrartcl Info: using compatibility default `afterindent=bysign' 81 | (scrartcl) for `\subsection on input line 4507. 82 | \scr@dte@subsubsection@maxnumwidth=\skip50 83 | Class scrartcl Info: using compatibility default `runin=bysign' 84 | (scrartcl) for `\subsubsection on input line 4517. 85 | Class scrartcl Info: using compatibility default `afterindent=bysign' 86 | (scrartcl) for `\subsubsection on input line 4517. 87 | \scr@dte@paragraph@maxnumwidth=\skip51 88 | Class scrartcl Info: using compatibility default `runin=bysign' 89 | (scrartcl) for `\paragraph on input line 4527. 90 | Class scrartcl Info: using compatibility default `afterindent=bysign' 91 | (scrartcl) for `\paragraph on input line 4527. 92 | \scr@dte@subparagraph@maxnumwidth=\skip52 93 | Class scrartcl Info: using compatibility default `runin=bysign' 94 | (scrartcl) for `\subparagraph on input line 4537. 95 | Class scrartcl Info: using compatibility default `afterindent=bysign' 96 | (scrartcl) for `\subparagraph on input line 4537. 97 | \abovecaptionskip=\skip53 98 | \belowcaptionskip=\skip54 99 | \c@pti@nb@sid@b@x=\box28 100 | Package tocbasic Info: omitting babel extension for `lof' 101 | (tocbasic) because of feature `nobabel' available 102 | (tocbasic) for `lof' on input line 5781. 103 | \scr@dte@figure@maxnumwidth=\skip55 104 | \c@figure=\count87 105 | Package tocbasic Info: omitting babel extension for `lot' 106 | (tocbasic) because of feature `nobabel' available 107 | (tocbasic) for `lot' on input line 5793. 108 | \scr@dte@table@maxnumwidth=\skip56 109 | \c@table=\count88 110 | Class scrartcl Info: Redefining `\numberline' on input line 5957. 111 | \bibindent=\dimen102 112 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/geometry/geometry.sty 113 | Package: geometry 2018/04/16 v5.8 Page Geometry 114 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ifpdf.sty 115 | Package: ifpdf 2018/09/07 v3.3 Provides the ifpdf switch 116 | ) (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ifvtex.sty 117 | Package: ifvtex 2016/05/16 v1.6 Detect VTeX and its facilities (HO) 118 | Package ifvtex Info: VTeX not detected. 119 | ) (/usr/local/texlive/2019/texmf-dist/tex/generic/ifxetex/ifxetex.sty 120 | Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional 121 | ) 122 | \Gm@cnth=\count89 123 | \Gm@cntv=\count90 124 | \c@Gm@tempcnt=\count91 125 | \Gm@bindingoffset=\dimen103 126 | \Gm@wd@mp=\dimen104 127 | \Gm@odd@mp=\dimen105 128 | \Gm@even@mp=\dimen106 129 | \Gm@layoutwidth=\dimen107 130 | \Gm@layoutheight=\dimen108 131 | \Gm@layouthoffset=\dimen109 132 | \Gm@layoutvoffset=\dimen110 133 | \Gm@dimlist=\toks15 134 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsmath.sty 135 | Package: amsmath 2018/12/01 v2.17b AMS math features 136 | \@mathmargin=\skip57 137 | 138 | For additional information on amsmath, use the `?' option. 139 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amstext.sty 140 | Package: amstext 2000/06/29 v2.01 AMS text 141 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsgen.sty 142 | File: amsgen.sty 1999/11/30 v2.0 generic functions 143 | \@emptytoks=\toks16 144 | \ex@=\dimen111 145 | )) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsbsy.sty 146 | Package: amsbsy 1999/11/29 v1.2d Bold Symbols 147 | \pmbraise@=\dimen112 148 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsopn.sty 149 | Package: amsopn 2016/03/08 v2.02 operator names 150 | ) 151 | \inf@bad=\count92 152 | LaTeX Info: Redefining \frac on input line 223. 153 | \uproot@=\count93 154 | \leftroot@=\count94 155 | LaTeX Info: Redefining \overline on input line 385. 156 | \classnum@=\count95 157 | \DOTSCASE@=\count96 158 | LaTeX Info: Redefining \ldots on input line 482. 159 | LaTeX Info: Redefining \dots on input line 485. 160 | LaTeX Info: Redefining \cdots on input line 606. 161 | \Mathstrutbox@=\box29 162 | \strutbox@=\box30 163 | \big@size=\dimen113 164 | LaTeX Font Info: Redeclaring font encoding OML on input line 729. 165 | LaTeX Font Info: Redeclaring font encoding OMS on input line 730. 166 | \macc@depth=\count97 167 | \c@MaxMatrixCols=\count98 168 | \dotsspace@=\muskip10 169 | \c@parentequation=\count99 170 | \dspbrk@lvl=\count100 171 | \tag@help=\toks17 172 | \row@=\count101 173 | \column@=\count102 174 | \maxfields@=\count103 175 | \andhelp@=\toks18 176 | \eqnshift@=\dimen114 177 | \alignsep@=\dimen115 178 | \tagshift@=\dimen116 179 | \tagwidth@=\dimen117 180 | \totwidth@=\dimen118 181 | \lineht@=\dimen119 182 | \@envbody=\toks19 183 | \multlinegap=\skip58 184 | \multlinetaggap=\skip59 185 | \mathdisplay@stack=\toks20 186 | LaTeX Info: Redefining \[ on input line 2844. 187 | LaTeX Info: Redefining \] on input line 2845. 188 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/amsfonts.sty 189 | Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support 190 | \symAMSa=\mathgroup4 191 | \symAMSb=\mathgroup5 192 | LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' 193 | (Font) U/euf/m/n --> U/euf/b/n on input line 106. 194 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/amssymb.sty 195 | Package: amssymb 2013/01/14 v3.01 AMS font symbols 196 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amscls/amsthm.sty 197 | Package: amsthm 2017/10/31 v2.20.4 198 | \thm@style=\toks21 199 | \thm@bodyfont=\toks22 200 | \thm@headfont=\toks23 201 | \thm@notefont=\toks24 202 | \thm@headpunct=\toks25 203 | \thm@preskip=\skip60 204 | \thm@postskip=\skip61 205 | \thm@headsep=\skip62 206 | \dth@everypar=\toks26 207 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/xcolor/xcolor.sty 208 | Package: xcolor 2016/05/11 v2.12 LaTeX color extensions (UK) 209 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics-cfg/color.cfg 210 | File: color.cfg 2016/01/02 v1.6 sample color configuration 211 | ) 212 | Package xcolor Info: Driver file: pdftex.def on input line 225. 213 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics-def/pdftex.def 214 | File: pdftex.def 2018/01/08 v1.0l Graphics/color driver for pdftex 215 | ) 216 | Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1348. 217 | Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1352. 218 | Package xcolor Info: Model `RGB' extended on input line 1364. 219 | Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1366. 220 | Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1367. 221 | Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1368. 222 | Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1369. 223 | Package xcolor Info: Model `Gray' substituted by `gray' on input line 1370. 224 | Package xcolor Info: Model `wave' substituted by `hsb' on input line 1371. 225 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/enumitem/enumitem.sty 226 | Package: enumitem 2019/02/04 v3.8 Customized lists 227 | \labelindent=\skip63 228 | \enit@outerparindent=\dimen120 229 | \enit@toks=\toks27 230 | \enit@inbox=\box31 231 | \enit@count@id=\count104 232 | \enitdp@description=\count105 233 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/inputenc.sty 234 | Package: inputenc 2018/08/11 v1.3c Input encoding file 235 | \inpenc@prehook=\toks28 236 | \inpenc@posthook=\toks29 237 | ) 238 | \c@theorem=\count106 239 | \c@corollary=\count107 240 | \c@definition=\count108 241 | \c@prop=\count109 242 | \c@ex=\count110 243 | (/usr/local/texlive/2019/texmf-dist/tex/latex/algorithm2e/algorithm2e.sty 244 | Package: algorithm2e 2017/07/18 v5.2 algorithms environments 245 | \c@AlgoLine=\count111 246 | (/usr/local/texlive/2019/texmf-dist/tex/latex/base/ifthen.sty 247 | Package: ifthen 2014/09/29 v1.1c Standard LaTeX ifthen package (DPC) 248 | ) 249 | \algocf@hangindent=\skip64 250 | (/usr/local/texlive/2019/texmf-dist/tex/latex/ifoddpage/ifoddpage.sty 251 | Package: ifoddpage 2016/04/23 v1.1 Conditionals for odd/even page detection 252 | \c@checkoddpage=\count112 253 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/tools/xspace.sty 254 | Package: xspace 2014/10/28 v1.13 Space after command names (DPC,MH) 255 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/relsize/relsize.sty 256 | Package: relsize 2013/03/29 ver 4.1 257 | ) 258 | \skiptotal=\skip65 259 | \skiplinenumber=\skip66 260 | \skiprule=\skip67 261 | \skiphlne=\skip68 262 | \skiptext=\skip69 263 | \skiplength=\skip70 264 | \algomargin=\skip71 265 | \skipalgocfslide=\skip72 266 | \algowidth=\dimen121 267 | \inoutsize=\dimen122 268 | \inoutindent=\dimen123 269 | \interspacetitleruled=\dimen124 270 | \interspacealgoruled=\dimen125 271 | \interspacetitleboxruled=\dimen126 272 | \algocf@ruledwidth=\skip73 273 | \algocf@inoutbox=\box32 274 | \algocf@inputbox=\box33 275 | \AlCapSkip=\skip74 276 | \AlCapHSkip=\skip75 277 | \algoskipindent=\skip76 278 | \algocf@nlbox=\box34 279 | \algocf@hangingbox=\box35 280 | \algocf@untilbox=\box36 281 | \algocf@skipuntil=\skip77 282 | \algocf@capbox=\box37 283 | \algocf@lcaptionbox=\skip78 284 | \algoheightruledefault=\skip79 285 | \algoheightrule=\skip80 286 | \algotitleheightruledefault=\skip81 287 | \algotitleheightrule=\skip82 288 | \c@algocfline=\count113 289 | \c@algocfproc=\count114 290 | \c@algocf=\count115 291 | \algocf@algoframe=\box38 292 | \algocf@algobox=\box39 293 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/hyperref.sty 294 | Package: hyperref 2018/11/30 v6.88e Hypertext links for LaTeX 295 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty 296 | Package: hobsub-hyperref 2016/05/16 v1.14 Bundle oberdiek, subset hyperref (HO) 297 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty 298 | Package: hobsub-generic 2016/05/16 v1.14 Bundle oberdiek, subset generic (HO) 299 | Package: hobsub 2016/05/16 v1.14 Construct package bundles (HO) 300 | Package: infwarerr 2016/05/16 v1.4 Providing info/warning/error messages (HO) 301 | Package: ltxcmds 2016/05/16 v1.23 LaTeX kernel commands for general use (HO) 302 | Package: ifluatex 2016/05/16 v1.4 Provides the ifluatex switch (HO) 303 | Package ifluatex Info: LuaTeX not detected. 304 | Package hobsub Info: Skipping package `ifvtex' (already loaded). 305 | Package: intcalc 2016/05/16 v1.2 Expandable calculations with integers (HO) 306 | Package hobsub Info: Skipping package `ifpdf' (already loaded). 307 | Package: etexcmds 2016/05/16 v1.6 Avoid name clashes with e-TeX commands (HO) 308 | Package: kvsetkeys 2016/05/16 v1.17 Key value parser (HO) 309 | Package: kvdefinekeys 2016/05/16 v1.4 Define keys (HO) 310 | Package: pdftexcmds 2018/09/10 v0.29 Utility functions of pdfTeX for LuaTeX (HO) 311 | Package pdftexcmds Info: LuaTeX not detected. 312 | Package pdftexcmds Info: \pdf@primitive is available. 313 | Package pdftexcmds Info: \pdf@ifprimitive is available. 314 | Package pdftexcmds Info: \pdfdraftmode found. 315 | Package: pdfescape 2016/05/16 v1.14 Implements pdfTeX's escape features (HO) 316 | Package: bigintcalc 2016/05/16 v1.4 Expandable calculations on big integers (HO) 317 | Package: bitset 2016/05/16 v1.2 Handle bit-vector datatype (HO) 318 | Package: uniquecounter 2016/05/16 v1.3 Provide unlimited unique counter (HO) 319 | ) 320 | Package hobsub Info: Skipping package `hobsub' (already loaded). 321 | Package: letltxmacro 2016/05/16 v1.5 Let assignment for LaTeX macros (HO) 322 | Package: hopatch 2016/05/16 v1.3 Wrapper for package hooks (HO) 323 | Package: xcolor-patch 2016/05/16 xcolor patch 324 | Package: atveryend 2016/05/16 v1.9 Hooks at the very end of document (HO) 325 | Package atveryend Info: \enddocument detected (standard20110627). 326 | Package: atbegshi 2016/06/09 v1.18 At begin shipout hook (HO) 327 | Package: refcount 2016/05/16 v3.5 Data extraction from label references (HO) 328 | Package: hycolor 2016/05/16 v1.8 Color options for hyperref/bookmark (HO) 329 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/auxhook.sty 330 | Package: auxhook 2016/05/16 v1.4 Hooks for auxiliary files (HO) 331 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/kvoptions.sty 332 | Package: kvoptions 2016/05/16 v3.12 Key value format for package options (HO) 333 | ) 334 | \@linkdim=\dimen127 335 | \Hy@linkcounter=\count116 336 | \Hy@pagecounter=\count117 337 | (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/pd1enc.def 338 | File: pd1enc.def 2018/11/30 v6.88e Hyperref: PDFDocEncoding definition (HO) 339 | Now handling font encoding PD1 ... 340 | ... no UTF-8 mapping file for font encoding PD1 341 | ) 342 | \Hy@SavedSpaceFactor=\count118 343 | (/usr/local/texlive/2019/texmf-dist/tex/latex/latexconfig/hyperref.cfg 344 | File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive 345 | ) 346 | Package hyperref Info: Hyper figures OFF on input line 4519. 347 | Package hyperref Info: Link nesting OFF on input line 4524. 348 | Package hyperref Info: Hyper index ON on input line 4527. 349 | Package hyperref Info: Plain pages OFF on input line 4534. 350 | Package hyperref Info: Backreferencing OFF on input line 4539. 351 | Package hyperref Info: Implicit mode ON; LaTeX internals redefined. 352 | Package hyperref Info: Bookmarks ON on input line 4772. 353 | \c@Hy@tempcnt=\count119 354 | (/usr/local/texlive/2019/texmf-dist/tex/latex/url/url.sty 355 | \Urlmuskip=\muskip11 356 | Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc. 357 | ) 358 | LaTeX Info: Redefining \url on input line 5125. 359 | \XeTeXLinkMargin=\dimen128 360 | \Fld@menulength=\count120 361 | \Field@Width=\dimen129 362 | \Fld@charsize=\dimen130 363 | Package hyperref Info: Hyper figures OFF on input line 6380. 364 | Package hyperref Info: Link nesting OFF on input line 6385. 365 | Package hyperref Info: Hyper index ON on input line 6388. 366 | Package hyperref Info: backreferencing OFF on input line 6395. 367 | Package hyperref Info: Link coloring OFF on input line 6400. 368 | Package hyperref Info: Link coloring with OCG OFF on input line 6405. 369 | Package hyperref Info: PDF/A mode OFF on input line 6410. 370 | LaTeX Info: Redefining \ref on input line 6450. 371 | LaTeX Info: Redefining \pageref on input line 6454. 372 | \Hy@abspage=\count121 373 | \c@Item=\count122 374 | \c@Hfootnote=\count123 375 | ) 376 | Package hyperref Info: Driver (autodetected): hpdftex. 377 | (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/hpdftex.def 378 | File: hpdftex.def 2018/11/30 v6.88e Hyperref driver for pdfTeX 379 | \Fld@listcount=\count124 380 | \c@bookmark@seq@number=\count125 381 | (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty 382 | Package: rerunfilecheck 2016/05/16 v1.8 Rerun checks for auxiliary files (HO) 383 | Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 282. 384 | ) 385 | \Hy@SectionHShift=\skip83 386 | ) 387 | Package hyperref Info: Option `colorlinks' set `true' on input line 55. 388 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/comp551.aux) 389 | \openout1 = `comp551.aux'. 390 | 391 | LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 62. 392 | LaTeX Font Info: ... okay on input line 62. 393 | LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 62. 394 | LaTeX Font Info: ... okay on input line 62. 395 | LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 62. 396 | LaTeX Font Info: ... okay on input line 62. 397 | LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 62. 398 | LaTeX Font Info: ... okay on input line 62. 399 | LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 62. 400 | LaTeX Font Info: ... okay on input line 62. 401 | LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 62. 402 | LaTeX Font Info: ... okay on input line 62. 403 | LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 62. 404 | LaTeX Font Info: ... okay on input line 62. 405 | 406 | *geometry* driver: auto-detecting 407 | *geometry* detected driver: pdftex 408 | *geometry* verbose mode - [ preamble ] result: 409 | * driver: pdftex 410 | * paper: 411 | * layout: 412 | * layoutoffset:(h,v)=(0.0pt,0.0pt) 413 | * modes: 414 | * h-part:(L,W,R)=(56.9055pt, 483.69693pt, 56.9055pt) 415 | * v-part:(T,H,B)=(56.9055pt, 731.23593pt, 56.9055pt) 416 | * \paperwidth=597.50793pt 417 | * \paperheight=845.04694pt 418 | * \textwidth=483.69693pt 419 | * \textheight=731.23593pt 420 | * \oddsidemargin=-15.36449pt 421 | * \evensidemargin=-15.36449pt 422 | * \topmargin=-52.7645pt 423 | * \headheight=17.0pt 424 | * \headsep=20.40001pt 425 | * \topskip=11.0pt 426 | * \footskip=47.6pt 427 | * \marginparwidth=59.7508pt 428 | * \marginparsep=12.8401pt 429 | * \columnsep=10.0pt 430 | * \skip\footins=10.0pt plus 4.0pt minus 2.0pt 431 | * \hoffset=0.0pt 432 | * \voffset=0.0pt 433 | * \mag=1000 434 | * \@twocolumnfalse 435 | * \@twosidefalse 436 | * \@mparswitchfalse 437 | * \@reversemarginfalse 438 | * (1in=72.27pt=25.4mm, 1cm=28.453pt) 439 | 440 | (/usr/local/texlive/2019/texmf-dist/tex/context/base/mkii/supp-pdf.mkii 441 | [Loading MPS to PDF converter (version 2006.09.02).] 442 | \scratchcounter=\count126 443 | \scratchdimen=\dimen131 444 | \scratchbox=\box40 445 | \nofMPsegments=\count127 446 | \nofMParguments=\count128 447 | \everyMPshowfont=\toks30 448 | \MPscratchCnt=\count129 449 | \MPscratchDim=\dimen132 450 | \MPnumerator=\count130 451 | \makeMPintoPDFobject=\count131 452 | \everyMPtoPDFconversion=\toks31 453 | ) 454 | \AtBeginShipoutBox=\box41 455 | Package hyperref Info: Link coloring ON on input line 62. 456 | (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/nameref.sty 457 | Package: nameref 2016/05/21 v2.44 Cross-referencing by name of section 458 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/gettitlestring.sty 459 | Package: gettitlestring 2016/05/16 v1.5 Cleanup title references (HO) 460 | ) 461 | \c@section@level=\count132 462 | ) 463 | LaTeX Info: Redefining \ref on input line 62. 464 | LaTeX Info: Redefining \pageref on input line 62. 465 | LaTeX Info: Redefining \nameref on input line 62. 466 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/comp551.out) (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/comp551.out) 467 | \@outlinefile=\write3 468 | \openout3 = `comp551.out'. 469 | 470 | Class scrartcl Info: loading recommended package `bookmark'. 471 | (scrartcl) Using `bookmark' together with `hyperref' is recommended, 472 | (scrartcl) because of handling of possible bookmark level gaps. 473 | (scrartcl) You can avoid loading `bookmark' with KOMA-Script option 474 | (scrartcl) `bookmarkpackage=false' before \begin{document} and 475 | (scrartcl) you can avoid this message with `\usepackage{bookmark}' 476 | (scrartcl) before \begin{document} on input line 62. 477 | (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/bookmark.sty 478 | Package: bookmark 2016/05/17 v1.26 PDF bookmarks (HO) 479 | (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/bkm-pdftex.def 480 | File: bkm-pdftex.def 2016/05/17 v1.26 bookmark driver for pdfTeX (HO) 481 | Package auxhook Info: \AddLineBeginMainAux comes a little late, 482 | (auxhook) because the main .aux file is already opened on input line 164. 483 | \BKM@id=\count133 484 | )) 485 | LaTeX Font Info: Try loading font information for U+msa on input line 65. 486 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/umsa.fd 487 | File: umsa.fd 2013/01/14 v3.01 AMS symbols A 488 | ) 489 | LaTeX Font Info: Try loading font information for U+msb on input line 65. 490 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/umsb.fd 491 | File: umsb.fd 2013/01/14 v3.01 AMS symbols B 492 | ) 493 | 494 | LaTeX Font Warning: Font shape `OT1/cmr/bx/sc' undefined 495 | (Font) using `OT1/cmr/bx/n' instead on input line 65. 496 | 497 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/comp551.toc) 498 | \tf@toc=\write4 499 | \openout4 = `comp551.toc'. 500 | 501 | [1 502 | 503 | 504 | {/usr/local/texlive/2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2] 505 | LaTeX Font Info: Try loading font information for OMS+cmr on input line 175. 506 | (/usr/local/texlive/2019/texmf-dist/tex/latex/base/omscmr.fd 507 | File: omscmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions 508 | ) 509 | LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10.95> not available 510 | (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 175. 511 | [3] [4] 512 | Overfull \hbox (9.3421pt too wide) in paragraph at lines 250--251 513 | []\OT1/cmr/m/n/10.95 We need to eval-u-ate on held-out data. This in-tro-duces the con-cept of a $[]$: 514 | [] 515 | 516 | [5] [6] [7] 517 | Package atveryend Info: Empty hook `BeforeClearDocument' on input line 415. 518 | [8] 519 | Package atveryend Info: Empty hook `AfterLastShipout' on input line 415. 520 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/comp551.aux) 521 | Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 415. 522 | Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 415. 523 | Package rerunfilecheck Info: File `comp551.out' has not changed. 524 | (rerunfilecheck) Checksum: . 525 | 526 | 527 | LaTeX Font Warning: Some font shapes were not available, defaults substituted. 528 | 529 | Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 415. 530 | ) 531 | Here is how much of TeX's memory you used: 532 | 10400 strings out of 492616 533 | 164225 string characters out of 6129481 534 | 397177 words of memory out of 5000000 535 | 14082 multiletter control sequences out of 15000+600000 536 | 13329 words of font info for 51 fonts, out of 8000000 for 9000 537 | 1141 hyphenation exceptions out of 8191 538 | 41i,16n,51p,9119b,553s stack positions out of 5000i,500n,10000p,200000b,80000s 539 | 540 | Output written on /Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/comp551.pdf (8 pages, 174724 bytes). 541 | PDF statistics: 542 | 360 PDF objects out of 1000 (max. 8388607) 543 | 333 compressed objects within 4 object streams 544 | 141 named destinations out of 1000 (max. 500000) 545 | 201 words of extra memory for PDF output out of 10000 (max. 10000000) 546 | 547 | -------------------------------------------------------------------------------- /.texpadtmp/comp551.out: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/comp551.out -------------------------------------------------------------------------------- /.texpadtmp/comp551.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/comp551.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/comp551.toc: -------------------------------------------------------------------------------- 1 | \contentsline {section}{\numberline {1}Week 1}{1}{section.1}% 2 | \contentsline {subsection}{\numberline {1.1}Learning Objectives}{1}{subsection.1.1}% 3 | \contentsline {subsection}{\numberline {1.2}What is Machine Learning?