├── .gitignore ├── README.md ├── cheat-sheet-example.Rmd ├── cheat-sheet-example.pdf ├── cheat-sheet-rmarkdown.Rproj └── template.tex /.gitignore: -------------------------------------------------------------------------------- 1 | .Rproj.user 2 | .Rhistory 3 | .RData 4 | .Ruserdata 5 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 2 | A [LaTex](https://www.latex-project.org/) template to use with [`{rmarkdown}`](https://rmarkdown.rstudio.com/) to create a compact cheat sheet for school. 3 | 4 | To use it, include the following in the YAML header of your Rmarkdown file. 5 | 6 | ``` 7 | --- 8 | output: 9 | pdf_document: 10 | template: {/path/to/template.tex} 11 | --- 12 | ``` -------------------------------------------------------------------------------- /cheat-sheet-example.Rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "" 3 | output: 4 | pdf_document: 5 | template: template.tex 6 | --- 7 | 8 | 9 | # Some Simple Examples 10 | 11 | ## One-line equation 12 | 13 | Euler's constant: $e = \mathop {\lim }\limits_{n \to \infty } \left( {1 + \frac{1}{n}} \right)^n$ 14 | 15 | ## Multi-line equation 16 | 17 | This renders as a "pop-up" in Rstudio if you've selected "Inline" with the "Show equation and image previews" option at Tools > Global Options... > Rmarkdown 18 | 19 | $$ 20 | \begin{array}{lcl} 21 | I &=& \int (x + 1) dx \\ 22 | &=& \frac{x^2}{2} + x + C. 23 | \end{array} 24 | $$ 25 | 26 | ## Comments with `\iffalse` (and closing `\fi`) 27 | 28 | You shouldn't see anything in the output PDF here (although there is an equation in the Rmarkdown document). 29 | 30 | \iffalse 31 | Integration by parts: $\int {u\frac{{dv}}{{dx}}} dx = uv - \int {\frac{{du}}{{dx}}} vdx$ 32 | \fi 33 | 34 | # A "Big" Test of Equations 35 | 36 | **Source:** [Griffith Quantum Mechanics Time Dependent Perturbation theory CheatSheet (UCB 137B final) on www.overleaf.com](https://www.overleaf.com/articles/griffith-quantum-mechanics-time-dependent-perturbation-theory-cheatsheet-ucb-137b-final/jwynrzctvqgp) 37 | 38 | \section{TIPT} 39 | \begin{align*} 40 | H = H_0 + H' \\ 41 | E_n = E_n^0 + E_n^1 \\ 42 | |\psi_n\rangle = |\psi_n^0\rangle + |\psi_n^1\rangle \\ 43 | E_n^1 = \langle \psi_n^0 | H' | \psi_n^0 \rangle \\ 44 | |\psi_n^1\rangle = \sum_{m\neq n} \frac{\langle \psi_m^0 | H' | \psi_n^0 \rangle}{E_n^0-E_m^0} | \psi_m^0\rangle 45 | \end{align*} 46 | 47 | \subsection{Degenerate Case} 48 | \begin{align*} 49 | \text{Degenerate space: } \{|i\rangle\} \to E\\ 50 | \quad W_{ab} = \langle a | H' | b \rangle \text{ Non-Diagonal} \\ 51 | \text{Eigenvalue and Eivenvectors} \to E_n^1, |\hat{i}\rangle 52 | \end{align*} 53 | 54 | 55 | \section{Variational Method} 56 | \begin{align*} 57 | \langle H \rangle(\lambda) &= 58 | \frac{\langle \psi(x,\lambda)|H|\psi(x,\lambda) \rangle}{\langle \psi(x,\lambda)|\psi(x,\lambda) \rangle} \\ 59 | \langle H \rangle(\lambda) &\geq E_{.g.s} \\ 60 | \frac{d}{d\lambda} \langle H \rangle(\lambda_0) = 0 &\Rightarrow 61 | \langle H \rangle(\lambda_0) \approx E_{.g.s} 62 | \end{align*} 63 | 64 | \section{WKB Method} 65 | \begin{align*} 66 | \frac{d^2 \psi(x)}{dx^2} &= -k^2(x) \psi(x)& \\ k(x)&=\frac1\hbar \sqrt{2m(E-V(x)} \\ 67 | \phi(x) &= \int^x k(x) dx \\ 68 | \psi(x) &= \frac1{\sqrt{k(x)}} (C_+ e^{i \phi(x)} + C_- e^{-i \phi(x)})\\ 69 | &= \frac1{\sqrt{k(x)}} (C_1 \sin{\phi(x)} + C_2 \cos{\phi(x)}) 70 | \end{align*} 71 | 72 | \subsection{Energy Level} 73 | \begin{align*} 74 | \int_{R_{classical}} k(x) dx = n\pi \\ 75 | \text{one $\infty$ wall} \quad n \to n-1/4 \\ 76 | \text{No $\infty$ wall} \quad n \to n-1/2 77 | \end{align*} 78 | 79 | \subsection{Tunneling} 80 | \begin{align*} 81 | T = e^{-2\gamma} \\ 82 | \gamma = \int_{R_{forbidden}} k(x) dx 83 | \end{align*} 84 | 85 | \section{TDPT} 86 | \begin{align*} 87 | H = H_0 + V(t) \\ 88 | \text{Eigenstate of $H_0$: } |n\rangle, E_n\\ 89 | \text{transition: } |i\rangle \to | f\rangle \\ 90 | V_{f i}(t) = \langle f | V(t) | i \rangle \\ 91 | \omega_{f i} = (E_f-E_i)/\hbar \\ 92 | c_f(T) = \frac{-i}{\hbar} \int_0^T V_{f i}(t) e^{-i \omega_{f i} t} dt 93 | \end{align*} 94 | 95 | \subsection{Constant Perturbation} 96 | \begin{align*} 97 | V(t) = \begin{cases} 98 | V, & 0 \leq t \leq T \\ 99 | 0, & \text{otherwise} 100 | \end{cases} \\ 101 | V_{fi}(t)= constant \\ 102 | P_{i\to f}(t)= |c_f(t)|^2 = 4 \frac{|V_{fi}|^2}{\hbar^2} \frac{\sin^2(\omega_{fi})t/2}{\omega_{fi}^2} \\ 103 | \omega_{fi} \to 0 \quad \text{(degenerate states):} \\ 104 | |c_f(t)|^2 = \frac{|V_{fi}|^2}{\hbar^2} t^2 105 | \end{align*} 106 | 107 | \subsection{Absorption} 108 | \begin{align*} 109 | V(t) = V \sin(\omega t) \\ 110 | P_{i\to f}(t) = \frac{|V_{fi}|^2}{\hbar^2} \frac{\sin^2((\omega_{fi}-\omega)t/2)}{(\omega_{fi}-\omega)^2} 111 | \end{align*} 112 | 113 | \subsection{Simulated Emission} 114 | \begin{align*} 115 | E_i > E_f,\quad \omega_{fi}<0 \\ 116 | P_{i\to f}(t) = \frac{|V_{fi}|^2}{\hbar^2} \frac{\sin^2((\omega_{fi}+\omega)t/2)}{(\omega_{fi}+\omega)^2} 117 | \end{align*} 118 | 119 | \subsection{Fermi Golden Rule} 120 | \begin{align*} 121 | E_i \to E_f\text{ (continuous states)} \\ 122 | P_{i\to f} = 123 | \frac{2\pi}{\hbar} |\langle f | V| i\rangle |^2 \rho(E_f) t \\ 124 | \end{align*} 125 | 126 | \subsection{Selection Rule} 127 | For spherical symmetric potential: 128 | \begin{align*} 129 | \langle n',l',m'| \vec{r} | n,l,m \rangle &\neq 0 \text{ when:} \\ 130 | \Delta l &= \pm 1 \text{ and:}\\ 131 | \Delta l &= \pm 1 \text{ or } 0 132 | \end{align*} 133 | 134 | 135 | \section{Scattering} 136 | \begin{align*} 137 | \psi(r,\theta) &= e^{ikz} + f(\theta) \frac{e^{ikr}}{r}, \text{ for large r} \\ 138 | k &= \frac{\sqrt{2mE}}\hbar \\ 139 | \frac{d \sigma}{d \Omega} &= |f(\theta)|^2 \\ 140 | \sigma &= \int d\omega \frac{d \sigma}{d \Omega} 141 | \end{align*} 142 | 143 | \subsection{Born Approximation} 144 | \begin{align*} 145 | f(\theta) = -\frac{m}{2\pi \hbar^2} \int V(\vec{r}) e^{i(\vec{k}'-\vec{k})\cdot \vec{r}} d^3\vec{r} 146 | \intertext{Low Energy:} 147 | f(\theta) = -\frac{m}{2\pi \hbar^2} \int V(\vec{r}) d^3\vec{r} 148 | \intertext{Spherical symmetric:} 149 | f(\theta) = -\frac{2m}{\hbar^2 \kappa} \int_0^\infty r V(r) \sin(\kappa r) dr \\ 150 | \kappa = 2k\sin(\theta/2) 151 | \end{align*} 152 | 153 | \subsubsection{Yukawa Potential} 154 | \begin{align*} 155 | V(r) = V_0 \frac{e^{-r/R}}{r} \\ 156 | f(\theta) = -\frac{2mV_0 R^2}{\hbar^2} \frac{1}{1+4k^2R^2\sin^2(\theta/2)} \\ 157 | \sigma = (\frac{2mV_0R^2}{\hbar^2})^2 \frac{4\pi}{1+4k^2R^2} 158 | \end{align*} 159 | 160 | \subsubsection{Rutherford Scattering} 161 | Let $V_0 = q_1q_2/4\pi \epsilon_0$, $R=\infty$: 162 | \begin{align*} 163 | f(\theta) = -\frac{2mq_1q_2}{4\pi\epsilon_0\hbar^2\kappa^2} 164 | \end{align*} 165 | 166 | \subsection{Partial Waves} 167 | \begin{align*} 168 | f(\theta) &= \frac1k \sum_{i=0}^\infty (2l+1)e^{i \delta_l} \sin(\delta_l) P_l(\cos(\theta)) \\ 169 | \sigma &= \frac{4\pi}{k^2}\sum_{l=0}^\infty (2l+1) \sin^2(\delta_l) 170 | \end{align*} 171 | 172 | \subsubsection{Optical Theorem} 173 | \begin{equation*} 174 | Im[f(0)] = \frac{k \sigma}{4\pi} 175 | \end{equation*} 176 | 177 | \subsubsection{Hard Ball} 178 | \begin{align*} 179 | \delta_l = \tan^{-1}(\frac{j_l(ka)}{\eta_l(ka)}) \\ 180 | ka << 1 \to \sigma = 4\pi a^2 181 | \end{align*} 182 | 183 | \section{Useful Models} 184 | 185 | \subsection{Density of States} 186 | \begin{align*} 187 | E &= \hbar^2 k^2 /2m \\ 188 | dN &= \frac{L^3}{(2\pi)^3} d^3k = \frac{L^3}{(2\pi)^3} d\Omega dk \\ 189 | dN &= \frac{L^3}{(2\pi)^3} 4\pi \frac{m}{\hbar^2 k} dE \\ 190 | \rho(E) &= \frac{dN}{dE} = \frac{L^3}{2\pi^2} \frac{mk}{\hbar^2} 191 | \end{align*} 192 | 193 | \subsection{infinite square well} 194 | \begin{align*} 195 | H(x) = \frac{p^2}{2m} + \begin{cases} 196 | 0, & 0\leq x\leq a \\ 197 | \infty, & \text{otherwise} 198 | \end{cases} \\ 199 | E_n = \frac1{2m} (\frac{n \pi \hbar}{a})^2 \\ 200 | \psi_n = \sqrt{\frac{2}{a}} \sin(\frac{n\pi x}{a}) e^{-iE_nt/\hbar} 201 | \end{align*} 202 | 203 | \subsection{Harmonic Oscillator} 204 | \begin{align*} 205 | H(x) &= \frac{p^2}{2m} + \frac12 m\omega^2x^2 \\ 206 | E_n &= (n+1/2)\hbar \omega \\ 207 | \psi_n(x) &= \frac1{\sqrt{2^n n!