}{2}{subsection.1.2}% 4 | \contentsline {subsubsection}{\numberline {1.2.1}Placing ML: Overlapping Fields}{2}{subsubsection.1.2.1}% 5 | \contentsline {subsection}{\numberline {1.3}A Useful Perspective on ML}{3}{subsection.1.3}% 6 | \contentsline {subsection}{\numberline {1.4}K-Nearest Neighbour}{3}{subsection.1.4}% 7 | \contentsline {section}{\numberline {2}Week 2}{3}{section.2}% 8 | \contentsline {subsection}{\numberline {2.1}Learning Objectives}{3}{subsection.2.1}% 9 | \contentsline {subsection}{\numberline {2.2}Linear Regression}{3}{subsection.2.2}% 10 | \contentsline {subsubsection}{\numberline {2.2.1}Failure Mode \# 1: Avoiding Singularities}{4}{subsubsection.2.2.1}% 11 | \contentsline {subsubsection}{\numberline {2.2.2}Failure Mode \# 2: Linear Function is a Bad Fit}{4}{subsubsection.2.2.2}% 12 | \contentsline {subsection}{\numberline {2.3}Input Features for Linear Regression -- Feature Engineering}{4}{subsection.2.3}% 13 | \contentsline {subsection}{\numberline {2.4}Overfitting \& Generalisation}{5}{subsection.2.4}% 14 | \contentsline {subsubsection}{\numberline {2.4.1}K-Fold Cross Validation}{5}{subsubsection.2.4.1}% 15 | \contentsline {section}{\numberline {3}Week 3}{6}{section.3}% 16 | \contentsline {subsection}{\numberline {3.1}Learning Objectives}{6}{subsection.3.1}% 17 | \contentsline {section}{\numberline {4}Week 4}{6}{section.4}% 18 | \contentsline {subsection}{\numberline {4.1}Learning Objects}{6}{subsection.4.1}% 19 | \contentsline {section}{\numberline {5}Week 5}{6}{section.5}% 20 | \contentsline {subsection}{\numberline {5.1}Learning Objectives}{6}{subsection.5.1}% 21 | \contentsline {section}{\numberline {6}Week 6}{6}{section.6}% 22 | \contentsline {subsection}{\numberline {6.1}Learning Objectives}{6}{subsection.6.1}% 23 | \contentsline {subsection}{\numberline {6.2}Perceptron}{7}{subsection.6.2}% 24 | \contentsline {subsubsection}{\numberline {6.2.1}How can we find the hyperplane?}{7}{subsubsection.6.2.1}% 25 | \contentsline {subsubsection}{\numberline {6.2.2}The Algorithm}{8}{subsubsection.6.2.2}% 26 | -------------------------------------------------------------------------------- /.texpadtmp/m247.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \providecommand\hyper@newdestlabel[2]{} 3 | \providecommand*\new@tpo@label[2]{} 4 | \providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} 5 | \HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined 6 | \global\let\oldcontentsline\contentsline 7 | \gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} 8 | \global\let\oldnewlabel\newlabel 9 | \gdef\newlabel#1#2{\newlabelxx{#1}#2} 10 | \gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} 11 | \AtEndDocument{\ifx\hyper@anchor\@undefined 12 | \let\contentsline\oldcontentsline 13 | \let\newlabel\oldnewlabel 14 | \fi} 15 | \fi} 16 | \global\let\hyper@last\relax 17 | \gdef\HyperFirstAtBeginDocument#1{#1} 18 | \providecommand\HyField@AuxAddToFields[1]{} 19 | \providecommand\HyField@AuxAddToCoFields[2]{} 20 | \providecommand\BKM@entry[2]{} 21 | \BKM@entry{id=1,dest={73656374696F6E2E31},srcline={86}}{496E74726F64756374696F6E} 22 | \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{section.1}\protected@file@percent } 23 | \BKM@entry{id=2,dest={73656374696F6E2E32},srcline={184}}{416273747261637420566563746F7220537061636573} 24 | \@writefile{toc}{\contentsline {section}{\numberline {2}Abstract Vector Spaces}{3}{section.2}\protected@file@percent } 25 | \BKM@entry{id=3,dest={73756273656374696F6E2E322E31},srcline={217}}{4D616E79204578616D706C6573206F6620566563746F7220537061636573} 26 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Many Examples of Vector Spaces}{4}{subsection.2.1}\protected@file@percent } 27 | \BKM@entry{id=4,dest={73756273656374696F6E2E322E32},srcline={280}}{436F6E73657175656E636573206F6620746865204178696F6D73} 28 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Consequences of the Axioms}{5}{subsection.2.2}\protected@file@percent } 29 | \BKM@entry{id=5,dest={73756273656374696F6E2E322E33},srcline={359}}{537562737061636573} 30 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Subspaces}{6}{subsection.2.3}\protected@file@percent } 31 | \BKM@entry{id=6,dest={73756273656374696F6E2E322E34},srcline={510}}{4C696E65617220436F6D62696E6174696F6E20616E64205370616E} 32 | \BKM@entry{id=7,dest={73756273656374696F6E2E322E35},srcline={574}}{4C696E65617220496E646570656E64656E636520616E6420446570656E64656E6365} 33 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Linear Combination and Span}{9}{subsection.2.4}\protected@file@percent } 34 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Linear Independence and Dependence}{10}{subsection.2.5}\protected@file@percent } 35 | \BKM@entry{id=8,dest={73756273656374696F6E2E322E36},srcline={687}}{4170706C69636174696F6E73205C285468656F7265746963616C5C29206F6620537465696E69747A2045786368616E6765204C656D6D61} 36 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Applications (Theoretical) of Steinitz Exchange Lemma}{11}{subsection.2.6}\protected@file@percent } 37 | \BKM@entry{id=9,dest={73656374696F6E2E33},srcline={791}}{4C696E656172204D617073} 38 | \BKM@entry{id=10,dest={73756273656374696F6E2E332E31},srcline={859}}{456E646F6D6F72706869736D73} 39 | \BKM@entry{id=11,dest={73756273656374696F6E2E332E32},srcline={876}}{436F6F7264696E61746520566563746F7273} 40 | \@writefile{toc}{\contentsline {section}{\numberline {3}Linear Maps}{13}{section.3}\protected@file@percent } 41 | \BKM@entry{id=12,dest={73756273656374696F6E2E332E33},srcline={891}}{526570726573656E746174696F6E73206F66204C696E656172204D617073206173204D61747269636573} 42 | \BKM@entry{id=13,dest={73756273656374696F6E2E332E34},srcline={918}}{436F6D706F736974696F6E206F66204C696E656172204D617073} 43 | \BKM@entry{id=14,dest={73756273656374696F6E2E332E35},srcline={927}}{4D617472697820526570726573656E746174696F6E73206F662049736F6D6F72706869736D73} 44 | \BKM@entry{id=15,dest={73756273656374696F6E2E332E36},srcline={932}}{4368616E6765206F66204261736973} 45 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Endomorphisms}{14}{subsection.3.1}\protected@file@percent } 46 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Coordinate Vectors}{14}{subsection.3.2}\protected@file@percent } 47 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Representations of Linear Maps as Matrices}{14}{subsection.3.3}\protected@file@percent } 48 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Composition of Linear Maps}{14}{subsection.3.4}\protected@file@percent } 49 | \BKM@entry{id=16,dest={73756273656374696F6E2E332E37},srcline={955}}{546865204E6F726D616C20466F726D2050726F626C656D} 50 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Matrix Representations of Isomorphisms}{15}{subsection.3.5}\protected@file@percent } 51 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.6}Change of Basis}{15}{subsection.3.6}\protected@file@percent } 52 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.7}The Normal Form Problem}{15}{subsection.3.7}\protected@file@percent } 53 | \BKM@entry{id=17,dest={73756273656374696F6E2E332E38},srcline={1040}}{436861726163746572697374696320506F6C796E6F6D69616C} 54 | \BKM@entry{id=18,dest={73756273656374696F6E2E332E39},srcline={1045}}{4E6F726D616C20466F726D20666F72204E6F6E2D446961676F6E616C697361626C65204D61747269636573} 55 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.8}Characteristic Polynomial}{16}{subsection.3.8}\protected@file@percent } 56 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.9}Normal Form for Non-Diagonalisable Matrices}{16}{subsection.3.9}\protected@file@percent } 57 | \BKM@entry{id=19,dest={73656374696F6E2E34},srcline={1068}}{4170706C69636174696F6E73206F66204C696E65617220416C6765627261205C28746F206F74686572206669656C6473206F66206D6174682E2E2E6E6F74207265616C206C696665203A2D505C29} 58 | \BKM@entry{id=20,dest={73756273656374696F6E2E342E31},srcline={1069}}{4D6174726978204578706F6E656E7469616C} 59 | \BKM@entry{id=21,dest={73656374696F6E2E35},srcline={1087}}{4F7274686F676F6E616C6974793A204120717569636B20696E74726F64756374696F6E} 60 | \BKM@entry{id=22,dest={73756273656374696F6E2E352E31},srcline={1088}}{5374616E6461726420696E6E65722070726F64756374206F6E20526E} 61 | \@writefile{toc}{\contentsline {section}{\numberline {4}Applications of Linear Algebra (to other fields of math...not real life :-P)}{17}{section.4}\protected@file@percent } 62 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Matrix Exponential}{17}{subsection.4.1}\protected@file@percent } 63 | \@writefile{toc}{\contentsline {section}{\numberline {5}Orthogonality: A quick introduction}{17}{section.5}\protected@file@percent } 64 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Standard inner product on $\mathbb {R}^n$}{17}{subsection.5.1}\protected@file@percent } 65 | \BKM@entry{id=23,dest={73756273656374696F6E2E352E32},srcline={1120}}{50726F70657274696573206F6620746865205374616E6461726420496E6E65722050726F64756374206F6E20436E} 66 | \BKM@entry{id=24,dest={73756273656374696F6E2E352E33},srcline={1153}}{4170706C69636174696F6E206F66204F7274686F676F6E616C697479205C284F7274686F676F6E616C20616E6420556E6974617279204D617472696365735C29} 67 | \BKM@entry{id=25,dest={73756273756273656374696F6E2E352E332E31},srcline={1154}}{4F7274686F676F6E616C2043617365} 68 | \BKM@entry{id=26,dest={73756273756273656374696F6E2E352E332E32},srcline={1157}}{556E69746172792043617365} 69 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Properties of the Standard Inner Product on $\mathbb {C}^n$}{18}{subsection.5.2}\protected@file@percent } 70 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Application of Orthogonality (Orthogonal and Unitary Matrices)}{18}{subsection.5.3}\protected@file@percent } 71 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.3.1}Orthogonal Case}{18}{subsubsection.5.3.1}\protected@file@percent } 72 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.3.2}Unitary Case}{18}{subsubsection.5.3.2}\protected@file@percent } 73 | \BKM@entry{id=27,dest={73756273656374696F6E2E352E34},srcline={1193}}{4F7274686F676F6E616C69747920616E6420556E69746172793A20446961676F6E616C69736174696F6E20616E6420557070657220547269616E67756C617269736174696F6E} 74 | \BKM@entry{id=28,dest={73756273756273656374696F6E2E352E342E31},srcline={1221}}{537065637472616C205468656F72656D3A20436F6D706C65782043617365} 75 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Orthogonality and Unitary: Diagonalisation and Upper Triangularisation}{19}{subsection.5.4}\protected@file@percent } 76 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.4.1}Spectral Theorem: Complex Case}{19}{subsubsection.5.4.1}\protected@file@percent } 77 | \BKM@entry{id=29,dest={73756273656374696F6E2E352E35},srcline={1274}}{4170706C69636174696F6E73206F6620746865205265616C20537065637472616C205468656F72656D} 78 | \BKM@entry{id=30,dest={73756273756273656374696F6E2E352E352E31},srcline={1275}}{5265616C2051756164726174696320466F726D73} 79 | \BKM@entry{id=31,dest={73656374696F6E2E36},srcline={1296}}{496E6E65722050726F6475637420537061636573} 80 | \BKM@entry{id=32,dest={73756273656374696F6E2E362E31},srcline={1300}}{4B203D2052} 81 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.5}Applications of the Real Spectral Theorem}{20}{subsection.5.5}\protected@file@percent } 82 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.5.1}Real Quadratic Forms}{20}{subsubsection.5.5.1}\protected@file@percent } 83 | \@writefile{toc}{\contentsline {section}{\numberline {6}Inner Product Spaces}{20}{section.6}\protected@file@percent } 84 | \BKM@entry{id=33,dest={73756273656374696F6E2E362E32},srcline={1329}}{436F6D706C657820496E6E65722050726F6475637420537061636573} 85 | \BKM@entry{id=34,dest={73756273656374696F6E2E362E33},srcline={1347}}{47656F6D65747279206F6E206120566563746F72205370616365} 86 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.1}$K = \mathbb {R}$}{21}{subsection.6.1}\protected@file@percent } 87 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Complex Inner Product Spaces}{21}{subsection.6.2}\protected@file@percent } 88 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.3}Geometry on a Vector Space}{21}{subsection.6.3}\protected@file@percent } 89 | \BKM@entry{id=35,dest={73656374696F6E2E37},srcline={1420}}{466F75726965722053657269657320696E203330204D696E75746573205B6E6F74206578616D696E61626C655D} 90 | \@writefile{toc}{\contentsline {section}{\numberline {7}Fourier Series in 30 Minutes [not examinable]}{22}{section.7}\protected@file@percent } 91 | \global\@namedef{scr@dte@section@lastmaxnumwidth}{10.84047pt} 92 | \global\@namedef{scr@dte@subsection@lastmaxnumwidth}{18.37163pt} 93 | \global\@namedef{scr@dte@subsubsection@lastmaxnumwidth}{26.8883pt} 94 | -------------------------------------------------------------------------------- /.texpadtmp/m247.log: -------------------------------------------------------------------------------- 1 | This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex 2019.7.26) 13 JUN 2020 00:47 2 | entering extended mode 3 | restricted \write18 enabled. 4 | file:line:error style messages enabled. 5 | %&-line parsing enabled. 6 | **m247.tex 7 | (./m247.tex 8 | LaTeX2e <2018-12-01> 9 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrartcl.cls 10 | Document Class: scrartcl 2019/02/01 v3.26b KOMA-Script document class (article) 11 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrkbase.sty 12 | Package: scrkbase 2019/02/01 v3.26b KOMA-Script package (KOMA-Script-dependent basics and keyval usage) 13 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrbase.sty 14 | Package: scrbase 2019/02/01 v3.26b KOMA-Script package (KOMA-Script-independent basics and keyval usage) 15 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics/keyval.sty 16 | Package: keyval 2014/10/28 v1.15 key=value parser (DPC) 17 | \KV@toks@=\toks14 18 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrlfile.sty 19 | Package: scrlfile 2019/02/01 v3.26b KOMA-Script package (loading files) 20 | ))) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/tocbasic.sty 21 | Package: tocbasic 2019/02/01 v3.26b KOMA-Script package (handling toc-files) 22 | \scr@dte@tocline@numberwidth=\skip41 23 | \scr@dte@tocline@numbox=\box27 24 | ) 25 | Package tocbasic Info: omitting babel extension for `toc' 26 | (tocbasic) because of feature `nobabel' available 27 | (tocbasic) for `toc' on input line 134. 28 | Package scrartcl Info: You've used standard option `11pt'. 29 | (scrartcl) This is correct! 30 | (scrartcl) Internally I'm using `fontsize=11pt'. 31 | (scrartcl) If you'd like to set the option with \KOMAoptions, 32 | (scrartcl) you'd have to use `fontsize=11pt' there 33 | (scrartcl) instead of `11pt', too. 34 | Class scrartcl Info: File `scrsize11pt.clo' used to setup font sizes on input line 2162. 35 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrsize11pt.clo 36 | File: scrsize11pt.clo 2019/02/01 v3.26b KOMA-Script font size class option (11pt) 37 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/typearea.sty 38 | Package: typearea 2019/02/01 v3.26b KOMA-Script package (type area) 39 | \ta@bcor=\skip42 40 | \ta@div=\count80 41 | \ta@hblk=\skip43 42 | \ta@vblk=\skip44 43 | \ta@temp=\skip45 44 | \footheight=\skip46 45 | Package typearea Info: These are the values describing the layout: 46 | (typearea) DIV = 10 47 | (typearea) BCOR = 0.0pt 48 | (typearea) \paperwidth = 597.50793pt 49 | (typearea) \textwidth = 418.25555pt 50 | (typearea) DIV departure = -6% 51 | (typearea) \evensidemargin = 17.3562pt 52 | (typearea) \oddsidemargin = 17.3562pt 53 | (typearea) \paperheight = 845.04694pt 54 | (typearea) \textheight = 595.80026pt 55 | (typearea) \topmargin = -25.16531pt 56 | (typearea) \headheight = 17.0pt 57 | (typearea) \headsep = 20.40001pt 58 | (typearea) \topskip = 11.0pt 59 | (typearea) \footskip = 47.6pt 60 | (typearea) \baselineskip = 13.6pt 61 | (typearea) on input line 1715. 62 | ) 63 | \c@part=\count81 64 | \c@section=\count82 65 | \c@subsection=\count83 66 | \c@subsubsection=\count84 67 | \c@paragraph=\count85 68 | \c@subparagraph=\count86 69 | \scr@dte@section@maxnumwidth=\skip47 70 | Class scrartcl Info: using compatibility default `runin=bysign' 71 | (scrartcl) for `\section on input line 4489. 72 | Class scrartcl Info: using compatibility default `afterindent=bysign' 73 | (scrartcl) for `\section on input line 4489. 74 | \scr@dte@part@maxnumwidth=\skip48 75 | Class scrartcl Info: using compatibility default `afterindent=false' 76 | (scrartcl) for `\part on input line 4497. 77 | \scr@dte@subsection@maxnumwidth=\skip49 78 | Class scrartcl Info: using compatibility default `runin=bysign' 79 | (scrartcl) for `\subsection on input line 4507. 80 | Class scrartcl Info: using compatibility default `afterindent=bysign' 81 | (scrartcl) for `\subsection on input line 4507. 82 | \scr@dte@subsubsection@maxnumwidth=\skip50 83 | Class scrartcl Info: using compatibility default `runin=bysign' 84 | (scrartcl) for `\subsubsection on input line 4517. 85 | Class scrartcl Info: using compatibility default `afterindent=bysign' 86 | (scrartcl) for `\subsubsection on input line 4517. 87 | \scr@dte@paragraph@maxnumwidth=\skip51 88 | Class scrartcl Info: using compatibility default `runin=bysign' 89 | (scrartcl) for `\paragraph on input line 4527. 90 | Class scrartcl Info: using compatibility default `afterindent=bysign' 91 | (scrartcl) for `\paragraph on input line 4527. 92 | \scr@dte@subparagraph@maxnumwidth=\skip52 93 | Class scrartcl Info: using compatibility default `runin=bysign' 94 | (scrartcl) for `\subparagraph on input line 4537. 95 | Class scrartcl Info: using compatibility default `afterindent=bysign' 96 | (scrartcl) for `\subparagraph on input line 4537. 97 | \abovecaptionskip=\skip53 98 | \belowcaptionskip=\skip54 99 | \c@pti@nb@sid@b@x=\box28 100 | Package tocbasic Info: omitting babel extension for `lof' 101 | (tocbasic) because of feature `nobabel' available 102 | (tocbasic) for `lof' on input line 5781. 103 | \scr@dte@figure@maxnumwidth=\skip55 104 | \c@figure=\count87 105 | Package tocbasic Info: omitting babel extension for `lot' 106 | (tocbasic) because of feature `nobabel' available 107 | (tocbasic) for `lot' on input line 5793. 108 | \scr@dte@table@maxnumwidth=\skip56 109 | \c@table=\count88 110 | Class scrartcl Info: Redefining `\numberline' on input line 5957. 111 | \bibindent=\dimen102 112 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/geometry/geometry.sty 113 | Package: geometry 2018/04/16 v5.8 Page Geometry 114 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ifpdf.sty 115 | Package: ifpdf 2018/09/07 v3.3 Provides the ifpdf switch 116 | ) (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ifvtex.sty 117 | Package: ifvtex 2016/05/16 v1.6 Detect VTeX and its facilities (HO) 118 | Package ifvtex Info: VTeX not detected. 119 | ) (/usr/local/texlive/2019/texmf-dist/tex/generic/ifxetex/ifxetex.sty 120 | Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional 121 | ) 122 | \Gm@cnth=\count89 123 | \Gm@cntv=\count90 124 | \c@Gm@tempcnt=\count91 125 | \Gm@bindingoffset=\dimen103 126 | \Gm@wd@mp=\dimen104 127 | \Gm@odd@mp=\dimen105 128 | \Gm@even@mp=\dimen106 129 | \Gm@layoutwidth=\dimen107 130 | \Gm@layoutheight=\dimen108 131 | \Gm@layouthoffset=\dimen109 132 | \Gm@layoutvoffset=\dimen110 133 | \Gm@dimlist=\toks15 134 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsmath.sty 135 | Package: amsmath 2018/12/01 v2.17b AMS math features 136 | \@mathmargin=\skip57 137 | 138 | For additional information on amsmath, use the `?' option. 139 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amstext.sty 140 | Package: amstext 2000/06/29 v2.01 AMS text 141 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsgen.sty 142 | File: amsgen.sty 1999/11/30 v2.0 generic functions 143 | \@emptytoks=\toks16 144 | \ex@=\dimen111 145 | )) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsbsy.sty 146 | Package: amsbsy 1999/11/29 v1.2d Bold Symbols 147 | \pmbraise@=\dimen112 148 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsopn.sty 149 | Package: amsopn 2016/03/08 v2.02 operator names 150 | ) 151 | \inf@bad=\count92 152 | LaTeX Info: Redefining \frac on input line 223. 153 | \uproot@=\count93 154 | \leftroot@=\count94 155 | LaTeX Info: Redefining \overline on input line 385. 156 | \classnum@=\count95 157 | \DOTSCASE@=\count96 158 | LaTeX Info: Redefining \ldots on input line 482. 159 | LaTeX Info: Redefining \dots on input line 485. 160 | LaTeX Info: Redefining \cdots on input line 606. 161 | \Mathstrutbox@=\box29 162 | \strutbox@=\box30 163 | \big@size=\dimen113 164 | LaTeX Font Info: Redeclaring font encoding OML on input line 729. 165 | LaTeX Font Info: Redeclaring font encoding OMS on input line 730. 166 | \macc@depth=\count97 167 | \c@MaxMatrixCols=\count98 168 | \dotsspace@=\muskip10 169 | \c@parentequation=\count99 170 | \dspbrk@lvl=\count100 171 | \tag@help=\toks17 172 | \row@=\count101 173 | \column@=\count102 174 | \maxfields@=\count103 175 | \andhelp@=\toks18 176 | \eqnshift@=\dimen114 177 | \alignsep@=\dimen115 178 | \tagshift@=\dimen116 179 | \tagwidth@=\dimen117 180 | \totwidth@=\dimen118 181 | \lineht@=\dimen119 182 | \@envbody=\toks19 183 | \multlinegap=\skip58 184 | \multlinetaggap=\skip59 185 | \mathdisplay@stack=\toks20 186 | LaTeX Info: Redefining \[ on input line 2844. 187 | LaTeX Info: Redefining \] on input line 2845. 188 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/amsfonts.sty 189 | Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support 190 | \symAMSa=\mathgroup4 191 | \symAMSb=\mathgroup5 192 | LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' 193 | (Font) U/euf/m/n --> U/euf/b/n on input line 106. 194 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/amssymb.sty 195 | Package: amssymb 2013/01/14 v3.01 AMS font symbols 196 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amscls/amsthm.sty 197 | Package: amsthm 2017/10/31 v2.20.4 198 | \thm@style=\toks21 199 | \thm@bodyfont=\toks22 200 | \thm@headfont=\toks23 201 | \thm@notefont=\toks24 202 | \thm@headpunct=\toks25 203 | \thm@preskip=\skip60 204 | \thm@postskip=\skip61 205 | \thm@headsep=\skip62 206 | \dth@everypar=\toks26 207 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/xcolor/xcolor.sty 208 | Package: xcolor 2016/05/11 v2.12 LaTeX color extensions (UK) 209 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics-cfg/color.cfg 210 | File: color.cfg 2016/01/02 v1.6 sample color configuration 211 | ) 212 | Package xcolor Info: Driver file: pdftex.def on input line 225. 213 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics-def/pdftex.def 214 | File: pdftex.def 2018/01/08 v1.0l Graphics/color driver for pdftex 215 | ) 216 | Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1348. 217 | Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1352. 218 | Package xcolor Info: Model `RGB' extended on input line 1364. 219 | Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1366. 220 | Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1367. 221 | Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1368. 222 | Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1369. 223 | Package xcolor Info: Model `Gray' substituted by `gray' on input line 1370. 224 | Package xcolor Info: Model `wave' substituted by `hsb' on input line 1371. 225 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/enumitem/enumitem.sty 226 | Package: enumitem 2019/02/04 v3.8 Customized lists 227 | \labelindent=\skip63 228 | \enit@outerparindent=\dimen120 229 | \enit@toks=\toks27 230 | \enit@inbox=\box31 231 | \enit@count@id=\count104 232 | \enitdp@description=\count105 233 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/inputenc.sty 234 | Package: inputenc 2018/08/11 v1.3c Input encoding file 235 | \inpenc@prehook=\toks28 236 | \inpenc@posthook=\toks29 237 | ) 238 | \c@theorem=\count106 239 | \c@corollary=\count107 240 | \c@definition=\count108 241 | \c@prop=\count109 242 | \c@ex=\count110 243 | (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/hyperref.sty 244 | Package: hyperref 2018/11/30 v6.88e Hypertext links for LaTeX 245 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty 246 | Package: hobsub-hyperref 2016/05/16 v1.14 Bundle oberdiek, subset hyperref (HO) 247 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty 248 | Package: hobsub-generic 2016/05/16 v1.14 Bundle oberdiek, subset generic (HO) 249 | Package: hobsub 2016/05/16 v1.14 Construct package bundles (HO) 250 | Package: infwarerr 2016/05/16 v1.4 Providing info/warning/error messages (HO) 251 | Package: ltxcmds 2016/05/16 v1.23 LaTeX kernel commands for general use (HO) 252 | Package: ifluatex 2016/05/16 v1.4 Provides the ifluatex switch (HO) 253 | Package ifluatex Info: LuaTeX not detected. 254 | Package hobsub Info: Skipping package `ifvtex' (already loaded). 255 | Package: intcalc 2016/05/16 v1.2 Expandable calculations with integers (HO) 256 | Package hobsub Info: Skipping package `ifpdf' (already loaded). 257 | Package: etexcmds 2016/05/16 v1.6 Avoid name clashes with e-TeX commands (HO) 258 | Package: kvsetkeys 2016/05/16 v1.17 Key value parser (HO) 259 | Package: kvdefinekeys 2016/05/16 v1.4 Define keys (HO) 260 | Package: pdftexcmds 2018/09/10 v0.29 Utility functions of pdfTeX for LuaTeX (HO) 261 | Package pdftexcmds Info: LuaTeX not detected. 262 | Package pdftexcmds Info: \pdf@primitive is available. 263 | Package pdftexcmds Info: \pdf@ifprimitive is available. 264 | Package pdftexcmds Info: \pdfdraftmode found. 265 | Package: pdfescape 2016/05/16 v1.14 Implements pdfTeX's escape features (HO) 266 | Package: bigintcalc 2016/05/16 v1.4 Expandable calculations on big integers (HO) 267 | Package: bitset 2016/05/16 v1.2 Handle bit-vector datatype (HO) 268 | Package: uniquecounter 2016/05/16 v1.3 Provide unlimited unique counter (HO) 269 | ) 270 | Package hobsub Info: Skipping package `hobsub' (already loaded). 271 | Package: letltxmacro 2016/05/16 v1.5 Let assignment for LaTeX macros (HO) 272 | Package: hopatch 2016/05/16 v1.3 Wrapper for package hooks (HO) 273 | Package: xcolor-patch 2016/05/16 xcolor patch 274 | Package: atveryend 2016/05/16 v1.9 Hooks at the very end of document (HO) 275 | Package atveryend Info: \enddocument detected (standard20110627). 276 | Package: atbegshi 2016/06/09 v1.18 At begin shipout hook (HO) 277 | Package: refcount 2016/05/16 v3.5 Data extraction from label references (HO) 278 | Package: hycolor 2016/05/16 v1.8 Color options for hyperref/bookmark (HO) 279 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/auxhook.sty 280 | Package: auxhook 2016/05/16 v1.4 Hooks for auxiliary files (HO) 281 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/kvoptions.sty 282 | Package: kvoptions 2016/05/16 v3.12 Key value format for package options (HO) 283 | ) 284 | \@linkdim=\dimen121 285 | \Hy@linkcounter=\count111 286 | \Hy@pagecounter=\count112 287 | (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/pd1enc.def 288 | File: pd1enc.def 2018/11/30 v6.88e Hyperref: PDFDocEncoding definition (HO) 289 | Now handling font encoding PD1 ... 290 | ... no UTF-8 mapping file for font encoding PD1 291 | ) 292 | \Hy@SavedSpaceFactor=\count113 293 | (/usr/local/texlive/2019/texmf-dist/tex/latex/latexconfig/hyperref.cfg 294 | File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive 295 | ) 296 | Package hyperref Info: Hyper figures OFF on input line 4519. 297 | Package hyperref Info: Link nesting OFF on input line 4524. 298 | Package hyperref Info: Hyper index ON on input line 4527. 299 | Package hyperref Info: Plain pages OFF on input line 4534. 300 | Package hyperref Info: Backreferencing OFF on input line 4539. 301 | Package hyperref Info: Implicit mode ON; LaTeX internals redefined. 302 | Package hyperref Info: Bookmarks ON on input line 4772. 303 | \c@Hy@tempcnt=\count114 304 | (/usr/local/texlive/2019/texmf-dist/tex/latex/url/url.sty 305 | \Urlmuskip=\muskip11 306 | Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc. 307 | ) 308 | LaTeX Info: Redefining \url on input line 5125. 309 | \XeTeXLinkMargin=\dimen122 310 | \Fld@menulength=\count115 311 | \Field@Width=\dimen123 312 | \Fld@charsize=\dimen124 313 | Package hyperref Info: Hyper figures OFF on input line 6380. 314 | Package hyperref Info: Link nesting OFF on input line 6385. 315 | Package hyperref Info: Hyper index ON on input line 6388. 316 | Package hyperref Info: backreferencing OFF on input line 6395. 317 | Package hyperref Info: Link coloring OFF on input line 6400. 318 | Package hyperref Info: Link coloring with OCG OFF on input line 6405. 319 | Package hyperref Info: PDF/A mode OFF on input line 6410. 320 | LaTeX Info: Redefining \ref on input line 6450. 321 | LaTeX Info: Redefining \pageref on input line 6454. 322 | \Hy@abspage=\count116 323 | \c@Item=\count117 324 | \c@Hfootnote=\count118 325 | ) 326 | Package hyperref Info: Driver (autodetected): hpdftex. 327 | (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/hpdftex.def 328 | File: hpdftex.def 2018/11/30 v6.88e Hyperref driver for pdfTeX 329 | \Fld@listcount=\count119 330 | \c@bookmark@seq@number=\count120 331 | (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty 332 | Package: rerunfilecheck 2016/05/16 v1.8 Rerun checks for auxiliary files (HO) 333 | Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 282. 334 | ) 335 | \Hy@SectionHShift=\skip64 336 | ) 337 | Package hyperref Info: Option `colorlinks' set `true' on input line 29. 338 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m247.aux) 339 | \openout1 = `m247.aux'. 340 | 341 | LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 81. 342 | LaTeX Font Info: ... okay on input line 81. 343 | LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 81. 344 | LaTeX Font Info: ... okay on input line 81. 345 | LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 81. 346 | LaTeX Font Info: ... okay on input line 81. 347 | LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 81. 348 | LaTeX Font Info: ... okay on input line 81. 349 | LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 81. 350 | LaTeX Font Info: ... okay on input line 81. 351 | LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 81. 352 | LaTeX Font Info: ... okay on input line 81. 353 | LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 81. 354 | LaTeX Font Info: ... okay on input line 81. 355 | 356 | *geometry* driver: auto-detecting 357 | *geometry* detected driver: pdftex 358 | *geometry* verbose mode - [ preamble ] result: 359 | * driver: pdftex 360 | * paper: 361 | * layout: 362 | * layoutoffset:(h,v)=(0.0pt,0.0pt) 363 | * modes: 364 | * h-part:(L,W,R)=(56.9055pt, 483.69693pt, 56.9055pt) 365 | * v-part:(T,H,B)=(56.9055pt, 731.23593pt, 56.9055pt) 366 | * \paperwidth=597.50793pt 367 | * \paperheight=845.04694pt 368 | * \textwidth=483.69693pt 369 | * \textheight=731.23593pt 370 | * \oddsidemargin=-15.36449pt 371 | * \evensidemargin=-15.36449pt 372 | * \topmargin=-52.7645pt 373 | * \headheight=17.0pt 374 | * \headsep=20.40001pt 375 | * \topskip=11.0pt 376 | * \footskip=47.6pt 377 | * \marginparwidth=59.7508pt 378 | * \marginparsep=12.8401pt 379 | * \columnsep=10.0pt 380 | * \skip\footins=10.0pt plus 4.0pt minus 2.0pt 381 | * \hoffset=0.0pt 382 | * \voffset=0.0pt 383 | * \mag=1000 384 | * \@twocolumnfalse 385 | * \@twosidefalse 386 | * \@mparswitchfalse 387 | * \@reversemarginfalse 388 | * (1in=72.27pt=25.4mm, 1cm=28.453pt) 389 | 390 | (/usr/local/texlive/2019/texmf-dist/tex/context/base/mkii/supp-pdf.mkii 391 | [Loading MPS to PDF converter (version 2006.09.02).] 392 | \scratchcounter=\count121 393 | \scratchdimen=\dimen125 394 | \scratchbox=\box32 395 | \nofMPsegments=\count122 396 | \nofMParguments=\count123 397 | \everyMPshowfont=\toks30 398 | \MPscratchCnt=\count124 399 | \MPscratchDim=\dimen126 400 | \MPnumerator=\count125 401 | \makeMPintoPDFobject=\count126 402 | \everyMPtoPDFconversion=\toks31 403 | ) 404 | \AtBeginShipoutBox=\box33 405 | Package hyperref Info: Link coloring ON on input line 81. 406 | (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/nameref.sty 407 | Package: nameref 2016/05/21 v2.44 Cross-referencing by name of section 408 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/gettitlestring.sty 409 | Package: gettitlestring 2016/05/16 v1.5 Cleanup title references (HO) 410 | ) 411 | \c@section@level=\count127 412 | ) 413 | LaTeX Info: Redefining \ref on input line 81. 414 | LaTeX Info: Redefining \pageref on input line 81. 415 | LaTeX Info: Redefining \nameref on input line 81. 416 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m247.out) (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m247.out) 417 | \@outlinefile=\write3 418 | \openout3 = `m247.out'. 419 | 420 | Class scrartcl Info: loading recommended package `bookmark'. 421 | (scrartcl) Using `bookmark' together with `hyperref' is recommended, 422 | (scrartcl) because of handling of possible bookmark level gaps. 423 | (scrartcl) You can avoid loading `bookmark' with KOMA-Script option 424 | (scrartcl) `bookmarkpackage=false' before \begin{document} and 425 | (scrartcl) you can avoid this message with `\usepackage{bookmark}' 426 | (scrartcl) before \begin{document} on input line 81. 427 | (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/bookmark.sty 428 | Package: bookmark 2016/05/17 v1.26 PDF bookmarks (HO) 429 | (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/bkm-pdftex.def 430 | File: bkm-pdftex.def 2016/05/17 v1.26 bookmark driver for pdfTeX (HO) 431 | Package auxhook Info: \AddLineBeginMainAux comes a little late, 432 | (auxhook) because the main .aux file is already opened on input line 164. 433 | \BKM@id=\count128 434 | )) 435 | LaTeX Font Info: Try loading font information for U+msa on input line 84. 436 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/umsa.fd 437 | File: umsa.fd 2013/01/14 v3.01 AMS symbols A 438 | ) 439 | LaTeX Font Info: Try loading font information for U+msb on input line 84. 440 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/umsb.fd 441 | File: umsb.fd 2013/01/14 v3.01 AMS symbols B 442 | ) 443 | 444 | LaTeX Font Warning: Font shape `OT1/cmr/bx/sc' undefined 445 | (Font) using `OT1/cmr/bx/n' instead on input line 84. 446 | 447 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m247.toc) 448 | \tf@toc=\write4 449 | \openout4 = `m247.toc'. 450 | 451 | [1 452 | 453 | 454 | {/usr/local/texlive/2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2] [3] 455 | Overfull \hbox (6.39722pt too wide) in paragraph at lines 227--229 456 | \OT1/cmr/m/n/10.95 This can be con-sid-ered a vec-tor space. Ad-di-tion is component-wise and mul-ti-pli-ca-tion is also component- 457 | [] 458 | 459 | [4] [5] 460 | Underfull \hbox (badness 10000) in paragraph at lines 378--382 461 | 462 | [] 463 | 464 | [6] 465 | LaTeX Font Info: Try loading font information for OMS+cmr on input line 383. 466 | (/usr/local/texlive/2019/texmf-dist/tex/latex/base/omscmr.fd 467 | File: omscmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions 468 | ) 469 | LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10.95> not available 470 | (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 383. 471 | [7] [8] 472 | Overfull \hbox (1.47504pt too wide) in paragraph at lines 547--548 473 | [][]\OT1/cmr/bx/n/10.95 Example 15. []\OT1/cmr/m/n/10.95 Let $\OML/cmm/m/it/10.95 V \OT1/cmr/m/n/10.95 = \U/msb/m/n/10.95 R[]$\OT1/cmr/m/n/10.95 . Then, the stan-dard ba-sis vec-tors: $\OML/cmm/m/it/10.95 e[] \OT1/cmr/m/n/10.95 = (1\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 0\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 0\OML/cmm/m/it/10.95 ; :::\OT1/cmr/m/n/10.95 )\OML/cmm/m/it/10.95 ; e[] \OT1/cmr/m/n/10.95 = (0\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 1\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 0\OML/cmm/m/it/10.95 ; :::\OT1/cmr/m/n/10.95 )\OML/cmm/m/it/10.95 ; :::; e[] \OT1/cmr/m/n/10.95 = 474 | [] 475 | 476 | 477 | Overfull \hbox (3.98615pt too wide) in paragraph at lines 577--578 478 | [][]\OT1/cmr/bx/n/10.95 Definition 8 \OT1/cmr/m/n/10.95 (Lin-ear In-de-pen-dence and De-pen-dence)\OT1/cmr/bx/n/10.95 . []\OT1/cmr/m/n/10.95 Let $(\OML/cmm/m/it/10.95 V; \OT1/cmr/m/n/10.95 +\OML/cmm/m/it/10.95 ; \OMS/cmsy/m/n/10.95 ^^A\OT1/cmr/m/n/10.95 )$ be a vec-tor space over $\OML/cmm/m/it/10.95 K$\OT1/cmr/m/n/10.95 , $\OML/cmm/m/it/10.95 v[]; :::; v[] \OMS/cmsy/m/n/10.95 2 479 | [] 480 | 481 | [9] 482 | Overfull \hbox (9.86275pt too wide) detected at line 630 483 | [] 484 | [] 485 | 486 | [10] [11] [12] [13] [14] [15] 487 | Overfull \hbox (6.37657pt too wide) in paragraph at lines 1017--1018 488 | [][]\OT1/cmr/bx/n/10.95 Theorem 40 \OT1/cmr/m/n/10.95 (Very Fun-da-men-tal and Im-por-tant)\OT1/cmr/bx/n/10.95 . []\OT1/cmr/m/n/10.95 Let $\OML/cmm/m/it/10.95 V$ \OT1/cmr/m/n/10.95 be a vec-tor space over $\OML/cmm/m/it/10.95 K$\OT1/cmr/m/n/10.95 , $\OML/cmm/m/it/10.95 V$ \OT1/cmr/m/n/10.95 finite-dimensional. 489 | [] 490 | 491 | 492 | Underfull \hbox (badness 10000) in paragraph at lines 1026--1030 493 | 494 | [] 495 | 496 | [16] 497 | 498 | Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): 499 | (hyperref) removing `math shift' on input line 1088. 500 | 501 | 502 | Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): 503 | (hyperref) removing `superscript' on input line 1088. 504 | 505 | 506 | Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): 507 | (hyperref) removing `math shift' on input line 1088. 508 | 509 | [17] 510 | 511 | Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): 512 | (hyperref) removing `math shift' on input line 1120. 513 | 514 | 515 | Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): 516 | (hyperref) removing `superscript' on input line 1120. 517 | 518 | 519 | Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): 520 | (hyperref) removing `math shift' on input line 1120. 521 | 522 | 523 | Underfull \hbox (badness 10000) in paragraph at lines 1158--1166 524 | 525 | [] 526 | 527 | 528 | Underfull \hbox (badness 10000) in paragraph at lines 1158--1166 529 | 530 | [] 531 | 532 | [18] [19] 533 | 534 | Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): 535 | (hyperref) removing `math shift' on input line 1300. 536 | 537 | 538 | Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): 539 | (hyperref) removing `math shift' on input line 1300. 540 | 541 | [20] [21] [22] 542 | Package atveryend Info: Empty hook `BeforeClearDocument' on input line 1494. 543 | [23] 544 | Package atveryend Info: Empty hook `AfterLastShipout' on input line 1494. 545 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m247.aux) 546 | Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 1494. 547 | Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 1494. 548 | Package rerunfilecheck Info: File `m247.out' has not changed. 549 | (rerunfilecheck) Checksum: . 550 | 551 | 552 | LaTeX Font Warning: Some font shapes were not available, defaults substituted. 553 | 554 | Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 1494. 555 | ) 556 | Here is how much of TeX's memory you used: 557 | 9669 strings out of 492616 558 | 150888 string characters out of 6129481 559 | 374582 words of memory out of 5000000 560 | 13137 multiletter control sequences out of 15000+600000 561 | 16220 words of font info for 62 fonts, out of 8000000 for 9000 562 | 1141 hyphenation exceptions out of 8191 563 | 41i,17n,51p,9116b,541s stack positions out of 5000i,500n,10000p,200000b,80000s 564 | 565 | Output written on /Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m247.pdf (23 pages, 289743 bytes). 566 | PDF statistics: 567 | 736 PDF objects out of 1000 (max. 8388607) 568 | 688 compressed objects within 7 object streams 569 | 369 named destinations out of 1000 (max. 500000) 570 | 281 words of extra memory for PDF output out of 10000 (max. 10000000) 571 | 572 | -------------------------------------------------------------------------------- /.texpadtmp/m247.out: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/m247.out -------------------------------------------------------------------------------- /.texpadtmp/m247.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/m247.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/m247.toc: -------------------------------------------------------------------------------- 1 | \contentsline {section}{\numberline {1}Introduction}{2}{section.1}% 2 | \contentsline {section}{\numberline {2}Abstract Vector Spaces}{3}{section.2}% 3 | \contentsline {subsection}{\numberline {2.1}Many Examples of Vector Spaces}{4}{subsection.2.1}% 4 | \contentsline {subsection}{\numberline {2.2}Consequences of the Axioms}{5}{subsection.2.2}% 5 | \contentsline {subsection}{\numberline {2.3}Subspaces}{6}{subsection.2.3}% 6 | \contentsline {subsection}{\numberline {2.4}Linear Combination and Span}{9}{subsection.2.4}% 7 | \contentsline {subsection}{\numberline {2.5}Linear Independence and Dependence}{10}{subsection.2.5}% 8 | \contentsline {subsection}{\numberline {2.6}Applications (Theoretical) of Steinitz Exchange Lemma}{11}{subsection.2.6}% 9 | \contentsline {section}{\numberline {3}Linear Maps}{13}{section.3}% 10 | \contentsline {subsection}{\numberline {3.1}Endomorphisms}{14}{subsection.3.1}% 11 | \contentsline {subsection}{\numberline {3.2}Coordinate Vectors}{14}{subsection.3.2}% 12 | \contentsline {subsection}{\numberline {3.3}Representations of Linear Maps as Matrices}{14}{subsection.3.3}% 13 | \contentsline {subsection}{\numberline {3.4}Composition of Linear Maps}{14}{subsection.3.4}% 14 | \contentsline {subsection}{\numberline {3.5}Matrix Representations of Isomorphisms}{15}{subsection.3.5}% 15 | \contentsline {subsection}{\numberline {3.6}Change of Basis}{15}{subsection.3.6}% 16 | \contentsline {subsection}{\numberline {3.7}The Normal Form Problem}{15}{subsection.3.7}% 17 | \contentsline {subsection}{\numberline {3.8}Characteristic Polynomial}{16}{subsection.3.8}% 18 | \contentsline {subsection}{\numberline {3.9}Normal Form for Non-Diagonalisable Matrices}{16}{subsection.3.9}% 19 | \contentsline {section}{\numberline {4}Applications of Linear Algebra (to other fields of math...not real life :-P)}{17}{section.4}% 20 | \contentsline {subsection}{\numberline {4.1}Matrix Exponential}{17}{subsection.4.1}% 21 | \contentsline {section}{\numberline {5}Orthogonality: A quick introduction}{17}{section.5}% 22 | \contentsline {subsection}{\numberline {5.1}Standard inner product on $\mathbb {R}^n$}{17}{subsection.5.1}% 23 | \contentsline {subsection}{\numberline {5.2}Properties of the Standard Inner Product on $\mathbb {C}^n$}{18}{subsection.5.2}% 24 | \contentsline {subsection}{\numberline {5.3}Application of Orthogonality (Orthogonal and Unitary Matrices)}{18}{subsection.5.3}% 25 | \contentsline {subsubsection}{\numberline {5.3.1}Orthogonal Case}{18}{subsubsection.5.3.1}% 26 | \contentsline {subsubsection}{\numberline {5.3.2}Unitary Case}{18}{subsubsection.5.3.2}% 27 | \contentsline {subsection}{\numberline {5.4}Orthogonality and Unitary: Diagonalisation and Upper Triangularisation}{19}{subsection.5.4}% 28 | \contentsline {subsubsection}{\numberline {5.4.1}Spectral Theorem: Complex Case}{19}{subsubsection.5.4.1}% 29 | \contentsline {subsection}{\numberline {5.5}Applications of the Real Spectral Theorem}{20}{subsection.5.5}% 30 | \contentsline {subsubsection}{\numberline {5.5.1}Real Quadratic Forms}{20}{subsubsection.5.5.1}% 31 | \contentsline {section}{\numberline {6}Inner Product Spaces}{20}{section.6}% 32 | \contentsline {subsection}{\numberline {6.1}$K = \mathbb {R}$}{21}{subsection.6.1}% 33 | \contentsline {subsection}{\numberline {6.2}Complex Inner Product Spaces}{21}{subsection.6.2}% 34 | \contentsline {subsection}{\numberline {6.3}Geometry on a Vector Space}{21}{subsection.6.3}% 35 | \contentsline {section}{\numberline {7}Fourier Series in 30 Minutes [not examinable]}{22}{section.7}% 36 | -------------------------------------------------------------------------------- /.texpadtmp/m254.