}} (\frac{m\omega}{\pi \hbar})^{1/4} e^{-\zeta^2/2} H_n(\zeta) \\ 208 | \zeta &= \sqrt{\frac{m\omega}{\hbar}x} 209 | \end{align*} 210 | 211 | \subsection{Virial Theorem} 212 | \begin{align*} 213 | 2 \langle T \rangle = \langle \vec{r} \cdot \nabla V \rangle 214 | \quad \text{(3D)}\\ 215 | 2 \langle T \rangle = \langle x \frac{dV}{dx} \rangle \quad \text{(1D)}\\ 216 | 2 \langle T \rangle = n \langle V \rangle \quad (V\propto r^n) \\ 217 | \langle T\rangle = -E_n, \quad \langle V \rangle = 2 E_n \quad \text{(hydrogen)}\\ 218 | \langle T\rangle = \langle V \rangle = E_n/2 \quad \text{(harmonic oscillator)}\\ 219 | \end{align*} 220 | 221 | \section{Math} 222 | 223 | \subsection{Legendre Polynomials} 224 | Domain: $(-1,1)$ \\ 225 | Even, Odd, Even, Odd ... 226 | \begin{align*} 227 | P_0(x) &= 1 \\ 228 | P_1(x) &= x \\ 229 | P_2(x) &= \frac12 (3x^2-1) \\ 230 | P_3(x) &= \frac12 (5x^3 - 3x) 231 | \end{align*} 232 | 233 | \subsection{Hankel Functions} 234 | Solution to Radial Shrodinger Equation: 235 | \begin{align*} 236 | -\frac{\hbar^2}{2m} \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 R_{El}) + [V(r) + \frac{\hbar^2 l (l+1)}{2m r^2}]R_{El} = E R_{El} \\ 237 | V = 0 \to R_{El} = j_l(kr) \\ 238 | V \neq 0 \to R_{El} = j_l(kr+\delta_l) \\ 239 | r \to \infty \Rightarrow R_{El} = \frac{\sin(kr-l\pi/2+\delta_l(E))}{kr} 240 | \end{align*} 241 | When $kr >> 1$ 242 | \begin{align*} 243 | j_l(kr) &\to \frac{\sin{kr-l\pi/2}}{kr} \\ 244 | \eta_l(kr) &\to \frac{-\cos{kr-l\pi/2}}{kr} \\ 245 | h_l(kr) &\to \frac{e^{i(kr-l\pi/2)}}{ikr} \\ 246 | h_l^*(kr) &\to \frac{e^{-i(kr-l\pi/2)}}{-ikr} \\ 247 | j_l(kr) &= \frac{1}{2} (h_l(kr)+h^*(kr)) 248 | \end{align*} 249 | 250 | \subsection{Hermite Polynomials} 251 | Domain: $(-\infty,\infty)$ \\ 252 | Even, Odd, Even, Odd ... 253 | \begin{align*} 254 | H_0(x) &= 1 \\ 255 | H_1(x) &= 2x \\ 256 | H_2(x) &= 4x^2-2 \\ 257 | H_3(x) &= 8x^3-12x 258 | \end{align*} 259 | 260 | \subsection{Spherical Harmonics} 261 | \begin{align*} 262 | |l,m \rangle &= Y_l^m(\theta, \phi) \\ 263 | Y_0^0(\theta,\phi) &= \frac12 \frac1{\sqrt{\pi}} \\ 264 | Y_1^0(\theta,\phi) &= \frac12 \sqrt{\frac3\pi} \cos{\theta} \\ 265 | Y_1^{-1}(\theta,\phi) &= \frac12 \sqrt{\frac{3}{2\pi}} \sin{\theta} e^{-i \phi} \\ 266 | Y_1^{-1}(\theta,\phi) &= -\frac12 \sqrt{\frac{3}{2\pi}} \sin{\theta} e^{i \phi} 267 | \end{align*} 268 | 269 | \subsection{Green's Function} 270 | For a Linear Operator $\hat{D}_x$ 271 | \begin{align*} 272 | \text{Homogeneous solution: }\hat{D}_x \psi_0(x) = 0 \\ 273 | \text{Hard Problem: }\hat{D}_x \psi(x) = f(x) \\ 274 | \text{Simple Problem: }\hat{D}_x G(x,x') = \delta(x-x') \\ 275 | \psi(x) = \psi_0(x) + \int_{\text{f Domain}} G(x,x') f(x') dx' 276 | \end{align*} 277 | 278 | \subsection{Some Integrals} 279 | \begin{align*} 280 | \Gamma(n+1) &= n! \\ 281 | \Gamma(z+1) &= z \Gamma(z) \\ 282 | \int_0^\infty x^n e^{-ax} dx &= \frac{n!