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \providecommand\hyper@newdestlabel[2]{} 3 | \providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} 4 | \HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined 5 | \global\let\oldcontentsline\contentsline 6 | \gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} 7 | \global\let\oldnewlabel\newlabel 8 | \gdef\newlabel#1#2{\newlabelxx{#1}#2} 9 | \gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} 10 | \AtEndDocument{\ifx\hyper@anchor\@undefined 11 | \let\contentsline\oldcontentsline 12 | \let\newlabel\oldnewlabel 13 | \fi} 14 | \fi} 15 | \global\let\hyper@last\relax 16 | \gdef\HyperFirstAtBeginDocument#1{#1} 17 | \providecommand\HyField@AuxAddToFields[1]{} 18 | \providecommand\HyField@AuxAddToCoFields[2]{} 19 | \providecommand \oddpage@label [2]{} 20 | \@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{section.1}\protected@file@percent } 21 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.1}{Countability of Finite Sets}}{2}{subsection.1.1}\protected@file@percent } 22 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.2}{Supremum and Infimum}}{3}{subsection.1.2}\protected@file@percent } 23 | \@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Point-Set Topology}}{5}{section.2}\protected@file@percent } 24 | \@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Sequences}}{7}{section.3}\protected@file@percent } 25 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{Some Results on Convergent Sequences}}{7}{subsection.3.1}\protected@file@percent } 26 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{Monotone Sequences}}{7}{subsection.3.2}\protected@file@percent } 27 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.3}{Subsequences}}{8}{subsection.3.3}\protected@file@percent } 28 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.4}{Cauchy Sequences}}{9}{subsection.3.4}\protected@file@percent } 29 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.5}{Divergence to $\pm \infty $}}{9}{subsection.3.5}\protected@file@percent } 30 | \@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Limits of Functions}}{9}{section.4}\protected@file@percent } 31 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.1}{Continuity}}{10}{subsection.4.1}\protected@file@percent } 32 | \@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Differentiation}}{11}{section.5}\protected@file@percent } 33 | \newlabel{tocindent-1}{0pt} 34 | \newlabel{tocindent0}{0pt} 35 | \newlabel{tocindent1}{19.4667pt} 36 | \newlabel{tocindent2}{32.18062pt} 37 | \newlabel{tocindent3}{0pt} 38 | \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.1}{Applications of the Mean Value Theorem}}{12}{subsection.5.1}\protected@file@percent } 39 | -------------------------------------------------------------------------------- /.texpadtmp/m254.log: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/m254.log -------------------------------------------------------------------------------- /.texpadtmp/m254.out: -------------------------------------------------------------------------------- 1 | \BOOKMARK [1][-]{section.1}{1. Introduction}{}% 1 2 | \BOOKMARK [2][-]{subsection.1.1}{1.1. Countability of Finite Sets}{section.1}% 2 3 | \BOOKMARK [2][-]{subsection.1.2}{1.2. Supremum and Infimum}{section.1}% 3 4 | \BOOKMARK [1][-]{section.2}{2. Point-Set Topology}{}% 4 5 | \BOOKMARK [1][-]{section.3}{3. Sequences}{}% 5 6 | \BOOKMARK [2][-]{subsection.3.1}{3.1. Some Results on Convergent Sequences}{section.3}% 6 7 | \BOOKMARK [2][-]{subsection.3.2}{3.2. Monotone Sequences}{section.3}% 7 8 | \BOOKMARK [2][-]{subsection.3.3}{3.3. Subsequences}{section.3}% 8 9 | \BOOKMARK [2][-]{subsection.3.4}{3.4. Cauchy Sequences}{section.3}% 9 10 | \BOOKMARK [2][-]{subsection.3.5}{3.5. Divergence to }{section.3}% 10 11 | \BOOKMARK [1][-]{section.4}{4. Limits of Functions}{}% 11 12 | \BOOKMARK [2][-]{subsection.4.1}{4.1. Continuity}{section.4}% 12 13 | \BOOKMARK [1][-]{section.5}{5. Differentiation}{}% 13 14 | \BOOKMARK [2][-]{subsection.5.1}{5.1. Applications of the Mean Value Theorem}{section.5}% 14 15 | -------------------------------------------------------------------------------- /.texpadtmp/m254.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/m254.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/m254.toc: -------------------------------------------------------------------------------- 1 | \contentsline {section}{\tocsection {}{1}{Introduction}}{1}{section.1}% 2 | \contentsline {subsection}{\tocsubsection {}{1.1}{Countability of Finite Sets}}{2}{subsection.1.1}% 3 | \contentsline {subsection}{\tocsubsection {}{1.2}{Supremum and Infimum}}{3}{subsection.1.2}% 4 | \contentsline {section}{\tocsection {}{2}{Point-Set Topology}}{5}{section.2}% 5 | \contentsline {section}{\tocsection {}{3}{Sequences}}{7}{section.3}% 6 | \contentsline {subsection}{\tocsubsection {}{3.1}{Some Results on Convergent Sequences}}{7}{subsection.3.1}% 7 | \contentsline {subsection}{\tocsubsection {}{3.2}{Monotone Sequences}}{7}{subsection.3.2}% 8 | \contentsline {subsection}{\tocsubsection {}{3.3}{Subsequences}}{8}{subsection.3.3}% 9 | \contentsline {subsection}{\tocsubsection {}{3.4}{Cauchy Sequences}}{9}{subsection.3.4}% 10 | \contentsline {subsection}{\tocsubsection {}{3.5}{Divergence to $\pm \infty $}}{9}{subsection.3.5}% 11 | \contentsline {section}{\tocsection {}{4}{Limits of Functions}}{9}{section.4}% 12 | \contentsline {subsection}{\tocsubsection {}{4.1}{Continuity}}{10}{subsection.4.1}% 13 | \contentsline {section}{\tocsection {}{5}{Differentiation}}{11}{section.5}% 14 | \contentsline {subsection}{\tocsubsection {}{5.1}{Applications of the Mean Value Theorem}}{12}{subsection.5.1}% 15 | -------------------------------------------------------------------------------- /.texpadtmp/m357.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \providecommand\hyper@newdestlabel[2]{} 3 | \providecommand*\new@tpo@label[2]{} 4 | \providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} 5 | \HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined 6 | \global\let\oldcontentsline\contentsline 7 | \gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} 8 | \global\let\oldnewlabel\newlabel 9 | \gdef\newlabel#1#2{\newlabelxx{#1}#2} 10 | \gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} 11 | \AtEndDocument{\ifx\hyper@anchor\@undefined 12 | \let\contentsline\oldcontentsline 13 | \let\newlabel\oldnewlabel 14 | \fi} 15 | \fi} 16 | \global\let\hyper@last\relax 17 | \gdef\HyperFirstAtBeginDocument#1{#1} 18 | \providecommand\HyField@AuxAddToFields[1]{} 19 | \providecommand\HyField@AuxAddToCoFields[2]{} 20 | \providecommand\BKM@entry[2]{} 21 | \BKM@entry{id=1,dest={73656374696F6E2E31},srcline={82}}{496E74726F64756374696F6E} 22 | \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}\protected@file@percent } 23 | \BKM@entry{id=2,dest={73656374696F6E2E32},srcline={105}}{50726F70657274696573206F662052616E646F6D2053616D706C6573} 24 | \@writefile{toc}{\contentsline {section}{\numberline {2}Properties of Random Samples}{2}{section.2}\protected@file@percent } 25 | \BKM@entry{id=3,dest={73756273656374696F6E2E322E31},srcline={322}}{53616D706C696E672066726F6D20746865204E6F726D616C20506F70756C6174696F6E} 26 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Sampling from the Normal Population}{6}{subsection.2.1}\protected@file@percent } 27 | \BKM@entry{id=4,dest={73756273656374696F6E2E322E32},srcline={476}}{5374616E6461726469736174696F6E} 28 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Standardisation}{9}{subsection.2.2}\protected@file@percent } 29 | \BKM@entry{id=5,dest={73756273656374696F6E2E322E33},srcline={533}}{462D54657374204261736973} 30 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}F-Test Basis}{10}{subsection.2.3}\protected@file@percent } 31 | \BKM@entry{id=6,dest={73756273656374696F6E2E322E34},srcline={570}}{4C696D6974696E672053616D706C6520446973747269627574696F6E73205C284173796D70746F746963735C29} 32 | \BKM@entry{id=7,dest={73756273756273656374696F6E2E322E342E31},srcline={595}}{5175657374696F6E2031} 33 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Limiting Sample Distributions (Asymptotics)}{11}{subsection.2.4}\protected@file@percent } 34 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.1}Question 1}{12}{subsubsection.2.4.1}\protected@file@percent } 35 | \BKM@entry{id=8,dest={73756273756273656374696F6E2E322E342E32},srcline={670}}{5175657374696F6E2032} 36 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.2}Question 2}{13}{subsubsection.2.4.2}\protected@file@percent } 37 | \BKM@entry{id=9,dest={73756273656374696F6E2E322E35},srcline={790}}{4F726465722053746174697374696373} 38 | \BKM@entry{id=10,dest={73656374696F6E2E33},srcline={816}}{506F696E7420457374696D6174696F6E} 39 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Order Statistics}{15}{subsection.2.5}\protected@file@percent } 40 | \BKM@entry{id=11,dest={73756273656374696F6E2E332E31},srcline={842}}{576179732057652043616E20436F6E73747275637420457374696D61746F7273} 41 | \BKM@entry{id=12,dest={73756273756273656374696F6E2E332E312E31},srcline={850}}{4D6574686F64206F66206D6F6D656E7473} 42 | \@writefile{toc}{\contentsline {section}{\numberline {3}Point Estimation}{16}{section.3}\protected@file@percent } 43 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Ways We Can Construct Estimators}{16}{subsection.3.1}\protected@file@percent } 44 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.1}Method of moments}{16}{subsubsection.3.1.1}\protected@file@percent } 45 | \BKM@entry{id=13,dest={73756273756273656374696F6E2E332E312E32},srcline={985}}{4D6574686F64206F66204D6178696D756D204C696B656C69686F6F64} 46 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.2}Method of Maximum Likelihood}{19}{subsubsection.3.1.2}\protected@file@percent } 47 | \BKM@entry{id=14,dest={73756273756273656374696F6E2E332E312E33},srcline={1176}}{496E76617269616E6365206F6620746865204D4C45205468656F72656D} 48 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.3}Invariance of the MLE Theorem}{22}{subsubsection.3.1.3}\protected@file@percent } 49 | \BKM@entry{id=15,dest={73756273756273656374696F6E2E332E312E34},srcline={1240}}{426179657369616E204D6574686F64} 50 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.4}Bayesian Method}{24}{subsubsection.3.1.4}\protected@file@percent } 51 | \BKM@entry{id=16,dest={73756273656374696F6E2E332E32},srcline={1302}}{4D6574686F64206F66204576616C756174696E6720457374696D61746F7273} 52 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Method of Evaluating Estimators}{25}{subsection.3.2}\protected@file@percent } 53 | \BKM@entry{id=17,dest={73756273656374696F6E2E332E33},srcline={1444}}{4265737420556E62696173656420457374696D61746F7273} 54 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Best Unbiased Estimators}{28}{subsection.3.3}\protected@file@percent } 55 | \BKM@entry{id=18,dest={73756273756273656374696F6E2E332E332E31},srcline={1566}}{47656F6D657472696320496E746572707265746174696F6E} 56 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.1}Geometric Interpretation}{30}{subsubsection.3.3.1}\protected@file@percent } 57 | \BKM@entry{id=19,dest={73656374696F6E2E34},srcline={1877}}{53756666696369656E637920616E6420436F6D706C6574656E657373} 58 | \BKM@entry{id=20,dest={73756273656374696F6E2E342E31},srcline={1928}}{50726F76696E67207468652053756666696369656E6379206F662053746174697374696373} 59 | \@writefile{toc}{\contentsline {section}{\numberline {4}Sufficiency and Completeness}{37}{section.4}\protected@file@percent } 60 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Proving the Sufficiency of Statistics}{38}{subsection.4.1}\protected@file@percent } 61 | \BKM@entry{id=21,dest={73756273656374696F6E2E342E32},srcline={2042}}{53756666696369656E742053746174697374696373} 62 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Sufficient Statistics}{40}{subsection.4.2}\protected@file@percent } 63 | \BKM@entry{id=22,dest={73756273656374696F6E2E342E33},srcline={2142}}{4170706C69636174696F6E73206F662053756666696369656E637920696E20506F696E7420457374696D6174696F6E} 64 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Applications of Sufficiency in Point Estimation}{42}{subsection.4.3}\protected@file@percent } 65 | \BKM@entry{id=23,dest={73656374696F6E2E35},srcline={2330}}{4879706F7468657369732054657374696E67} 66 | \BKM@entry{id=24,dest={73756273656374696F6E2E352E31},srcline={2331}}{4261736963205465726D696E6F6C6F6779} 67 | \@writefile{toc}{\contentsline {section}{\numberline {5}Hypothesis Testing}{45}{section.5}\protected@file@percent } 68 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Basic Terminology}{45}{subsection.5.1}\protected@file@percent } 69 | \BKM@entry{id=25,dest={73756273656374696F6E2E352E32},srcline={2502}}{4C696B656C69686F6F6420526174696F205465737473} 70 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Likelihood Ratio Tests}{48}{subsection.5.2}\protected@file@percent } 71 | \global\@namedef{scr@dte@section@lastmaxnumwidth}{10.84047pt} 72 | \global\@namedef{scr@dte@subsection@lastmaxnumwidth}{18.37163pt} 73 | \global\@namedef{scr@dte@subsubsection@lastmaxnumwidth}{26.8883pt} 74 | -------------------------------------------------------------------------------- /.texpadtmp/m357.log: -------------------------------------------------------------------------------- 1 | This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex 2019.7.26) 30 MAR 2020 15:06 2 | entering extended mode 3 | restricted \write18 enabled. 4 | file:line:error style messages enabled. 5 | %&-line parsing enabled. 6 | **m357.tex 7 | (./m357.tex 8 | LaTeX2e <2018-12-01> 9 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrartcl.cls 10 | Document Class: scrartcl 2019/02/01 v3.26b KOMA-Script document class (article) 11 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrkbase.sty 12 | Package: scrkbase 2019/02/01 v3.26b KOMA-Script package (KOMA-Script-dependent basics and keyval usage) 13 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrbase.sty 14 | Package: scrbase 2019/02/01 v3.26b KOMA-Script package (KOMA-Script-independent basics and keyval usage) 15 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics/keyval.sty 16 | Package: keyval 2014/10/28 v1.15 key=value parser (DPC) 17 | \KV@toks@=\toks14 18 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrlfile.sty 19 | Package: scrlfile 2019/02/01 v3.26b KOMA-Script package (loading files) 20 | ))) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/tocbasic.sty 21 | Package: tocbasic 2019/02/01 v3.26b KOMA-Script package (handling toc-files) 22 | \scr@dte@tocline@numberwidth=\skip41 23 | \scr@dte@tocline@numbox=\box27 24 | ) 25 | Package tocbasic Info: omitting babel extension for `toc' 26 | (tocbasic) because of feature `nobabel' available 27 | (tocbasic) for `toc' on input line 134. 28 | Package scrartcl Info: You've used standard option `11pt'. 29 | (scrartcl) This is correct! 30 | (scrartcl) Internally I'm using `fontsize=11pt'. 31 | (scrartcl) If you'd like to set the option with \KOMAoptions, 32 | (scrartcl) you'd have to use `fontsize=11pt' there 33 | (scrartcl) instead of `11pt', too. 34 | Class scrartcl Info: File `scrsize11pt.clo' used to setup font sizes on input line 2162. 35 | (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/scrsize11pt.clo 36 | File: scrsize11pt.clo 2019/02/01 v3.26b KOMA-Script font size class option (11pt) 37 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/koma-script/typearea.sty 38 | Package: typearea 2019/02/01 v3.26b KOMA-Script package (type area) 39 | \ta@bcor=\skip42 40 | \ta@div=\count80 41 | \ta@hblk=\skip43 42 | \ta@vblk=\skip44 43 | \ta@temp=\skip45 44 | \footheight=\skip46 45 | Package typearea Info: These are the values describing the layout: 46 | (typearea) DIV = 10 47 | (typearea) BCOR = 0.0pt 48 | (typearea) \paperwidth = 597.50793pt 49 | (typearea) \textwidth = 418.25555pt 50 | (typearea) DIV departure = -6% 51 | (typearea) \evensidemargin = 17.3562pt 52 | (typearea) \oddsidemargin = 17.3562pt 53 | (typearea) \paperheight = 845.04694pt 54 | (typearea) \textheight = 595.80026pt 55 | (typearea) \topmargin = -25.16531pt 56 | (typearea) \headheight = 17.0pt 57 | (typearea) \headsep = 20.40001pt 58 | (typearea) \topskip = 11.0pt 59 | (typearea) \footskip = 47.6pt 60 | (typearea) \baselineskip = 13.6pt 61 | (typearea) on input line 1715. 62 | ) 63 | \c@part=\count81 64 | \c@section=\count82 65 | \c@subsection=\count83 66 | \c@subsubsection=\count84 67 | \c@paragraph=\count85 68 | \c@subparagraph=\count86 69 | \scr@dte@section@maxnumwidth=\skip47 70 | Class scrartcl Info: using compatibility default `runin=bysign' 71 | (scrartcl) for `\section on input line 4489. 72 | Class scrartcl Info: using compatibility default `afterindent=bysign' 73 | (scrartcl) for `\section on input line 4489. 74 | \scr@dte@part@maxnumwidth=\skip48 75 | Class scrartcl Info: using compatibility default `afterindent=false' 76 | (scrartcl) for `\part on input line 4497. 77 | \scr@dte@subsection@maxnumwidth=\skip49 78 | Class scrartcl Info: using compatibility default `runin=bysign' 79 | (scrartcl) for `\subsection on input line 4507. 80 | Class scrartcl Info: using compatibility default `afterindent=bysign' 81 | (scrartcl) for `\subsection on input line 4507. 82 | \scr@dte@subsubsection@maxnumwidth=\skip50 83 | Class scrartcl Info: using compatibility default `runin=bysign' 84 | (scrartcl) for `\subsubsection on input line 4517. 85 | Class scrartcl Info: using compatibility default `afterindent=bysign' 86 | (scrartcl) for `\subsubsection on input line 4517. 87 | \scr@dte@paragraph@maxnumwidth=\skip51 88 | Class scrartcl Info: using compatibility default `runin=bysign' 89 | (scrartcl) for `\paragraph on input line 4527. 90 | Class scrartcl Info: using compatibility default `afterindent=bysign' 91 | (scrartcl) for `\paragraph on input line 4527. 92 | \scr@dte@subparagraph@maxnumwidth=\skip52 93 | Class scrartcl Info: using compatibility default `runin=bysign' 94 | (scrartcl) for `\subparagraph on input line 4537. 95 | Class scrartcl Info: using compatibility default `afterindent=bysign' 96 | (scrartcl) for `\subparagraph on input line 4537. 97 | \abovecaptionskip=\skip53 98 | \belowcaptionskip=\skip54 99 | \c@pti@nb@sid@b@x=\box28 100 | Package tocbasic Info: omitting babel extension for `lof' 101 | (tocbasic) because of feature `nobabel' available 102 | (tocbasic) for `lof' on input line 5781. 103 | \scr@dte@figure@maxnumwidth=\skip55 104 | \c@figure=\count87 105 | Package tocbasic Info: omitting babel extension for `lot' 106 | (tocbasic) because of feature `nobabel' available 107 | (tocbasic) for `lot' on input line 5793. 108 | \scr@dte@table@maxnumwidth=\skip56 109 | \c@table=\count88 110 | Class scrartcl Info: Redefining `\numberline' on input line 5957. 111 | \bibindent=\dimen102 112 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/geometry/geometry.sty 113 | Package: geometry 2018/04/16 v5.8 Page Geometry 114 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ifpdf.sty 115 | Package: ifpdf 2018/09/07 v3.3 Provides the ifpdf switch 116 | ) (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ifvtex.sty 117 | Package: ifvtex 2016/05/16 v1.6 Detect VTeX and its facilities (HO) 118 | Package ifvtex Info: VTeX not detected. 119 | ) (/usr/local/texlive/2019/texmf-dist/tex/generic/ifxetex/ifxetex.sty 120 | Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional 121 | ) 122 | \Gm@cnth=\count89 123 | \Gm@cntv=\count90 124 | \c@Gm@tempcnt=\count91 125 | \Gm@bindingoffset=\dimen103 126 | \Gm@wd@mp=\dimen104 127 | \Gm@odd@mp=\dimen105 128 | \Gm@even@mp=\dimen106 129 | \Gm@layoutwidth=\dimen107 130 | \Gm@layoutheight=\dimen108 131 | \Gm@layouthoffset=\dimen109 132 | \Gm@layoutvoffset=\dimen110 133 | \Gm@dimlist=\toks15 134 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsmath.sty 135 | Package: amsmath 2018/12/01 v2.17b AMS math features 136 | \@mathmargin=\skip57 137 | 138 | For additional information on amsmath, use the `?' option. 139 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amstext.sty 140 | Package: amstext 2000/06/29 v2.01 AMS text 141 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsgen.sty 142 | File: amsgen.sty 1999/11/30 v2.0 generic functions 143 | \@emptytoks=\toks16 144 | \ex@=\dimen111 145 | )) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsbsy.sty 146 | Package: amsbsy 1999/11/29 v1.2d Bold Symbols 147 | \pmbraise@=\dimen112 148 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsopn.sty 149 | Package: amsopn 2016/03/08 v2.02 operator names 150 | ) 151 | \inf@bad=\count92 152 | LaTeX Info: Redefining \frac on input line 223. 153 | \uproot@=\count93 154 | \leftroot@=\count94 155 | LaTeX Info: Redefining \overline on input line 385. 156 | \classnum@=\count95 157 | \DOTSCASE@=\count96 158 | LaTeX Info: Redefining \ldots on input line 482. 159 | LaTeX Info: Redefining \dots on input line 485. 160 | LaTeX Info: Redefining \cdots on input line 606. 161 | \Mathstrutbox@=\box29 162 | \strutbox@=\box30 163 | \big@size=\dimen113 164 | LaTeX Font Info: Redeclaring font encoding OML on input line 729. 165 | LaTeX Font Info: Redeclaring font encoding OMS on input line 730. 166 | \macc@depth=\count97 167 | \c@MaxMatrixCols=\count98 168 | \dotsspace@=\muskip10 169 | \c@parentequation=\count99 170 | \dspbrk@lvl=\count100 171 | \tag@help=\toks17 172 | \row@=\count101 173 | \column@=\count102 174 | \maxfields@=\count103 175 | \andhelp@=\toks18 176 | \eqnshift@=\dimen114 177 | \alignsep@=\dimen115 178 | \tagshift@=\dimen116 179 | \tagwidth@=\dimen117 180 | \totwidth@=\dimen118 181 | \lineht@=\dimen119 182 | \@envbody=\toks19 183 | \multlinegap=\skip58 184 | \multlinetaggap=\skip59 185 | \mathdisplay@stack=\toks20 186 | LaTeX Info: Redefining \[ on input line 2844. 187 | LaTeX Info: Redefining \] on input line 2845. 188 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/amsfonts.sty 189 | Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support 190 | \symAMSa=\mathgroup4 191 | \symAMSb=\mathgroup5 192 | LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' 193 | (Font) U/euf/m/n --> U/euf/b/n on input line 106. 194 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/amssymb.sty 195 | Package: amssymb 2013/01/14 v3.01 AMS font symbols 196 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amscls/amsthm.sty 197 | Package: amsthm 2017/10/31 v2.20.4 198 | \thm@style=\toks21 199 | \thm@bodyfont=\toks22 200 | \thm@headfont=\toks23 201 | \thm@notefont=\toks24 202 | \thm@headpunct=\toks25 203 | \thm@preskip=\skip60 204 | \thm@postskip=\skip61 205 | \thm@headsep=\skip62 206 | \dth@everypar=\toks26 207 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/xcolor/xcolor.sty 208 | Package: xcolor 2016/05/11 v2.12 LaTeX color extensions (UK) 209 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics-cfg/color.cfg 210 | File: color.cfg 2016/01/02 v1.6 sample color configuration 211 | ) 212 | Package xcolor Info: Driver file: pdftex.def on input line 225. 213 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics-def/pdftex.def 214 | File: pdftex.def 2018/01/08 v1.0l Graphics/color driver for pdftex 215 | ) 216 | Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1348. 217 | Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1352. 218 | Package xcolor Info: Model `RGB' extended on input line 1364. 219 | Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1366. 220 | Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1367. 221 | Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1368. 222 | Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1369. 223 | Package xcolor Info: Model `Gray' substituted by `gray' on input line 1370. 224 | Package xcolor Info: Model `wave' substituted by `hsb' on input line 1371. 225 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/enumitem/enumitem.sty 226 | Package: enumitem 2019/02/04 v3.8 Customized lists 227 | \labelindent=\skip63 228 | \enit@outerparindent=\dimen120 229 | \enit@toks=\toks27 230 | \enit@inbox=\box31 231 | \enit@count@id=\count104 232 | \enitdp@description=\count105 233 | ) 234 | 235 | Class scrartcl Warning: Usage of package `fancyhdr' together 236 | (scrartcl) with a KOMA-Script class is not recommended. 237 | (scrartcl) I'd suggest to use 238 | (scrartcl) package `scrlayer' or `scrlayer-scrpage', because 239 | (scrartcl) they support KOMA-Script classes. 240 | (scrartcl) With `fancyhdr' several features of class `scrartcl' 241 | (scrartcl) like options `headsepline', `footsepline' or command 242 | (scrartcl) `\MakeMarkcase' and the commands `\setkomafont' and 243 | (scrartcl) `\addtokomafont' for the page style elements need 244 | (scrartcl) explicite user intervention to work. 245 | (scrartcl) Nevertheless, using requested 246 | (scrartcl) package `fancyhdr' on input line 9. 247 | 248 | (/usr/local/texlive/2019/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty 249 | Package: fancyhdr 2019/01/31 v3.10 Extensive control of page headers and footers 250 | \f@nch@headwidth=\skip64 251 | \f@nch@O@elh=\skip65 252 | \f@nch@O@erh=\skip66 253 | \f@nch@O@olh=\skip67 254 | \f@nch@O@orh=\skip68 255 | \f@nch@O@elf=\skip69 256 | \f@nch@O@erf=\skip70 257 | \f@nch@O@olf=\skip71 258 | \f@nch@O@orf=\skip72 259 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/float/float.sty 260 | Package: float 2001/11/08 v1.3d Float enhancements (AL) 261 | \c@float@type=\count106 262 | \float@exts=\toks28 263 | \float@box=\box32 264 | \@float@everytoks=\toks29 265 | \@floatcapt=\box33 266 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/inputenc.sty 267 | Package: inputenc 2018/08/11 v1.3c Input encoding file 268 | \inpenc@prehook=\toks30 269 | \inpenc@posthook=\toks31 270 | ) 271 | \c@theorem=\count107 272 | \c@corollary=\count108 273 | \c@definition=\count109 274 | \c@prop=\count110 275 | \c@ex=\count111 276 | (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/hyperref.sty 277 | Package: hyperref 2018/11/30 v6.88e Hypertext links for LaTeX 278 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty 279 | Package: hobsub-hyperref 2016/05/16 v1.14 Bundle oberdiek, subset hyperref (HO) 280 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty 281 | Package: hobsub-generic 2016/05/16 v1.14 Bundle oberdiek, subset generic (HO) 282 | Package: hobsub 2016/05/16 v1.14 Construct package bundles (HO) 283 | Package: infwarerr 2016/05/16 v1.4 Providing info/warning/error messages (HO) 284 | Package: ltxcmds 2016/05/16 v1.23 LaTeX kernel commands for general use (HO) 285 | Package: ifluatex 2016/05/16 v1.4 Provides the ifluatex switch (HO) 286 | Package ifluatex Info: LuaTeX not detected. 287 | Package hobsub Info: Skipping package `ifvtex' (already loaded). 288 | Package: intcalc 2016/05/16 v1.2 Expandable calculations with integers (HO) 289 | Package hobsub Info: Skipping package `ifpdf' (already loaded). 290 | Package: etexcmds 2016/05/16 v1.6 Avoid name clashes with e-TeX commands (HO) 291 | Package: kvsetkeys 2016/05/16 v1.17 Key value parser (HO) 292 | Package: kvdefinekeys 2016/05/16 v1.4 Define keys (HO) 293 | Package: pdftexcmds 2018/09/10 v0.29 Utility functions of pdfTeX for LuaTeX (HO) 294 | Package pdftexcmds Info: LuaTeX not detected. 295 | Package pdftexcmds Info: \pdf@primitive is available. 296 | Package pdftexcmds Info: \pdf@ifprimitive is available. 297 | Package pdftexcmds Info: \pdfdraftmode found. 298 | Package: pdfescape 2016/05/16 v1.14 Implements pdfTeX's escape features (HO) 299 | Package: bigintcalc 2016/05/16 v1.4 Expandable calculations on big integers (HO) 300 | Package: bitset 2016/05/16 v1.2 Handle bit-vector datatype (HO) 301 | Package: uniquecounter 2016/05/16 v1.3 Provide unlimited unique counter (HO) 302 | ) 303 | Package hobsub Info: Skipping package `hobsub' (already loaded). 304 | Package: letltxmacro 2016/05/16 v1.5 Let assignment for LaTeX macros (HO) 305 | Package: hopatch 2016/05/16 v1.3 Wrapper for package hooks (HO) 306 | Package: xcolor-patch 2016/05/16 xcolor patch 307 | Package: atveryend 2016/05/16 v1.9 Hooks at the very end of document (HO) 308 | Package atveryend Info: \enddocument detected (standard20110627). 309 | Package: atbegshi 2016/06/09 v1.18 At begin shipout hook (HO) 310 | Package: refcount 2016/05/16 v3.5 Data extraction from label references (HO) 311 | Package: hycolor 2016/05/16 v1.8 Color options for hyperref/bookmark (HO) 312 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/auxhook.sty 313 | Package: auxhook 2016/05/16 v1.4 Hooks for auxiliary files (HO) 314 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/kvoptions.sty 315 | Package: kvoptions 2016/05/16 v3.12 Key value format for package options (HO) 316 | ) 317 | \@linkdim=\dimen121 318 | \Hy@linkcounter=\count112 319 | \Hy@pagecounter=\count113 320 | (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/pd1enc.def 321 | File: pd1enc.def 2018/11/30 v6.88e Hyperref: PDFDocEncoding definition (HO) 322 | Now handling font encoding PD1 ... 323 | ... no UTF-8 mapping file for font encoding PD1 324 | ) 325 | \Hy@SavedSpaceFactor=\count114 326 | (/usr/local/texlive/2019/texmf-dist/tex/latex/latexconfig/hyperref.cfg 327 | File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive 328 | ) 329 | Package hyperref Info: Hyper figures OFF on input line 4519. 330 | Package hyperref Info: Link nesting OFF on input line 4524. 331 | Package hyperref Info: Hyper index ON on input line 4527. 332 | Package hyperref Info: Plain pages OFF on input line 4534. 333 | Package hyperref Info: Backreferencing OFF on input line 4539. 334 | Package hyperref Info: Implicit mode ON; LaTeX internals redefined. 335 | Package hyperref Info: Bookmarks ON on input line 4772. 336 | \c@Hy@tempcnt=\count115 337 | (/usr/local/texlive/2019/texmf-dist/tex/latex/url/url.sty 338 | \Urlmuskip=\muskip11 339 | Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc. 340 | ) 341 | LaTeX Info: Redefining \url on input line 5125. 342 | \XeTeXLinkMargin=\dimen122 343 | \Fld@menulength=\count116 344 | \Field@Width=\dimen123 345 | \Fld@charsize=\dimen124 346 | Package hyperref Info: Hyper figures OFF on input line 6380. 347 | Package hyperref Info: Link nesting OFF on input line 6385. 348 | Package hyperref Info: Hyper index ON on input line 6388. 349 | Package hyperref Info: backreferencing OFF on input line 6395. 350 | Package hyperref Info: Link coloring OFF on input line 6400. 351 | Package hyperref Info: Link coloring with OCG OFF on input line 6405. 352 | Package hyperref Info: PDF/A mode OFF on input line 6410. 353 | LaTeX Info: Redefining \ref on input line 6450. 354 | LaTeX Info: Redefining \pageref on input line 6454. 355 | \Hy@abspage=\count117 356 | \c@Item=\count118 357 | \c@Hfootnote=\count119 358 | ) 359 | Package hyperref Info: Driver (autodetected): hpdftex. 360 | (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/hpdftex.def 361 | File: hpdftex.def 2018/11/30 v6.88e Hyperref driver for pdfTeX 362 | \Fld@listcount=\count120 363 | \c@bookmark@seq@number=\count121 364 | (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty 365 | Package: rerunfilecheck 2016/05/16 v1.8 Rerun checks for auxiliary files (HO) 366 | Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 282. 367 | ) 368 | \Hy@SectionHShift=\skip73 369 | ) 370 | Package hyperref Info: Option `colorlinks' set `true' on input line 30. 371 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m357.aux) 372 | \openout1 = `m357.aux'. 373 | 374 | LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 63. 375 | LaTeX Font Info: ... okay on input line 63. 376 | LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 63. 377 | LaTeX Font Info: ... okay on input line 63. 378 | LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 63. 379 | LaTeX Font Info: ... okay on input line 63. 380 | LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 63. 381 | LaTeX Font Info: ... okay on input line 63. 382 | LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 63. 383 | LaTeX Font Info: ... okay on input line 63. 384 | LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 63. 385 | LaTeX Font Info: ... okay on input line 63. 386 | LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 63. 387 | LaTeX Font Info: ... okay on input line 63. 388 | 389 | *geometry* driver: auto-detecting 390 | *geometry* detected driver: pdftex 391 | *geometry* verbose mode - [ preamble ] result: 392 | * driver: pdftex 393 | * paper: 394 | * layout: 395 | * layoutoffset:(h,v)=(0.0pt,0.0pt) 396 | * modes: 397 | * h-part:(L,W,R)=(62.59596pt, 472.31601pt, 62.59596pt) 398 | * v-part:(T,H,B)=(62.59596pt, 719.85501pt, 62.59596pt) 399 | * \paperwidth=597.50793pt 400 | * \paperheight=845.04694pt 401 | * \textwidth=472.31601pt 402 | * \textheight=719.85501pt 403 | * \oddsidemargin=-9.67403pt 404 | * \evensidemargin=-9.67403pt 405 | * \topmargin=-47.07404pt 406 | * \headheight=17.0pt 407 | * \headsep=20.40001pt 408 | * \topskip=11.0pt 409 | * \footskip=47.6pt 410 | * \marginparwidth=59.7508pt 411 | * \marginparsep=12.8401pt 412 | * \columnsep=10.0pt 413 | * \skip\footins=10.0pt plus 4.0pt minus 2.0pt 414 | * \hoffset=0.0pt 415 | * \voffset=0.0pt 416 | * \mag=1000 417 | * \@twocolumnfalse 418 | * \@twosidefalse 419 | * \@mparswitchfalse 420 | * \@reversemarginfalse 421 | * (1in=72.27pt=25.4mm, 1cm=28.453pt) 422 | 423 | (/usr/local/texlive/2019/texmf-dist/tex/context/base/mkii/supp-pdf.mkii 424 | [Loading MPS to PDF converter (version 2006.09.02).] 425 | \scratchcounter=\count122 426 | \scratchdimen=\dimen125 427 | \scratchbox=\box34 428 | \nofMPsegments=\count123 429 | \nofMParguments=\count124 430 | \everyMPshowfont=\toks32 431 | \MPscratchCnt=\count125 432 | \MPscratchDim=\dimen126 433 | \MPnumerator=\count126 434 | \makeMPintoPDFobject=\count127 435 | \everyMPtoPDFconversion=\toks33 436 | ) 437 | \AtBeginShipoutBox=\box35 438 | Package hyperref Info: Link coloring ON on input line 63. 439 | (/usr/local/texlive/2019/texmf-dist/tex/latex/hyperref/nameref.sty 440 | Package: nameref 2016/05/21 v2.44 Cross-referencing by name of section 441 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/gettitlestring.sty 442 | Package: gettitlestring 2016/05/16 v1.5 Cleanup title references (HO) 443 | ) 444 | \c@section@level=\count128 445 | ) 446 | LaTeX Info: Redefining \ref on input line 63. 447 | LaTeX Info: Redefining \pageref on input line 63. 448 | LaTeX Info: Redefining \nameref on input line 63. 449 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m357.out) (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m357.out) 450 | \@outlinefile=\write3 451 | \openout3 = `m357.out'. 452 | 453 | Class scrartcl Info: loading recommended package `bookmark'. 454 | (scrartcl) Using `bookmark' together with `hyperref' is recommended, 455 | (scrartcl) because of handling of possible bookmark level gaps. 456 | (scrartcl) You can avoid loading `bookmark' with KOMA-Script option 457 | (scrartcl) `bookmarkpackage=false' before \begin{document} and 458 | (scrartcl) you can avoid this message with `\usepackage{bookmark}' 459 | (scrartcl) before \begin{document} on input line 63. 460 | (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/bookmark.sty 461 | Package: bookmark 2016/05/17 v1.26 PDF bookmarks (HO) 462 | (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/bkm-pdftex.def 463 | File: bkm-pdftex.def 2016/05/17 v1.26 bookmark driver for pdfTeX (HO) 464 | Package auxhook Info: \AddLineBeginMainAux comes a little late, 465 | (auxhook) because the main .aux file is already opened on input line 164. 466 | \BKM@id=\count129 467 | )) 468 | LaTeX Font Info: Try loading font information for U+msa on input line 66. 469 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/umsa.fd 470 | File: umsa.fd 2013/01/14 v3.01 AMS symbols A 471 | ) 472 | LaTeX Font Info: Try loading font information for U+msb on input line 66. 473 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsfonts/umsb.fd 474 | File: umsb.fd 2013/01/14 v3.01 AMS symbols B 475 | ) 476 | 477 | LaTeX Font Warning: Font shape `OT1/cmr/bx/sc' undefined 478 | (Font) using `OT1/cmr/bx/n' instead on input line 66. 479 | 480 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m357.toc) 481 | \tf@toc=\write4 482 | \openout4 = `m357.toc'. 483 | 484 | [1 485 | 486 | 487 | {/usr/local/texlive/2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] 488 | Overfull \hbox (4.87898pt too wide) in paragraph at lines 137--139 489 | \OT1/cmr/m/n/10.95 the ran-dom vari-able $\OML/cmm/m/it/10.95 T\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 X[]; :::; X[]\OT1/cmr/m/n/10.95 )$ is called a $[]$. The dis-tri-bu-tion of the statis-tic, $\OML/cmm/m/it/10.95 T\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 X[]; :::; X[]\OT1/cmr/m/n/10.95 )$ 490 | [] 491 | 492 | [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] 493 | Overfull \hbox (2.7696pt too wide) in paragraph at lines 724--726 494 | \OT1/cmr/m/n/10.95 This is not ex-actly the CMT; this ex-am-ple pro-vides the mo-ti-va-tion for de-vel-op-ing the $[]$. 495 | [] 496 | 497 | [14] [15] [16] [17] 498 | LaTeX Font Info: Try loading font information for OMS+cmr on input line 954. 499 | (/usr/local/texlive/2019/texmf-dist/tex/latex/base/omscmr.fd 500 | File: omscmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions 501 | ) 502 | LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10.95> not available 503 | (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 954. 504 | [18] [19] 505 | Overfull \hbox (12.02504pt too wide) in paragraph at lines 1072--1073 506 | []\OT1/cmr/m/n/10.95 If $\OML/cmm/m/it/10.95 `$ \OT1/cmr/m/n/10.95 is dif-fer-en-tiable, we can look for the max-i-mum by solv-ing the so-called $[]$: 507 | [] 508 | 509 | [20] [21] [22] [23] [24] [25] [26] [27] [28] 510 | Overfull \hbox (53.11208pt too wide) detected at line 1512 511 | [] 512 | [] 513 | 514 | [29] [30] [31] [32] [33] [34] [35] [36] [37] 515 | Overfull \hbox (8.4436pt too wide) in paragraph at lines 1940--1941 516 | [][]\OT1/cmr/bx/n/10.95 Theorem 23 \OT1/cmr/m/n/10.95 (Ney-men--Fisher Cri-te-rion)\OT1/cmr/bx/n/10.95 . []\OT1/cmr/m/n/10.95 Let $\OML/cmm/m/it/10.95 f\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 x[]; :::; x[]\OT1/cmr/m/n/10.95 ; \OML/cmm/m/it/10.95 ^^R\OT1/cmr/m/n/10.95 )$ de-note the joint PMF/PDF of $(\OML/cmm/m/it/10.95 x[]; :::x[]\OT1/cmr/m/n/10.95 )$, 517 | [] 518 | 519 | 520 | Underfull \hbox (badness 10000) in paragraph at lines 1959--1964 521 | 522 | [] 523 | 524 | [38] [39] 525 | Overfull \hbox (13.03648pt too wide) in paragraph at lines 2066--2067 526 | [][]\OT1/cmr/bx/n/10.95 Theorem 24 \OT1/cmr/m/n/10.95 (Lehman-n-Schafte Cri-teriea)\OT1/cmr/bx/n/10.95 . []\OT1/cmr/m/n/10.95 Sup-pose that $(\OML/cmm/m/it/10.95 X[]; :::; X[]\OT1/cmr/m/n/10.95 )$ has a PDF/PMF $\OML/cmm/m/it/10.95 f\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 x[]; :::; x[]\OT1/cmr/m/n/10.95 ; \OML/cmm/m/it/10.95 ^^R\OT1/cmr/m/n/10.95 )$, 527 | [] 528 | 529 | [40] [41] 530 | Overfull \hbox (8.62418pt too wide) in paragraph at lines 2138--2140 531 | \OT1/cmr/m/n/10.95 does not de-pend on $\OML/cmm/m/it/10.95 ^^R$ \OT1/cmr/m/n/10.95 if $[][] \OML/cmm/m/it/10.95 x[] \OT1/cmr/m/n/10.95 = [][] \OML/cmm/m/it/10.95 y[]$ \OT1/cmr/m/n/10.95 and $[][] \OML/cmm/m/it/10.95 x[] \OT1/cmr/m/n/10.95 = [][] \OML/cmm/m/it/10.95 y[]$\OT1/cmr/m/n/10.95 . So, $([][](\OML/cmm/m/it/10.95 x[]\OT1/cmr/m/n/10.95 )$, 532 | [] 533 | 534 | 535 | Overfull \hbox (20.31284pt too wide) in paragraph at lines 2169--2170 536 | []\OT1/cmr/m/n/10.95 Var$[][\OML/cmm/m/it/10.95 W\OT1/cmr/m/n/10.95 ] = [][][\U/msb/m/n/10.95 E[] []\OT1/cmr/m/n/10.95 ] + \U/msb/m/n/10.95 E[] [] \OT1/cmr/m/n/10.95 = [][][\OML/cmm/m/it/10.95 W[]\OT1/cmr/m/n/10.95 ] + \U/msb/m/n/10.95 E[] []$\OT1/cmr/m/n/10.95 . Since the $\U/msb/m/n/10.95 E[] []$ 537 | [] 538 | 539 | [42] [43] [44] [45] [46] [47] [48] 540 | Package atveryend Info: Empty hook `BeforeClearDocument' on input line 2542. 541 | [49] 542 | Package atveryend Info: Empty hook `AfterLastShipout' on input line 2542. 543 | (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m357.aux) 544 | Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 2542. 545 | Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 2542. 546 | Package rerunfilecheck Info: File `m357.out' has not changed. 547 | (rerunfilecheck) Checksum: . 548 | 549 | 550 | LaTeX Font Warning: Some font shapes were not available, defaults substituted. 551 | 552 | Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 2542. 553 | ) 554 | (\end occurred inside a group at level 1) 555 | 556 | ### simple group (level 1) entered at line 80 ({) 557 | ### bottom level 558 | Here is how much of TeX's memory you used: 559 | 9774 strings out of 492616 560 | 152071 string characters out of 6129481 561 | 379369 words of memory out of 5000000 562 | 13291 multiletter control sequences out of 15000+600000 563 | 14904 words of font info for 57 fonts, out of 8000000 for 9000 564 | 1141 hyphenation exceptions out of 8191 565 | 41i,24n,51p,9118b,687s stack positions out of 5000i,500n,10000p,200000b,80000s 566 | 567 | Output written on /Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/m357.pdf (49 pages, 433441 bytes). 568 | PDF statistics: 569 | 719 PDF objects out of 1000 (max. 8388607) 570 | 643 compressed objects within 7 object streams 571 | 311 named destinations out of 1000 (max. 500000) 572 | 201 words of extra memory for PDF output out of 10000 (max. 10000000) 573 | 574 | -------------------------------------------------------------------------------- /.texpadtmp/m357.out: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/m357.out -------------------------------------------------------------------------------- /.texpadtmp/m357.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/m357.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/m357.toc: -------------------------------------------------------------------------------- 1 | \contentsline {section}{\numberline {1}Introduction}{1}{section.1}% 2 | \contentsline {section}{\numberline {2}Properties of Random Samples}{2}{section.2}% 3 | \contentsline {subsection}{\numberline {2.1}Sampling from the Normal Population}{6}{subsection.2.1}% 4 | \contentsline {subsection}{\numberline {2.2}Standardisation}{9}{subsection.2.2}% 5 | \contentsline {subsection}{\numberline {2.3}F-Test Basis}{10}{subsection.2.3}% 6 | \contentsline {subsection}{\numberline {2.4}Limiting Sample Distributions (Asymptotics)}{11}{subsection.2.4}% 7 | \contentsline {subsubsection}{\numberline {2.4.1}Question 1}{12}{subsubsection.2.4.1}% 8 | \contentsline {subsubsection}{\numberline {2.4.2}Question 2}{13}{subsubsection.2.4.2}% 9 | \contentsline {subsection}{\numberline {2.5}Order Statistics}{15}{subsection.2.5}% 10 | \contentsline {section}{\numberline {3}Point Estimation}{16}{section.3}% 11 | \contentsline {subsection}{\numberline {3.1}Ways We Can Construct Estimators}{16}{subsection.3.1}% 12 | \contentsline {subsubsection}{\numberline {3.1.1}Method of moments}{16}{subsubsection.3.1.1}% 13 | \contentsline {subsubsection}{\numberline {3.1.2}Method of Maximum Likelihood}{19}{subsubsection.3.1.2}% 14 | \contentsline {subsubsection}{\numberline {3.1.3}Invariance of the MLE Theorem}{22}{subsubsection.3.1.3}% 15 | \contentsline {subsubsection}{\numberline {3.1.4}Bayesian Method}{24}{subsubsection.3.1.4}% 16 | \contentsline {subsection}{\numberline {3.2}Method of Evaluating Estimators}{25}{subsection.3.2}% 17 | \contentsline {subsection}{\numberline {3.3}Best Unbiased Estimators}{28}{subsection.3.3}% 18 | \contentsline {subsubsection}{\numberline {3.3.1}Geometric Interpretation}{30}{subsubsection.3.3.1}% 19 | \contentsline {section}{\numberline {4}Sufficiency and Completeness}{37}{section.4}% 20 | \contentsline {subsection}{\numberline {4.1}Proving the Sufficiency of Statistics}{38}{subsection.4.1}% 21 | \contentsline {subsection}{\numberline {4.2}Sufficient Statistics}{40}{subsection.4.2}% 22 | \contentsline {subsection}{\numberline {4.3}Applications of Sufficiency in Point Estimation}{42}{subsection.4.3}% 23 | \contentsline {section}{\numberline {5}Hypothesis Testing}{45}{section.5}% 24 | \contentsline {subsection}{\numberline {5.1}Basic Terminology}{45}{subsection.5.1}% 25 | \contentsline {subsection}{\numberline {5.2}Likelihood Ratio Tests}{48}{subsection.5.2}% 26 | -------------------------------------------------------------------------------- /.texpadtmp/m454.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \babel@aux{nil}{} 3 | \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}\protected@file@percent } 4 | \@writefile{loe}{\contentsline {definition}{\numberline {1}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Riemann Integral}}{1}\protected@file@percent } 5 | \@writefile{loe}{\contentsline {theorem}{\numberline {1}\leavevmode {\color {blue}Theorem}}{1}\protected@file@percent } 6 | \@writefile{loe}{\contentsline {definition}{\numberline {2}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Length}}{1}\protected@file@percent } 7 | \@writefile{loe}{\contentsline {definition}{\numberline {3}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Outer Measure}}{1}\protected@file@percent } 8 | \@writefile{loe}{\contentsline {prop}{\numberline {1}\leavevmode {\color {red}Proposition}}{1}\protected@file@percent } 9 | \@writefile{loe}{\contentsline {prop}{\numberline {2}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Monotonicity of outer measure}}{1}\protected@file@percent } 10 | \@writefile{loe}{\contentsline {prop}{\numberline {3}\leavevmode {\color {red}Proposition}}{1}\protected@file@percent } 11 | \@writefile{loe}{\contentsline {prop}{\numberline {4}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Translation invariance of outer measure}}{1}\protected@file@percent } 12 | \@writefile{loe}{\contentsline {prop}{\numberline {5}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Countable Subadditivity of outer measure}}{1}\protected@file@percent } 13 | \@writefile{loe}{\contentsline {definition}{\numberline {4}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Lebesgue Measure}}{1}\protected@file@percent } 14 | \@writefile{loe}{\contentsline {prop}{\numberline {6}\leavevmode {\color {red}Proposition}}{1}\protected@file@percent } 15 | \@writefile{loe}{\contentsline {prop}{\numberline {7}\leavevmode {\color {red}Proposition}}{2}\protected@file@percent } 16 | \@writefile{loe}{\contentsline {theorem}{\numberline {2}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Excision Property}}{2}\protected@file@percent } 17 | \@writefile{loe}{\contentsline {prop}{\numberline {8}\leavevmode {\color {red}Proposition}}{2}\protected@file@percent } 18 | \@writefile{loe}{\contentsline {prop}{\numberline {9}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Continuity of Lebesgue Measure}}{2}\protected@file@percent } 19 | \@writefile{loe}{\contentsline {prop}{\numberline {10}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Translation Invariance of Measurable Sets}}{2}\protected@file@percent } 20 | \@writefile{loe}{\contentsline {prop}{\numberline {11}\leavevmode {\color {red}Proposition}}{2}\protected@file@percent } 21 | \@writefile{loe}{\contentsline {theorem}{\numberline {3}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Characterisation of Measurable Sets}}{2}\protected@file@percent } 22 | \@writefile{loe}{\contentsline {theorem}{\numberline {4}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Vitali}}{2}\protected@file@percent } 23 | \@writefile{loe}{\contentsline {definition}{\numberline {5}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Cantor Set}}{2}\protected@file@percent } 24 | \@writefile{loe}{\contentsline {theorem}{\numberline {5}\leavevmode {\color {blue}Theorem}}{2}\protected@file@percent } 25 | \@writefile{loe}{\contentsline {definition}{\numberline {6}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {$\sigma $-algebra}}{3}\protected@file@percent } 26 | \@writefile{loe}{\contentsline {prop}{\numberline {12}\leavevmode {\color {red}Proposition}}{3}\protected@file@percent } 27 | \@writefile{loe}{\contentsline {definition}{\numberline {7}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Borel Sets}}{3}\protected@file@percent } 28 | \@writefile{loe}{\contentsline {prop}{\numberline {13}\leavevmode {\color {red}Proposition}}{3}\protected@file@percent } 29 | \@writefile{loe}{\contentsline {definition}{\numberline {8}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Cantor Lebesgue Function}}{3}\protected@file@percent } 30 | \@writefile{loe}{\contentsline {prop}{\numberline {14}\leavevmode {\color {red}Proposition}}{3}\protected@file@percent } 31 | \@writefile{toc}{\contentsline {section}{\numberline {2}Lebesgue Measurable Functions}{3}\protected@file@percent } 32 | \@writefile{loe}{\contentsline {prop}{\numberline {15}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Lebesgue Measurable Function}}{3}\protected@file@percent } 33 | \@writefile{loe}{\contentsline {prop}{\numberline {16}\leavevmode {\color {red}Proposition}}{3}\protected@file@percent } 34 | \@writefile{loe}{\contentsline {prop}{\numberline {17}\leavevmode {\color {red}Proposition}}{3}\protected@file@percent } 35 | \@writefile{loe}{\contentsline {definition}{\numberline {9}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Almost Everywhere}}{3}\protected@file@percent } 36 | \@writefile{loe}{\contentsline {prop}{\numberline {18}\leavevmode {\color {red}Proposition}}{3}\protected@file@percent } 37 | \@writefile{loe}{\contentsline {prop}{\numberline {19}\leavevmode {\color {red}Proposition}}{4}\protected@file@percent } 38 | \@writefile{loe}{\contentsline {definition}{\numberline {10}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Characteristic Function}}{4}\protected@file@percent } 39 | \@writefile{loe}{\contentsline {definition}{\numberline {11}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Simple Functions}}{4}\protected@file@percent } 40 | \@writefile{loe}{\contentsline {prop}{\numberline {20}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Properties of Measurable Functions}}{4}\protected@file@percent } 41 | \@writefile{loe}{\contentsline {definition}{\numberline {12}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Uniform and pointwise convergence}}{4}\protected@file@percent } 42 | \@writefile{loe}{\contentsline {prop}{\numberline {21}\leavevmode {\color {red}Proposition}}{4}\protected@file@percent } 43 | \@writefile{loe}{\contentsline {prop}{\numberline {22}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Simple Approximation Lemma}}{4}\protected@file@percent } 44 | \@writefile{loe}{\contentsline {theorem}{\numberline {6}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Simple Approximation Theorem}}{4}\protected@file@percent } 45 | \@writefile{loe}{\contentsline {theorem}{\numberline {7}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Egoroff's Theorem}}{5}\protected@file@percent } 46 | \@writefile{loe}{\contentsline {theorem}{\numberline {8}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Lusin's Theorem}}{5}\protected@file@percent } 47 | \@writefile{toc}{\contentsline {section}{\numberline {3}The Lebesgue Integral}{5}\protected@file@percent } 48 | \@writefile{loe}{\contentsline {definition}{\numberline {13}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Integral -- Case of Simple Functions on a Set of Finite Measure}}{5}\protected@file@percent } 49 | \@writefile{loe}{\contentsline {definition}{\numberline {14}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Integral -- Case of Measurable, Bounded Functions on a Set of Finite Measure}}{5}\protected@file@percent } 50 | \@writefile{loe}{\contentsline {theorem}{\numberline {9}\leavevmode {\color {blue}Theorem}}{5}\protected@file@percent } 51 | \@writefile{loe}{\contentsline {theorem}{\numberline {10}\leavevmode {\color {blue}Theorem}}{5}\protected@file@percent } 52 | \@writefile{loe}{\contentsline {prop}{\numberline {23}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Properties of the Integral}}{5}\protected@file@percent } 53 | \@writefile{loe}{\contentsline {lemma}{\numberline {11}Lemma\thmtformatoptarg {Independence of Representation}}{6}\protected@file@percent } 54 | \@writefile{loe}{\contentsline {theorem}{\numberline {12}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Bounded Convergence Theorem}}{6}\protected@file@percent } 55 | \@writefile{loe}{\contentsline {definition}{\numberline {15}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Integral in the case of a Non-Negative, Measurable Function on a Set of Possibly Infinite Measure}}{6}\protected@file@percent } 56 | \@writefile{loe}{\contentsline {prop}{\numberline {24}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Properties of the Integral}}{6}\protected@file@percent } 57 | \@writefile{loe}{\contentsline {theorem}{\numberline {13}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Chebyshev's Inequality}}{6}\protected@file@percent } 58 | \@writefile{loe}{\contentsline {corollary}{\numberline {1}Corollary}{7}\protected@file@percent } 59 | \@writefile{loe}{\contentsline {corollary}{\numberline {2}Corollary}{7}\protected@file@percent } 60 | \@writefile{loe}{\contentsline {lemma}{\numberline {14}Lemma\thmtformatoptarg {Fatou's Lemma}}{7}\protected@file@percent } 61 | \@writefile{loe}{\contentsline {theorem}{\numberline {15}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Monotone Convergence Theorem}}{7}\protected@file@percent } 62 | \@writefile{loe}{\contentsline {corollary}{\numberline {3}Corollary}{7}\protected@file@percent } 63 | \@writefile{loe}{\contentsline {definition}{\numberline {16}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Integral in the case of Possibly Sign-Changing Functions}}{7}\protected@file@percent } 64 | \@writefile{loe}{\contentsline {prop}{\numberline {25}\leavevmode {\color {red}Proposition}}{7}\protected@file@percent } 65 | \@writefile{loe}{\contentsline {prop}{\numberline {26}\leavevmode {\color {red}Proposition}}{7}\protected@file@percent } 66 | \@writefile{loe}{\contentsline {theorem}{\numberline {16}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Dominated Convergence Theorem}}{7}\protected@file@percent } 67 | \@writefile{loe}{\contentsline {corollary}{\numberline {4}Corollary\thmtformatoptarg {Countable Additivity of Lebesgue Integration}}{8}\protected@file@percent } 68 | \@writefile{loe}{\contentsline {corollary}{\numberline {5}Corollary\thmtformatoptarg {Continuity of Lebesgue Integration}}{8}\protected@file@percent } 69 | \@writefile{toc}{\contentsline {section}{\numberline {4}Integration and Differentiation}{8}\protected@file@percent } 70 | \@writefile{loe}{\contentsline {definition}{\numberline {17}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Differentiable}}{8}\protected@file@percent } 71 | \@writefile{loe}{\contentsline {theorem}{\numberline {17}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Monster Theorem}}{8}\protected@file@percent } 72 | \@writefile{loe}{\contentsline {definition}{\numberline {18}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Bounded Variation}}{8}\protected@file@percent } 73 | \@writefile{loe}{\contentsline {prop}{\numberline {27}\leavevmode {\color {red}Proposition}}{8}\protected@file@percent } 74 | \@writefile{loe}{\contentsline {theorem}{\numberline {18}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Characterisation of Functions of Bounded Variation}}{8}\protected@file@percent } 75 | \@writefile{loe}{\contentsline {definition}{\numberline {19}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Absolutely Continuous}}{8}\protected@file@percent } 76 | \@writefile{loe}{\contentsline {theorem}{\numberline {19}\leavevmode {\color {blue}Theorem}}{8}\protected@file@percent } 77 | \@writefile{loe}{\contentsline {theorem}{\numberline {20}\leavevmode {\color {blue}Theorem}}{8}\protected@file@percent } 78 | \@writefile{loe}{\contentsline {lemma}{\numberline {21}Lemma}{9}\protected@file@percent } 79 | \@writefile{loe}{\contentsline {corollary}{\numberline {6}Corollary}{9}\protected@file@percent } 80 | \@writefile{loe}{\contentsline {corollary}{\numberline {7}Corollary}{9}\protected@file@percent } 81 | \@writefile{toc}{\contentsline {section}{\numberline {5}Lebesgue Measure and Integration in $\mathbb {R}^d$, $d \geq 2$}{9}\protected@file@percent } 82 | \@writefile{loe}{\contentsline {definition}{\numberline {20}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Outer Measure}}{9}\protected@file@percent } 83 | \@writefile{loe}{\contentsline {prop}{\numberline {28}\leavevmode {\color {red}Proposition}}{9}\protected@file@percent } 84 | \@writefile{loe}{\contentsline {theorem}{\numberline {22}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Fubini's Theorem in $\mathbb {R}^d$}}{9}\protected@file@percent } 85 | \newlabel{tocindent-1}{0pt} 86 | \newlabel{tocindent0}{0pt} 87 | \newlabel{tocindent1}{0pt} 88 | \newlabel{tocindent2}{0pt} 89 | \newlabel{tocindent3}{0pt} 90 | \@writefile{loe}{\contentsline {theorem}{\numberline {23}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Tonelli's Theorem; Fubini's Theorem for non-negative measurable functions}}{10}\protected@file@percent } 91 | \@writefile{loe}{\contentsline {corollary}{\numberline {8}Corollary}{10}\protected@file@percent } 92 | \@writefile{loe}{\contentsline {corollary}{\numberline {9}Corollary\thmtformatoptarg {General Version of Tonelli's Theorem}}{10}\protected@file@percent } 93 | \@writefile{loe}{\contentsline {corollary}{\numberline {10}Corollary\thmtformatoptarg {General Version of Fubini's Theorem}}{10}\protected@file@percent } 94 | \@writefile{loe}{\contentsline {theorem}{\numberline {24}\leavevmode {\color {blue}Theorem}}{10}\protected@file@percent } 95 | \@writefile{loe}{\contentsline {corollary}{\numberline {11}Corollary}{10}\protected@file@percent } 96 | \@writefile{loe}{\contentsline {theorem}{\numberline {25}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Formula for the Integral of a non-negative measurable function in terms of a region in $\mathbb {R}^d$}}{10}\protected@file@percent } 97 | -------------------------------------------------------------------------------- /.texpadtmp/m454.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/m454.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/m458.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \providecommand\hyper@newdestlabel[2]{} 3 | \providecommand*\new@tpo@label[2]{} 4 | \providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} 5 | \HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined 6 | \global\let\oldcontentsline\contentsline 7 | \gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} 8 | \global\let\oldnewlabel\newlabel 9 | \gdef\newlabel#1#2{\newlabelxx{#1}#2} 10 | \gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} 11 | \AtEndDocument{\ifx\hyper@anchor\@undefined 12 | \let\contentsline\oldcontentsline 13 | \let\newlabel\oldnewlabel 14 | \fi} 15 | \fi} 16 | \global\let\hyper@last\relax 17 | \gdef\HyperFirstAtBeginDocument#1{#1} 18 | \providecommand\HyField@AuxAddToFields[1]{} 19 | \providecommand\HyField@AuxAddToCoFields[2]{} 20 | \providecommand\BKM@entry[2]{} 21 | \BKM@entry{id=1,dest={73656374696F6E2E31},srcline={85}}{496E74726F64756374696F6E} 22 | \BKM@entry{id=2,dest={73756273656374696F6E2E312E31},srcline={87}}{4475616C20537061636573} 23 | \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}\protected@file@percent } 24 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Dual Spaces}{2}{subsection.1.1}\protected@file@percent } 25 | \BKM@entry{id=3,dest={73756273656374696F6E2E312E32},srcline={170}}{4E6F74696F6E732066726F6D204D756C74697661726961626C652043616C} 26 | \BKM@entry{id=4,dest={73756273756273656374696F6E2E312E322E31},srcline={219}}{446976657267656E6365} 27 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Notions from Multivariable Cal}{3}{subsection.1.2}\protected@file@percent } 28 | \BKM@entry{id=5,dest={73756273756273656374696F6E2E312E322E32},srcline={235}}{477265656E2773205468656F72656D} 29 | \BKM@entry{id=6,dest={73656374696F6E2E32},srcline={264}}{4D616E69666F6C647320696E205233} 30 | \BKM@entry{id=7,dest={73756273656374696F6E2E322E31},srcline={266}}{446566696E6974696F6E73} 31 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {1.2.1}Divergence}{4}{subsubsection.1.2.1}\protected@file@percent } 32 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {1.2.2}Green's Theorem}{4}{subsubsection.1.2.2}\protected@file@percent } 33 | \@writefile{toc}{\contentsline {section}{\numberline {2}Manifolds in $\mathbb {R}^3$}{4}{section.2}\protected@file@percent } 34 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Definitions}{4}{subsection.2.1}\protected@file@percent } 35 | \BKM@entry{id=8,dest={73756273656374696F6E2E322E32},srcline={308}}{536D6F6F7468204D6170732066726F6D204D6D204E6E} 36 | \BKM@entry{id=9,dest={73756273656374696F6E2E322E33},srcline={323}}{4368616E6765206F6620436F6F7264696E61746573} 37 | \BKM@entry{id=10,dest={73756273656374696F6E2E322E34},srcline={325}}{4D756C74692D4C696E65617220416C6765627261} 38 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Smooth Maps from $M^m \rightarrow N^n$}{5}{subsection.2.2}\protected@file@percent } 39 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Change of Coordinates}{5}{subsection.2.3}\protected@file@percent } 40 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Multi-Linear Algebra}{5}{subsection.2.4}\protected@file@percent } 41 | \BKM@entry{id=11,dest={73756273656374696F6E2E322E35},srcline={391}}{446966666572656E7469616C20466F726D7320696E204D6E} 42 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Differential Forms in $M^n$}{6}{subsection.2.5}\protected@file@percent } 43 | \BKM@entry{id=12,dest={73756273656374696F6E2E322E36},srcline={635}}{4368616E6765206F66205661726961626C657320666F7220496E74656772616C7320696E20526E} 44 | \BKM@entry{id=13,dest={73756273656374696F6E2E322E37},srcline={637}}{496E746567726174696E672061206E2D466F726D206F6E204D6E205C284D205C29} 45 | \BKM@entry{id=14,dest={73756273756273656374696F6E2E322E372E31},srcline={640}}{4C696E6520496E74656772616C73} 46 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Change of Variables for Integrals in $\mathbb {R}^n$}{10}{subsection.2.6}\protected@file@percent } 47 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.7}Integrating a $n$-Form on $M^n$ ($\DOTSI \intop \ilimits@ _{M}^{} \omega $)}{10}{subsection.2.7}\protected@file@percent } 48 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.7.1}Line Integrals}{11}{subsubsection.2.7.1}\protected@file@percent } 49 | \BKM@entry{id=15,dest={73756273756273656374696F6E2E322E372E32},srcline={734}}{5375726661636520496E74656772616C73} 50 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.7.2}Surface Integrals}{12}{subsubsection.2.7.2}\protected@file@percent } 51 | \BKM@entry{id=16,dest={73756273756273656374696F6E2E322E372E33},srcline={872}}{47656E6572616C697365642053746F6B657327205468656F72656D} 52 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.7.3}Generalised Stokes' Theorem}{15}{subsubsection.2.7.3}\protected@file@percent } 53 | \newlabel{stokes}{{23}{15}{}{equation.2.23}{}} 54 | \BKM@entry{id=17,dest={73656374696F6E2E33},srcline={972}}{437572766573} 55 | \BKM@entry{id=18,dest={73756273656374696F6E2E332E31},srcline={974}}{446566696E6974696F6E73} 56 | \BKM@entry{id=19,dest={73756273756273656374696F6E2E332E312E31},srcline={1011}}{526567756C61722043757276657320616E64204172636C656E677468} 57 | \@writefile{toc}{\contentsline {section}{\numberline {3}Curves}{17}{section.3}\protected@file@percent } 58 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Definitions}{17}{subsection.3.1}\protected@file@percent } 59 | \BKM@entry{id=20,dest={73756273756273656374696F6E2E332E312E32},srcline={1030}}{54686520566563746F722050726F6475637420696E205233} 60 | \BKM@entry{id=21,dest={73756273656374696F6E2E332E32},srcline={1059}}{4672656E65742D536572726574204672616D65} 61 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.1}Regular Curves and Arclength}{18}{subsubsection.3.1.1}\protected@file@percent } 62 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.2}The Vector Product in $\mathbb {R}^3$}{18}{subsubsection.3.1.2}\protected@file@percent } 63 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Frenet-Serret Frame}{18}{subsection.3.2}\protected@file@percent } 64 | \BKM@entry{id=22,dest={73756273656374696F6E2E332E33},srcline={1131}}{476C6F62616C2050726F70657274696573206F6620437572766573} 65 | \BKM@entry{id=23,dest={73756273756273656374696F6E2E332E332E31},srcline={1133}}{5468652049736F706172616D657472696320496E657175616C697479} 66 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Global Properties of Curves}{19}{subsection.3.3}\protected@file@percent } 67 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.1}The Isoparametric Inequality}{19}{subsubsection.3.3.1}\protected@file@percent } 68 | \BKM@entry{id=24,dest={73756273756273656374696F6E2E332E332E32},srcline={1152}}{4361756368792043726F66746F6E20466F726D756C61} 69 | \BKM@entry{id=25,dest={73656374696F6E2E34},srcline={1179}}{5375726661636573} 70 | \BKM@entry{id=26,dest={73756273656374696F6E2E342E31},srcline={1181}}{446566696E6974696F6E73} 71 | \BKM@entry{id=27,dest={73756273656374696F6E2E342E32},srcline={1201}}{526567756C6172205375726661636573} 72 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.2}Cauchy Crofton Formula}{20}{subsubsection.3.3.2}\protected@file@percent } 73 | \@writefile{toc}{\contentsline {section}{\numberline {4}Surfaces}{20}{section.4}\protected@file@percent } 74 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Definitions}{20}{subsection.4.1}\protected@file@percent } 75 | \BKM@entry{id=28,dest={73756273656374696F6E2E342E33},srcline={1250}}{446966666572656E746961626C652046756E6374696F6E73206F6E205375726661636573} 76 | \BKM@entry{id=29,dest={73756273656374696F6E2E342E34},srcline={1252}}{54616E67656E7420506C616E65} 77 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Regular Surfaces}{21}{subsection.4.2}\protected@file@percent } 78 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Differentiable Functions on Surfaces}{21}{subsection.4.3}\protected@file@percent } 79 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Tangent Plane}{21}{subsection.4.4}\protected@file@percent } 80 | \BKM@entry{id=30,dest={73756273656374696F6E2E342E35},srcline={1292}}{46697273742046756E64616D656E74616C20466F726D3A2041726561} 81 | \BKM@entry{id=31,dest={73756273756273656374696F6E2E342E352E31},srcline={1304}}{4465726976696E67207468652046697273742046756E64616D656E74616C20466F726D20476976656E206120426173697320616E64206120506172616D6574657269736174696F6E} 82 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.5}First Fundamental Form: Area}{22}{subsection.4.5}\protected@file@percent } 83 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {4.5.1}Deriving the First Fundamental Form Given a Basis and a Parameterisation}{22}{subsubsection.4.5.1}\protected@file@percent } 84 | \BKM@entry{id=32,dest={73756273756273656374696F6E2E342E352E32},srcline={1325}}{4578616D706C6573206F662046697273742046756E64616D656E74616C20466F726D73} 85 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {4.5.2}Examples of First Fundamental Forms}{23}{subsubsection.4.5.2}\protected@file@percent } 86 | \BKM@entry{id=33,dest={73656374696F6E2E35},srcline={1386}}{546865204761757373204D6170} 87 | \BKM@entry{id=34,dest={73756273656374696F6E2E352E31},srcline={1389}}{54686520446566696E6974696F6E206F6620746865204761757373204D617020616E64206974732046756E64616D656E74616C2050726F70657274696573} 88 | \@writefile{toc}{\contentsline {section}{\numberline {5}The Gauss Map}{24}{section.5}\protected@file@percent } 89 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}The Definition of the Gauss Map and its Fundamental Properties}{24}{subsection.5.1}\protected@file@percent } 90 | \newlabel{curve}{{13}{26}{Meusnier}{prop.13}{}} 91 | \BKM@entry{id=35,dest={73756273656374696F6E2E352E32},srcline={1562}}{52756C656420537572666163657320616E64204D696E696D616C205375726661636573} 92 | \BKM@entry{id=36,dest={73756273756273656374696F6E2E352E322E31},srcline={1563}}{52756C6564205375726661636573} 93 | \BKM@entry{id=37,dest={73756273756273656374696F6E2E352E322E32},srcline={1579}}{4D696E696D616C2053757266616365} 94 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Ruled Surfaces and Minimal Surfaces}{27}{subsection.5.2}\protected@file@percent } 95 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.1}Ruled Surfaces}{27}{subsubsection.5.2.1}\protected@file@percent } 96 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.2}Minimal Surface}{27}{subsubsection.5.2.2}\protected@file@percent } 97 | \global\@namedef{scr@dte@section@lastmaxnumwidth}{10.84047pt} 98 | \global\@namedef{scr@dte@subsection@lastmaxnumwidth}{18.37163pt} 99 | \global\@namedef{scr@dte@subsubsection@lastmaxnumwidth}{26.8883pt} 100 | -------------------------------------------------------------------------------- /.texpadtmp/m458.out: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/m458.out -------------------------------------------------------------------------------- /.texpadtmp/m458.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/m458.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/m458.toc: -------------------------------------------------------------------------------- 1 | \contentsline {section}{\numberline {1}Introduction}{1}{section.1}% 2 | \contentsline {subsection}{\numberline {1.1}Dual Spaces}{2}{subsection.1.1}% 3 | \contentsline {subsection}{\numberline {1.2}Notions from Multivariable Cal}{3}{subsection.1.2}% 4 | \contentsline {subsubsection}{\numberline {1.2.1}Divergence}{4}{subsubsection.1.2.1}% 5 | \contentsline {subsubsection}{\numberline {1.2.2}Green's Theorem}{4}{subsubsection.1.2.2}% 6 | \contentsline {section}{\numberline {2}Manifolds in $\mathbb {R}^3$}{4}{section.2}% 7 | \contentsline {subsection}{\numberline {2.1}Definitions}{4}{subsection.2.1}% 8 | \contentsline {subsection}{\numberline {2.2}Smooth Maps from $M^m \rightarrow N^n$}{5}{subsection.2.2}% 9 | \contentsline {subsection}{\numberline {2.3}Change of Coordinates}{5}{subsection.2.3}% 10 | \contentsline {subsection}{\numberline {2.4}Multi-Linear Algebra}{5}{subsection.2.4}% 11 | \contentsline {subsection}{\numberline {2.5}Differential Forms in $M^n$}{6}{subsection.2.5}% 12 | \contentsline {subsection}{\numberline {2.6}Change of Variables for Integrals in $\mathbb {R}^n$}{10}{subsection.2.6}% 13 | \contentsline {subsection}{\numberline {2.7}Integrating a $n$-Form on $M^n$ ($\DOTSI \intop \ilimits@ _{M}^{} \omega $)}{10}{subsection.2.7}% 14 | \contentsline {subsubsection}{\numberline {2.7.1}Line Integrals}{11}{subsubsection.2.7.1}% 15 | \contentsline {subsubsection}{\numberline {2.7.2}Surface Integrals}{12}{subsubsection.2.7.2}% 16 | \contentsline {subsubsection}{\numberline {2.7.3}Generalised Stokes' Theorem}{15}{subsubsection.2.7.3}% 17 | \contentsline {section}{\numberline {3}Curves}{17}{section.3}% 18 | \contentsline {subsection}{\numberline {3.1}Definitions}{17}{subsection.3.1}% 19 | \contentsline {subsubsection}{\numberline {3.1.1}Regular Curves and Arclength}{18}{subsubsection.3.1.1}% 20 | \contentsline {subsubsection}{\numberline {3.1.2}The Vector Product in $\mathbb {R}^3$}{18}{subsubsection.3.1.2}% 21 | \contentsline {subsection}{\numberline {3.2}Frenet-Serret Frame}{18}{subsection.3.2}% 22 | \contentsline {subsection}{\numberline {3.3}Global Properties of Curves}{19}{subsection.3.3}% 23 | \contentsline {subsubsection}{\numberline {3.3.1}The Isoparametric Inequality}{19}{subsubsection.3.3.1}% 24 | \contentsline {subsubsection}{\numberline {3.3.2}Cauchy Crofton Formula}{20}{subsubsection.3.3.2}% 25 | \contentsline {section}{\numberline {4}Surfaces}{20}{section.4}% 26 | \contentsline {subsection}{\numberline {4.1}Definitions}{20}{subsection.4.1}% 27 | \contentsline {subsection}{\numberline {4.2}Regular Surfaces}{21}{subsection.4.2}% 28 | \contentsline {subsection}{\numberline {4.3}Differentiable Functions on Surfaces}{21}{subsection.4.3}% 29 | \contentsline {subsection}{\numberline {4.4}Tangent Plane}{21}{subsection.4.4}% 30 | \contentsline {subsection}{\numberline {4.5}First Fundamental Form: Area}{22}{subsection.4.5}% 31 | \contentsline {subsubsection}{\numberline {4.5.1}Deriving the First Fundamental Form Given a Basis and a Parameterisation}{22}{subsubsection.4.5.1}% 32 | \contentsline {subsubsection}{\numberline {4.5.2}Examples of First Fundamental Forms}{23}{subsubsection.4.5.2}% 33 | \contentsline {section}{\numberline {5}The Gauss Map}{24}{section.5}% 34 | \contentsline {subsection}{\numberline {5.1}The Definition of the Gauss Map and its Fundamental Properties}{24}{subsection.5.1}% 35 | \contentsline {subsection}{\numberline {5.2}Ruled Surfaces and Minimal Surfaces}{27}{subsection.5.2}% 36 | \contentsline {subsubsection}{\numberline {5.2.1}Ruled Surfaces}{27}{subsubsection.5.2.1}% 37 | \contentsline {subsubsection}{\numberline {5.2.2}Minimal Surface}{27}{subsubsection.5.2.2}% 38 | -------------------------------------------------------------------------------- /.texpadtmp/m475.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \providecommand*\new@tpo@label[2]{} 3 | \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}\protected@file@percent } 4 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Domains and Boundary Conditions}{2}\protected@file@percent } 5 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.1}What are the main boundary conditions?}{2}\protected@file@percent } 6 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Classification of PDEs}{3}\protected@file@percent } 7 | \@writefile{toc}{\contentsline {section}{\numberline {2}Diffusion}{4}\protected@file@percent } 8 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Derivation and Setting Up $(n=1)$}{4}\protected@file@percent } 9 | \newlabel{generalphyslaws}{{20}{5}} 10 | \global\@namedef{scr@dte@section@lastmaxnumwidth}{10.84047pt} 11 | \global\@namedef{scr@dte@subsection@lastmaxnumwidth}{18.37163pt} 12 | \global\@namedef{scr@dte@subsubsection@lastmaxnumwidth}{26.8883pt} 13 | -------------------------------------------------------------------------------- /.texpadtmp/m475.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/m475.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/m475.toc: -------------------------------------------------------------------------------- 1 | \contentsline {section}{\numberline {1}Introduction}{1}% 2 | \contentsline {subsection}{\numberline {1.1}Domains and Boundary Conditions}{2}% 3 | \contentsline {subsubsection}{\numberline {1.1.1}What are the main boundary conditions?}{2}% 4 | \contentsline {subsection}{\numberline {1.2}Classification of PDEs}{3}% 5 | \contentsline {section}{\numberline {2}Diffusion}{4}% 6 | \contentsline {subsection}{\numberline {2.1}Derivation and Setting Up $(n=1)$}{4}% 7 | -------------------------------------------------------------------------------- /.texpadtmp/math455ch11.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \babel@aux{nil}{} 3 | \@writefile{toc}{\contentsline {section}{\numberline {11.1}Open Sets, Closed Sets, Bases, and Sub-bases}{11-1}\protected@file@percent } 4 | \@writefile{loe}{\contentsline {definition}{\numberline {1}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Open Sets}}{11-1}\protected@file@percent } 5 | \@writefile{loe}{\contentsline {prop}{\numberline {1}\leavevmode {\color {red}Proposition}}{11-1}\protected@file@percent } 6 | \@writefile{loe}{\contentsline {ex}{\numberline {1}\leavevmode {\color {Maroon}Example}\thmtformatoptarg {Metric Topology}}{11-1}\protected@file@percent } 7 | \@writefile{loe}{\contentsline {ex}{\numberline {2}\leavevmode {\color {Maroon}Example}\thmtformatoptarg {Discrete Topology}}{11-1}\protected@file@percent } 8 | \@writefile{loe}{\contentsline {ex}{\numberline {3}\leavevmode {\color {Maroon}Example}\thmtformatoptarg {Trivial Topology}}{11-1}\protected@file@percent } 9 | \@writefile{loe}{\contentsline {definition}{\numberline {2}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Topological Subspaces}}{11-1}\protected@file@percent } 10 | \@writefile{loe}{\contentsline {definition}{\numberline {3}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Base for the Topology}}{11-1}\protected@file@percent } 11 | \@writefile{loe}{\contentsline {prop}{\numberline {2}\leavevmode {\color {red}Proposition}}{11-2}\protected@file@percent } 12 | \@writefile{loe}{\contentsline {definition}{\numberline {4}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Product Topology}}{11-2}\protected@file@percent } 13 | \@writefile{loe}{\contentsline {definition}{\numberline {5}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Sub-base}}{11-2}\protected@file@percent } 14 | \@writefile{loe}{\contentsline {definition}{\numberline {6}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Closure}}{11-2}\protected@file@percent } 15 | \@writefile{loe}{\contentsline {prop}{\numberline {3}\leavevmode {\color {red}Proposition}}{11-2}\protected@file@percent } 16 | \@writefile{loe}{\contentsline {prop}{\numberline {4}\leavevmode {\color {red}Proposition}}{11-2}\protected@file@percent } 17 | \@writefile{loe}{\contentsline {prop}{\numberline {5}\leavevmode {\color {red}Proposition}}{11-2}\protected@file@percent } 18 | \@writefile{toc}{\contentsline {section}{\numberline {11.2}Separation Properties}{11-2}\protected@file@percent } 19 | \@writefile{loe}{\contentsline {definition}{\numberline {7}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Neighbourhood}}{11-2}\protected@file@percent } 20 | \@writefile{loe}{\contentsline {definition}{\numberline {8}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Separated by Neighbourhoods}}{11-2}\protected@file@percent } 21 | \@writefile{loe}{\contentsline {definition}{\numberline {9}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Separation Properties of Topological Spaces}}{11-2}\protected@file@percent } 22 | \@writefile{loe}{\contentsline {prop}{\numberline {6}\leavevmode {\color {red}Proposition}}{11-3}\protected@file@percent } 23 | \@writefile{loe}{\contentsline {prop}{\numberline {7}\leavevmode {\color {red}Proposition}}{11-3}\protected@file@percent } 24 | \@writefile{loe}{\contentsline {lemma}{\numberline {1}Lemma}{11-3}\protected@file@percent } 25 | \@writefile{loe}{\contentsline {prop}{\numberline {8}\leavevmode {\color {red}Proposition}}{11-3}\protected@file@percent } 26 | -------------------------------------------------------------------------------- /.texpadtmp/math455ch11.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/math455ch11.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/math455ch8.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \babel@aux{nil}{} 3 | \@writefile{toc}{\contentsline {section}{\numberline {8.1}Riesz Representation Theorem for the Dual of $L^p$, $1 \leq p < \infty $}{8-1}\protected@file@percent } 4 | \@writefile{loe}{\contentsline {definition}{\numberline {1}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Linear Functional}}{8-1}\protected@file@percent } 5 | \@writefile{loe}{\contentsline {definition}{\numberline {2}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Bounded}}{8-1}\protected@file@percent } 6 | \@writefile{loe}{\contentsline {prop}{\numberline {1}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Continuity Property of a Bounded Linear Functional}}{8-1}\protected@file@percent } 7 | \@writefile{loe}{\contentsline {prop}{\numberline {2}\leavevmode {\color {red}Proposition}}{8-1}\protected@file@percent } 8 | \@writefile{loe}{\contentsline {prop}{\numberline {3}\leavevmode {\color {red}Proposition}}{8-1}\protected@file@percent } 9 | \@writefile{loe}{\contentsline {prop}{\numberline {4}\leavevmode {\color {red}Proposition}}{8-1}\protected@file@percent } 10 | \@writefile{loe}{\contentsline {lemma}{\numberline {1}Lemma}{8-1}\protected@file@percent } 11 | \@writefile{loe}{\contentsline {theorem}{\numberline {2}\leavevmode {\color {blue}Theorem}}{8-2}\protected@file@percent } 12 | \@writefile{loe}{\contentsline {theorem}{\numberline {3}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Riesz-Representation Theorem for the Dual of $L^p(E)$}}{8-2}\protected@file@percent } 13 | \@writefile{toc}{\contentsline {section}{\numberline {8.2}Weak Sequential Convergence in $L^p$}{8-2}\protected@file@percent } 14 | \@writefile{loe}{\contentsline {definition}{\numberline {3}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Converge Weakly}}{8-2}\protected@file@percent } 15 | \@writefile{loe}{\contentsline {definition}{\numberline {4}\leavevmode {\color {OliveGreen}Definition}}{8-2}\protected@file@percent } 16 | \@writefile{loe}{\contentsline {theorem}{\numberline {4}\leavevmode {\color {blue}Theorem}}{8-2}\protected@file@percent } 17 | \@writefile{loe}{\contentsline {corollary}{\numberline {1}Corollary}{8-2}\protected@file@percent } 18 | \@writefile{loe}{\contentsline {definition}{\numberline {5}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Linear Span}}{8-2}\protected@file@percent } 19 | \@writefile{loe}{\contentsline {prop}{\numberline {5}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Characterisation of Weak Convergence in $L^p(E)$}}{8-3}\protected@file@percent } 20 | \@writefile{loe}{\contentsline {theorem}{\numberline {5}\leavevmode {\color {blue}Theorem}}{8-3}\protected@file@percent } 21 | \@writefile{loe}{\contentsline {theorem}{\numberline {6}\leavevmode {\color {blue}Theorem}}{8-3}\protected@file@percent } 22 | \@writefile{loe}{\contentsline {lemma}{\numberline {7}Lemma\thmtformatoptarg {Riemann-Lebesgue Lemma; used in Fourier Series :-)}}{8-3}\protected@file@percent } 23 | \@writefile{loe}{\contentsline {theorem}{\numberline {8}\leavevmode {\color {blue}Theorem}}{8-3}\protected@file@percent } 24 | \@writefile{loe}{\contentsline {theorem}{\numberline {9}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Vitali Convergence Theorem}}{8-3}\protected@file@percent } 25 | \@writefile{loe}{\contentsline {theorem}{\numberline {10}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Radon-Riesz Theorem}}{8-3}\protected@file@percent } 26 | \@writefile{loe}{\contentsline {corollary}{\numberline {2}Corollary}{8-3}\protected@file@percent } 27 | \@writefile{toc}{\contentsline {section}{\numberline {8.3}Weak Sequential Compactness (``Compactness Found!'')}{8-3}\protected@file@percent } 28 | \@writefile{loe}{\contentsline {theorem}{\numberline {11}\leavevmode {\color {blue}Theorem}}{8-3}\protected@file@percent } 29 | \@writefile{loe}{\contentsline {theorem}{\numberline {12}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Helly's Theorem}}{8-3}\protected@file@percent } 30 | \@writefile{loe}{\contentsline {definition}{\numberline {6}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Weakly Sequentially Compact (Compact in the ``weak topology''}}{8-4}\protected@file@percent } 31 | \@writefile{loe}{\contentsline {theorem}{\numberline {13}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {The Unit Ball is Weakly Sequentially Compact}}{8-4}\protected@file@percent } 32 | -------------------------------------------------------------------------------- /.texpadtmp/math455ch8.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/math455ch8.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/math455ch9.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \babel@aux{nil}{} 3 | \@writefile{toc}{\contentsline {section}{\numberline {9.1}Examples of Metric Spaces}{9-1}\protected@file@percent } 4 | \@writefile{loe}{\contentsline {definition}{\numberline {1}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Metric Space}}{9-1}\protected@file@percent } 5 | \@writefile{loe}{\contentsline {definition}{\numberline {2}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Discrete Metric}}{9-1}\protected@file@percent } 6 | \@writefile{loe}{\contentsline {definition}{\numberline {3}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Metric Subspace}}{9-1}\protected@file@percent } 7 | \@writefile{loe}{\contentsline {exmp}{\numberline {9.1.1}Example\thmtformatoptarg {Examples of metric spaces}}{9-1}\protected@file@percent } 8 | \@writefile{loe}{\contentsline {definition}{\numberline {4}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Product Metric}}{9-1}\protected@file@percent } 9 | \@writefile{loe}{\contentsline {definition}{\numberline {5}\leavevmode {\color {OliveGreen}Definition}}{9-2}\protected@file@percent } 10 | \@writefile{loe}{\contentsline {definition}{\numberline {6}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Isometry}}{9-2}\protected@file@percent } 11 | \@writefile{toc}{\contentsline {section}{\numberline {9.2}Open Sets, Closed Sets, and Convergent Sequences}{9-2}\protected@file@percent } 12 | \@writefile{loe}{\contentsline {definition}{\numberline {7}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Open Ball}}{9-2}\protected@file@percent } 13 | \@writefile{loe}{\contentsline {prop}{\numberline {1}\leavevmode {\color {red}Proposition}}{9-2}\protected@file@percent } 14 | \@writefile{loe}{\contentsline {prop}{\numberline {2}\leavevmode {\color {red}Proposition}}{9-2}\protected@file@percent } 15 | \@writefile{loe}{\contentsline {definition}{\numberline {8}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Closure}}{9-2}\protected@file@percent } 16 | \@writefile{loe}{\contentsline {prop}{\numberline {3}\leavevmode {\color {red}Proposition}}{9-2}\protected@file@percent } 17 | \@writefile{loe}{\contentsline {definition}{\numberline {9}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Converge}}{9-2}\protected@file@percent } 18 | \@writefile{loe}{\contentsline {prop}{\numberline {4}\leavevmode {\color {red}Proposition}}{9-2}\protected@file@percent } 19 | \@writefile{toc}{\contentsline {section}{\numberline {9.3}Continuous Mappings Between Metric Spaces}{9-2}\protected@file@percent } 20 | \@writefile{loe}{\contentsline {definition}{\numberline {10}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Continuous}}{9-2}\protected@file@percent } 21 | \@writefile{loe}{\contentsline {prop}{\numberline {5}\leavevmode {\color {red}Proposition}\thmtformatoptarg {$\varepsilon $-$\delta $ criteria for continuity}}{9-3}\protected@file@percent } 22 | \@writefile{loe}{\contentsline {prop}{\numberline {6}\leavevmode {\color {red}Proposition}}{9-3}\protected@file@percent } 23 | \@writefile{loe}{\contentsline {prop}{\numberline {7}\leavevmode {\color {red}Proposition}}{9-3}\protected@file@percent } 24 | \@writefile{loe}{\contentsline {definition}{\numberline {11}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Uniformly Continuous}}{9-3}\protected@file@percent } 25 | \@writefile{loe}{\contentsline {definition}{\numberline {12}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Lipschitz}}{9-3}\protected@file@percent } 26 | \@writefile{toc}{\contentsline {section}{\numberline {9.4}Complete Metric Spaces}{9-3}\protected@file@percent } 27 | \@writefile{loe}{\contentsline {definition}{\numberline {13}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Cauchy}}{9-3}\protected@file@percent } 28 | \@writefile{loe}{\contentsline {definition}{\numberline {14}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Complete}}{9-3}\protected@file@percent } 29 | \@writefile{loe}{\contentsline {prop}{\numberline {8}\leavevmode {\color {red}Proposition}}{9-3}\protected@file@percent } 30 | \@writefile{loe}{\contentsline {prop}{\numberline {9}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Characterisation of Complete Subspaces of Metric Spaces}}{9-3}\protected@file@percent } 31 | \@writefile{loe}{\contentsline {theorem}{\numberline {1}\leavevmode {\color {blue}Theorem}}{9-3}\protected@file@percent } 32 | \@writefile{loe}{\contentsline {definition}{\numberline {15}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Diameter}}{9-3}\protected@file@percent } 33 | \@writefile{loe}{\contentsline {definition}{\numberline {16}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Contracting Sequence}}{9-3}\protected@file@percent } 34 | \@writefile{loe}{\contentsline {theorem}{\numberline {2}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Cantor Intersection Theorem}}{9-4}\protected@file@percent } 35 | \@writefile{loe}{\contentsline {theorem}{\numberline {3}\leavevmode {\color {blue}Theorem}}{9-4}\protected@file@percent } 36 | \@writefile{toc}{\contentsline {section}{\numberline {9.5}Compact Metric Spaces}{9-4}\protected@file@percent } 37 | \@writefile{loe}{\contentsline {definition}{\numberline {17}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Compact Metric Space}}{9-4}\protected@file@percent } 38 | \@writefile{loe}{\contentsline {definition}{\numberline {18}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Finite Intersection Property}}{9-4}\protected@file@percent } 39 | \@writefile{loe}{\contentsline {prop}{\numberline {10}\leavevmode {\color {red}Proposition}\thmtformatoptarg {Compactness in terms of closed sets}}{9-4}\protected@file@percent } 40 | \@writefile{loe}{\contentsline {definition}{\numberline {19}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Totally Bounded}}{9-4}\protected@file@percent } 41 | \@writefile{loe}{\contentsline {definition}{\numberline {20}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {$\varepsilon $-net}}{9-4}\protected@file@percent } 42 | \@writefile{loe}{\contentsline {prop}{\numberline {11}\leavevmode {\color {red}Proposition}}{9-4}\protected@file@percent } 43 | \@writefile{loe}{\contentsline {prop}{\numberline {12}\leavevmode {\color {red}Proposition}}{9-4}\protected@file@percent } 44 | \@writefile{loe}{\contentsline {definition}{\numberline {21}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Sequentially Compact}}{9-4}\protected@file@percent } 45 | \@writefile{loe}{\contentsline {theorem}{\numberline {4}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Characterisation of Compactness for a metric space}}{9-4}\protected@file@percent } 46 | \@writefile{loe}{\contentsline {theorem}{\numberline {5}\leavevmode {\color {blue}Theorem}}{9-5}\protected@file@percent } 47 | \@writefile{loe}{\contentsline {prop}{\numberline {13}\leavevmode {\color {red}Proposition}}{9-5}\protected@file@percent } 48 | \@writefile{loe}{\contentsline {theorem}{\numberline {6}\leavevmode {\color {blue}Theorem}\thmtformatoptarg {Extreme Value Theorem}}{9-5}\protected@file@percent } 49 | \@writefile{loe}{\contentsline {definition}{\numberline {22}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Lebesgue Number}}{9-5}\protected@file@percent } 50 | \@writefile{loe}{\contentsline {lemma}{\numberline {7}Lemma}{9-5}\protected@file@percent } 51 | \@writefile{loe}{\contentsline {prop}{\numberline {14}\leavevmode {\color {red}Proposition}}{9-5}\protected@file@percent } 52 | \@writefile{toc}{\contentsline {section}{\numberline {9.6}Separable Metric Spaces}{9-5}\protected@file@percent } 53 | \@writefile{loe}{\contentsline {definition}{\numberline {23}\leavevmode {\color {OliveGreen}Definition}\thmtformatoptarg {Dense \& Separable}}{9-5}\protected@file@percent } 54 | \@writefile{loe}{\contentsline {prop}{\numberline {15}\leavevmode {\color {red}Proposition}}{9-5}\protected@file@percent } 55 | \@writefile{loe}{\contentsline {prop}{\numberline {16}\leavevmode {\color {red}Proposition}}{9-5}\protected@file@percent } 56 | \@writefile{loe}{\contentsline {prop}{\numberline {17}\leavevmode {\color {red}Proposition}}{9-5}\protected@file@percent } 57 | \@writefile{loe}{\contentsline {theorem}{\numberline {8}\leavevmode {\color {blue}Theorem}}{9-5}\protected@file@percent } 58 | -------------------------------------------------------------------------------- /.texpadtmp/math455ch9.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/math455ch9.synctex.gz -------------------------------------------------------------------------------- /.texpadtmp/mechanics.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \@writefile{toc}{\contentsline {section}{\numberline {1}Dimensional Analysis}{1}\protected@file@percent } 3 | \@writefile{toc}{\contentsline {section}{\numberline {2}Kinematics}{1}\protected@file@percent } 4 | \@writefile{toc}{\contentsline {section}{\numberline {3}Uniform Circular Motion}{2}\protected@file@percent } 5 | \@writefile{toc}{\contentsline {section}{\numberline {4}Newton's Laws of Motion}{2}\protected@file@percent } 6 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Weight, Weightlessness in Free fall, and Weight in Orbit}{3}\protected@file@percent } 7 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Friction}{3}\protected@file@percent } 8 | \@writefile{toc}{\contentsline {section}{\numberline {5}Hooke's Law, Springs, Pendulums, and Simple Harmonic Motion}{3}\protected@file@percent } 9 | \@writefile{toc}{\contentsline {section}{\numberline {6}Work, Kinetic and Potential Energy, Gravitation, and Conservative Forces}{4}\protected@file@percent } 10 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Work: One-Dimensional Case}{4}\protected@file@percent } 11 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Work: Three-Dimensional Case}{4}\protected@file@percent } 12 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.3}Newton's Law of Gravitation}{5}\protected@file@percent } 13 | \@writefile{toc}{\contentsline {section}{\numberline {7}Air Drag, Resistive Forces, Conservative Forces, and Terminal Velocity}{5}\protected@file@percent } 14 | -------------------------------------------------------------------------------- /.texpadtmp/mechanics.log: -------------------------------------------------------------------------------- 1 | This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex 2019.7.26) 30 MAY 2020 20:08 2 | entering extended mode 3 | restricted \write18 enabled. 4 | file:line:error style messages enabled. 5 | %&-line parsing enabled. 6 | **mechanics.tex 7 | (./mechanics.tex 8 | LaTeX2e <2018-12-01> 9 | (/usr/local/texlive/2019/texmf-dist/tex/latex/base/article.cls 10 | Document Class: article 2018/09/03 v1.4i Standard LaTeX document class 11 | (/usr/local/texlive/2019/texmf-dist/tex/latex/base/size11.clo 12 | File: size11.clo 2018/09/03 v1.4i Standard LaTeX file (size option) 13 | ) 14 | \c@part=\count80 15 | \c@section=\count81 16 | \c@subsection=\count82 17 | \c@subsubsection=\count83 18 | \c@paragraph=\count84 19 | \c@subparagraph=\count85 20 | \c@figure=\count86 21 | \c@table=\count87 22 | \abovecaptionskip=\skip41 23 | \belowcaptionskip=\skip42 24 | \bibindent=\dimen102 25 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/geometry/geometry.sty 26 | Package: geometry 2018/04/16 v5.8 Page Geometry 27 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics/keyval.sty 28 | Package: keyval 2014/10/28 v1.15 key=value parser (DPC) 29 | \KV@toks@=\toks14 30 | ) (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ifpdf.sty 31 | Package: ifpdf 2018/09/07 v3.3 Provides the ifpdf switch 32 | ) (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ifvtex.sty 33 | Package: ifvtex 2016/05/16 v1.6 Detect VTeX and its facilities (HO) 34 | Package ifvtex Info: VTeX not detected. 35 | ) (/usr/local/texlive/2019/texmf-dist/tex/generic/ifxetex/ifxetex.sty 36 | Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional 37 | ) 38 | \Gm@cnth=\count88 39 | \Gm@cntv=\count89 40 | \c@Gm@tempcnt=\count90 41 | \Gm@bindingoffset=\dimen103 42 | \Gm@wd@mp=\dimen104 43 | \Gm@odd@mp=\dimen105 44 | \Gm@even@mp=\dimen106 45 | \Gm@layoutwidth=\dimen107 46 | \Gm@layoutheight=\dimen108 47 | \Gm@layouthoffset=\dimen109 48 | \Gm@layoutvoffset=\dimen110 49 | \Gm@dimlist=\toks15 50 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsmath.sty 51 | Package: amsmath 2018/12/01 v2.17b AMS math features 52 | \@mathmargin=\skip43 53 | 54 | For additional information on amsmath, use the `?' option. 55 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amstext.sty 56 | Package: amstext 2000/06/29 v2.01 AMS text 57 | (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsgen.sty 58 | File: amsgen.sty 1999/11/30 v2.0 generic functions 59 | \@emptytoks=\toks16 60 | \ex@=\dimen111 61 | )) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsbsy.sty 62 | Package: amsbsy 1999/11/29 v1.2d Bold Symbols 63 | \pmbraise@=\dimen112 64 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/amsmath/amsopn.sty 65 | Package: amsopn 2016/03/08 v2.02 operator names 66 | ) 67 | \inf@bad=\count91 68 | LaTeX Info: Redefining \frac on input line 223. 69 | \uproot@=\count92 70 | \leftroot@=\count93 71 | LaTeX Info: Redefining \overline on input line 385. 72 | \classnum@=\count94 73 | \DOTSCASE@=\count95 74 | LaTeX Info: Redefining \ldots on input line 482. 75 | LaTeX Info: Redefining \dots on input line 485. 76 | LaTeX Info: Redefining \cdots on input line 606. 77 | \Mathstrutbox@=\box27 78 | \strutbox@=\box28 79 | \big@size=\dimen113 80 | LaTeX Font Info: Redeclaring font encoding OML on input line 729. 81 | LaTeX Font Info: Redeclaring font encoding OMS on input line 730. 82 | \macc@depth=\count96 83 | \c@MaxMatrixCols=\count97 84 | \dotsspace@=\muskip10 85 | \c@parentequation=\count98 86 | \dspbrk@lvl=\count99 87 | \tag@help=\toks17 88 | \row@=\count100 89 | \column@=\count101 90 | \maxfields@=\count102 91 | \andhelp@=\toks18 92 | \eqnshift@=\dimen114 93 | \alignsep@=\dimen115 94 | \tagshift@=\dimen116 95 | \tagwidth@=\dimen117 96 | \totwidth@=\dimen118 97 | \lineht@=\dimen119 98 | \@envbody=\toks19 99 | \multlinegap=\skip44 100 | \multlinetaggap=\skip45 101 | \mathdisplay@stack=\toks20 102 | LaTeX Info: Redefining \[ on input line 2844. 103 | LaTeX Info: Redefining \] on input line 2845. 104 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/enumitem/enumitem.sty 105 | Package: enumitem 2019/02/04 v3.8 Customized lists 106 | \labelindent=\skip46 107 | \enit@outerparindent=\dimen120 108 | \enit@toks=\toks21 109 | \enit@inbox=\box29 110 | \enit@count@id=\count103 111 | \enitdp@description=\count104 112 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics/graphicx.sty 113 | Package: graphicx 2017/06/01 v1.1a Enhanced LaTeX Graphics (DPC,SPQR) 114 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics/graphics.sty 115 | Package: graphics 2017/06/25 v1.2c Standard LaTeX Graphics (DPC,SPQR) 116 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics/trig.sty 117 | Package: trig 2016/01/03 v1.10 sin cos tan (DPC) 118 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics-cfg/graphics.cfg 119 | File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration 120 | ) 121 | Package graphics Info: Driver file: pdftex.def on input line 99. 122 | (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics-def/pdftex.def 123 | File: pdftex.def 2018/01/08 v1.0l Graphics/color driver for pdftex 124 | )) 125 | \Gin@req@height=\dimen121 126 | \Gin@req@width=\dimen122 127 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/float/float.sty 128 | Package: float 2001/11/08 v1.3d Float enhancements (AL) 129 | \c@float@type=\count105 130 | \float@exts=\toks22 131 | \float@box=\box30 132 | \@float@everytoks=\toks23 133 | \@floatcapt=\box31 134 | ) (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/mechanics.aux) 135 | \openout1 = `mechanics.aux'. 136 | 137 | LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 13. 138 | LaTeX Font Info: ... okay on input line 13. 139 | LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 13. 140 | LaTeX Font Info: ... okay on input line 13. 141 | LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 13. 142 | LaTeX Font Info: ... okay on input line 13. 143 | LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 13. 144 | LaTeX Font Info: ... okay on input line 13. 145 | LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 13. 146 | LaTeX Font Info: ... okay on input line 13. 147 | LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 13. 148 | LaTeX Font Info: ... okay on input line 13. 149 | 150 | *geometry* driver: auto-detecting 151 | *geometry* detected driver: pdftex 152 | *geometry* verbose mode - [ preamble ] result: 153 | * driver: pdftex 154 | * paper: 155 | * layout: 156 | * layoutoffset:(h,v)=(0.0pt,0.0pt) 157 | * modes: 158 | * h-part:(L,W,R)=(56.9055pt, 500.484pt, 56.9055pt) 159 | * v-part:(T,H,B)=(56.9055pt, 681.15898pt, 56.9055pt) 160 | * \paperwidth=614.295pt 161 | * \paperheight=794.96999pt 162 | * \textwidth=500.484pt 163 | * \textheight=681.15898pt 164 | * \oddsidemargin=-15.36449pt 165 | * \evensidemargin=-15.36449pt 166 | * \topmargin=-52.36449pt 167 | * \headheight=12.0pt 168 | * \headsep=25.0pt 169 | * \topskip=11.0pt 170 | * \footskip=30.0pt 171 | * \marginparwidth=59.0pt 172 | * \marginparsep=10.0pt 173 | * \columnsep=10.0pt 174 | * \skip\footins=10.0pt plus 4.0pt minus 2.0pt 175 | * \hoffset=0.0pt 176 | * \voffset=0.0pt 177 | * \mag=1000 178 | * \@twocolumnfalse 179 | * \@twosidefalse 180 | * \@mparswitchfalse 181 | * \@reversemarginfalse 182 | * (1in=72.27pt=25.4mm, 1cm=28.453pt) 183 | 184 | (/usr/local/texlive/2019/texmf-dist/tex/context/base/mkii/supp-pdf.mkii 185 | [Loading MPS to PDF converter (version 2006.09.02).] 186 | \scratchcounter=\count106 187 | \scratchdimen=\dimen123 188 | \scratchbox=\box32 189 | \nofMPsegments=\count107 190 | \nofMParguments=\count108 191 | \everyMPshowfont=\toks24 192 | \MPscratchCnt=\count109 193 | \MPscratchDim=\dimen124 194 | \MPnumerator=\count110 195 | \makeMPintoPDFobject=\count111 196 | \everyMPtoPDFconversion=\toks25 197 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty 198 | Package: epstopdf-base 2016/05/15 v2.6 Base part for package epstopdf 199 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/infwarerr.sty 200 | Package: infwarerr 2016/05/16 v1.4 Providing info/warning/error messages (HO) 201 | ) (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/grfext.sty 202 | Package: grfext 2016/05/16 v1.2 Manage graphics extensions (HO) 203 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/kvdefinekeys.sty 204 | Package: kvdefinekeys 2016/05/16 v1.4 Define keys (HO) 205 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ltxcmds.sty 206 | Package: ltxcmds 2016/05/16 v1.23 LaTeX kernel commands for general use (HO) 207 | ))) (/usr/local/texlive/2019/texmf-dist/tex/latex/oberdiek/kvoptions.sty 208 | Package: kvoptions 2016/05/16 v3.12 Key value format for package options (HO) 209 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty 210 | Package: kvsetkeys 2016/05/16 v1.17 Key value parser (HO) 211 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/etexcmds.sty 212 | Package: etexcmds 2016/05/16 v1.6 Avoid name clashes with e-TeX commands (HO) 213 | (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/ifluatex.sty 214 | Package: ifluatex 2016/05/16 v1.4 Provides the ifluatex switch (HO) 215 | Package ifluatex Info: LuaTeX not detected. 216 | )))) (/usr/local/texlive/2019/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty 217 | Package: pdftexcmds 2018/09/10 v0.29 Utility functions of pdfTeX for LuaTeX (HO) 218 | Package pdftexcmds Info: LuaTeX not detected. 219 | Package pdftexcmds Info: \pdf@primitive is available. 220 | Package pdftexcmds Info: \pdf@ifprimitive is available. 221 | Package pdftexcmds Info: \pdfdraftmode found. 222 | ) 223 | Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 438. 224 | Package grfext Info: Graphics extension search list: 225 | (grfext) [.pdf,.png,.jpg,.mps,.jpeg,.jbig2,.jb2,.PDF,.PNG,.JPG,.JPEG,.JBIG2,.JB2,.eps] 226 | (grfext) \AppendGraphicsExtensions on input line 456. 227 | (/usr/local/texlive/2019/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg 228 | File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live 229 | )) 230 | LaTeX Font Info: Try loading font information for OMS+cmr on input line 24. 231 | (/usr/local/texlive/2019/texmf-dist/tex/latex/base/omscmr.fd 232 | File: omscmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions 233 | ) 234 | LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10.95> not available 235 | (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 24. 236 | [1 237 | 238 | {/usr/local/texlive/2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2] [3] [4] [5] [6] (/Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/mechanics.aux) ) 239 | Here is how much of TeX's memory you used: 240 | 2937 strings out of 492616 241 | 41903 string characters out of 6129481 242 | 123959 words of memory out of 5000000 243 | 6823 multiletter control sequences out of 15000+600000 244 | 10984 words of font info for 39 fonts, out of 8000000 for 9000 245 | 1141 hyphenation exceptions out of 8191 246 | 41i,12n,32p,329b,422s stack positions out of 5000i,500n,10000p,200000b,80000s 247 | 248 | Output written on /Users/shereenelaidi/Desktop/mathnotes/.texpadtmp/mechanics.pdf (6 pages, 185226 bytes). 249 | PDF statistics: 250 | 83 PDF objects out of 1000 (max. 8388607) 251 | 59 compressed objects within 1 object stream 252 | 0 named destinations out of 1000 (max. 500000) 253 | 1 words of extra memory for PDF output out of 10000 (max. 10000000) 254 | 255 | -------------------------------------------------------------------------------- /.texpadtmp/mechanics.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/.texpadtmp/mechanics.synctex.gz -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Math Notes 2 | This repository contains assorted math, physics, and computer science notes from my degree. 3 | * `calculus-and-analysis/`: calculus, differential equations, and PDEs. 4 | * `calculus.pdf`: summary of Calculus 1 (derivatives) to calculus 4 (vector calculus). 5 | * `math-141.pdf`: course notes of Calculus 2 (Fall 2017). 6 | * `math-222.pdf`: course notes of Calculus 3 (Winter 2018). 7 | * `math-254.pdf`: summary notes of Analysis 1 (Fall 2018). 8 | * `math-454.pdf`: summary notes of Analysis 3 (Fall 2019). 9 | * `math-455-final.pdf, math-455-midterm.pdf`: summary notes of Analysis 4 (Winter 2020). 10 | * `math-475.pdf`: summary notes of PDEs (Fall 2019). 11 | * `geometry/`: differential geometry. 12 | * `math-458.pdf`: course notes for Differential Geometry (Winter 2020). 13 | * `linear-algebra/`: linear algebra and algebra. 14 | * `math-133.pdf`: summary notes of Linear Algebra and Geometry (Fall 2017). 15 | * `math-247.pdf`: summary notes of Applied Linear Algebra (Winter 2018). 16 | * `physics/`: assorted physics notes and reports. 17 | * `math-470.pdf`: slides from mathematical quantum mechanics report. 18 | * `phys-514.pdf`: course notes from General Relativity (incomplete) (Winter 2021). 19 | * `prob-and-stats/`: assorted class notes of probability and statistics. 20 | * `math-357.pdf`: course notes of Statistics (Winter 2020). 21 | * `math-587.pdf`: course notes of Advanced Probability Theory 1 (Fall 2021). 22 | * `math-589.pdf`: course notes of Advanced Probability Theory 2 (Winter 2022). 23 | * `reports/`: 24 | * `ergodic-theory.pdf`: final project for Non-Linear Dynamics and Chaos (Fall 2019). 25 | * `lie-groups-and-PDE.pdf`: final project for PDEs 2 (Winter 2023). 26 | * `lorentzian-causality-theory.pdf`: final report for DRP (Fall 2019). 27 | * `teaching/`: assorted materials from teaching and tutoring. 28 | * `calculus/`: 29 | * `math314-meeting-1-suggested-exercises.pdf`: from Stewart's calculus. 30 | * `math314-meeting-1.pdf`: from Stewart's calculus. 31 | * `linear-algebra/`: 32 | * `math133-midterm1-fact-sheet-fall-2021.pdf`: summary sheet for Midterm 1 of Math 133 (Fall 2021). -------------------------------------------------------------------------------- /calculus-and-analysis/calculus.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/calculus-and-analysis/calculus.pdf -------------------------------------------------------------------------------- /calculus-and-analysis/math-141.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/calculus-and-analysis/math-141.pdf -------------------------------------------------------------------------------- /calculus-and-analysis/math-222.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/calculus-and-analysis/math-222.pdf -------------------------------------------------------------------------------- /calculus-and-analysis/math-254.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/calculus-and-analysis/math-254.pdf -------------------------------------------------------------------------------- /calculus-and-analysis/math-454.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/calculus-and-analysis/math-454.pdf -------------------------------------------------------------------------------- /calculus-and-analysis/math-455-final.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/calculus-and-analysis/math-455-final.pdf -------------------------------------------------------------------------------- /calculus-and-analysis/math-455-midterm.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/calculus-and-analysis/math-455-midterm.pdf -------------------------------------------------------------------------------- /calculus-and-analysis/math-475.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/calculus-and-analysis/math-475.pdf -------------------------------------------------------------------------------- /geometry/math-458.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/geometry/math-458.pdf -------------------------------------------------------------------------------- /linear-algebra/math-133.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/linear-algebra/math-133.pdf -------------------------------------------------------------------------------- /linear-algebra/math-247.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/linear-algebra/math-247.pdf -------------------------------------------------------------------------------- /physics/Math-470.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/physics/Math-470.pdf -------------------------------------------------------------------------------- /physics/phys-514.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/physics/phys-514.pdf -------------------------------------------------------------------------------- /prob-and-stats/math-357.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/prob-and-stats/math-357.pdf -------------------------------------------------------------------------------- /prob-and-stats/math-587.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/prob-and-stats/math-587.pdf -------------------------------------------------------------------------------- /prob-and-stats/math-589.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/prob-and-stats/math-589.pdf -------------------------------------------------------------------------------- /reports/ergodictheory1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/reports/ergodictheory1.pdf -------------------------------------------------------------------------------- /reports/lie-groups-and-PDE.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/reports/lie-groups-and-PDE.pdf -------------------------------------------------------------------------------- /reports/lorentzian-causality-theory.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/reports/lorentzian-causality-theory.pdf -------------------------------------------------------------------------------- /source-code/parallel-transport.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/source-code/parallel-transport.png -------------------------------------------------------------------------------- /teaching/calculus/math314-meeting-1-suggested-exercises.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/teaching/calculus/math314-meeting-1-suggested-exercises.pdf -------------------------------------------------------------------------------- /teaching/calculus/math314-meeting-1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/teaching/calculus/math314-meeting-1.pdf -------------------------------------------------------------------------------- /teaching/linear-algebra/math133-midterm1-fact-sheet-fall-2021.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/ShereenElaidi/mathnotes/cff32188e6cd25a16f6a49666a4ea7684bb91293/teaching/linear-algebra/math133-midterm1-fact-sheet-fall-2021.pdf --------------------------------------------------------------------------------