}{a^{n+1}} \\ 283 | \int_0^\infty e^{-ax^b} dx &= a^{-1/b} \Gamma(1/b+1) \\ 284 | \int_0^\infty e^{-ax} \sin{bx} dx &= \frac{b}{a^2+b^2} \\ 285 | \int_0^\infty e^{-ax} \cos{bx} dx &= \frac{a}{a^2+b^2} \\ 286 | \int_{-\infty}^\infty e^{-ax^2+bx} dx &= \sqrt{\frac{\pi}{a}} e^{\frac{b^2}{4a}} \\ 287 | \int_0^\infty e^{-ax^2}x^n dx &= I_n(a)\\ 288 | I_0=\frac12 \sqrt{\frac{\pi}{a}}, I_1&=\frac{1}{2a}, I_2=\frac1{4a} \sqrt{\frac{\pi}{a}}, I_3=\frac{1}{2a^2} 289 | \end{align*} 290 | 291 | # A "Big" Test of Words 292 | 293 | **Source: `clipr::write_clip(stringi::stri_rand_lipsum(10))`** 294 | 295 | Lorem ipsum dolor sit amet, consequat lacinia in turpis tellus finibus. Luctus 296 | enim, urna fringilla pharetra eros. Conubia vestibulum vel mollis sem non donec 297 | per, eget sed. Mollis vulputate, vestibulum semper dolor senectus et. In leo, 298 | interdum sagittis litora. Sed amet, nec et sodales placerat risus quam vitae, 299 | maximus maecenas, ut. Risus enim adipiscing sodales eu nec nulla tempor eu. 300 | Turpis sed erat eget pellentesque. Blandit ut quisque a conubia ipsum non 301 | sociosqu neque. Dui quam commodo. Dolor ante lacus ligula tellus nunc egestas, 302 | ultricies. Laoreet condimentum sit. Vitae erat hac donec sem fames sed sed, 303 | consequat neque tempor sed. Suspendisse, nibh amet ac congue taciti elementum 304 | lectus, lacus egestas felis sem. Dictum, vulputate nulla semper, taciti amet 305 | conubia et ligula augue, nec. In tellus semper sed vestibulum. Nisi scelerisque 306 | cum tellus in sed quisque egestas ultrices neque maecenas, purus in. Feugiat dui 307 | vestibulum in quis leo nullam quis. Leo aliquet curae velit nascetur accumsan, 308 | aliquam. Eleifend, ut non id imperdiet senectus ut tempor neque. Sed ut dui 309 | suscipit. Facilisis nullam cubilia, dui, risus eu velit ullamcorper imperdiet. 310 | In ex tempus sed eu massa, tempus, vel. Sit non ligula vel, auctor lectus justo 311 | suspendisse malesuada dolor. Sed quis, at, porttitor habitant, nunc sed risus 312 | posuere. Ligula sed adipiscing fusce pretium mi, fames eu. Amet at tincidunt 313 | phasellus tincidunt nascetur tincidunt amet, vitae orci placerat enim. Vel 314 | dapibus ultrices aliquam. Sed facilisis sed posuere varius sodales blandit duis. 315 | Enim malesuada, phasellus bibendum blandit nisl ex. Lobortis quis varius sed 316 | venenatis eleifend eu, sollicitudin non tellus. Cubilia nullam mattis ut nam 317 | scelerisque ante sem cras. Donec, ligula diam non finibus mauris duis platea 318 | placerat, natoque, ac nullam. Fames nunc ac id risus vitae eget himenaeos. Nibh 319 | lectus in rutrum mi, quis ultrices magnis, elit at, morbi ligula. Faucibus dolor 320 | nunc, posuere in tortor eget enim potenti maximus malesuada. Consequat 321 | ullamcorper amet neque blandit sed magna. Ac enim nam leo non blandit 322 | scelerisque ut erat facilisis. Metus vestibulum bibendum in non. Ac, leo viverra 323 | orci risus sapien vitae. Luctus vitae cum, dictum ligula sapien. Vitae sem massa 324 | faucibus netus morbi habitasse mi vehicula. Sollicitudin aliquam non egestas 325 | litora cursus non diam. Lacus vehicula magna sit non lobortis non auctor 326 | sollicitudin feugiat rhoncus nostra vitae mollis magna. Magna commodo ut lacus 327 | aenean. Libero, porta ante. Justo quam consectetur risus varius. Blandit gravida 328 | eros tempus lectus nibh tortor faucibus conubia cursus conubia, egestas mi. 329 | Viverra torquent eu ut nostra elit magnis nisi quis. Ligula maecenas montes nibh 330 | habitant dignissim velit ut ut egestas pulvinar in ac. Aenean lorem luctus 331 | sociis primis fusce odio himenaeos. Dictum ligula curae pellentesque tempor 332 | nisl. Commodo gravida commodo. Dui, in sagittis cubilia, viverra mi fusce, dis. 333 | Praesent pellentesque sed sodales sit est turpis magna eu velit curabitur 334 | volutpat conubia hac finibus. Nec, dolor volutpat venenatis condimentum fusce. 335 | Suspendisse, convallis eleifend sed tortor. Dignissim pretium, quis. Erat sed 336 | sed sem eu sit, nunc quis phasellus tristique, donec. Suscipit adipiscing 337 | himenaeos amet et sem erat euismod. Vel mauris velit donec enim. Phasellus enim 338 | interdum nulla, mi vel sed sed aenean nam aliquam inceptos. Nulla habitant ut 339 | condimentum quisque dolor. Finibus orci ornare ac iaculis ipsum ex. Vestibulum 340 | diam dictum amet non. Tempus habitant tincidunt condimentum non. Pulvinar 341 | sociosqu consectetur malesuada malesuada eleifend urna litora vestibulum nisl 342 | penatibus. Ac a porta donec urna massa ut varius placerat montes vitae. Per 343 | dolor eget vitae suspendisse libero vitae. Adipiscing maecenas aliquam odio 344 | felis. Litora auctor dolor. Et et vel, et id orci. Non nec amet facilisis 345 | gravida vitae quis condimentum torquent? Sed mi ipsum tellus proin sed, eget, 346 | ultricies dolor, sed. Et eu scelerisque id commodo, nulla nec dictumst nec. 347 | Molestie maximus interdum imperdiet lacus et. Finibus lorem mi lectus, non, 348 | nulla aliquam est sed? Ridiculus libero, posuere dolor blandit elementum eros 349 | neque. Fusce odio vivamus placerat non, class ut eu. Et eget molestie maximus 350 | neque in montes ut dui tincidunt id. Id mauris sed quisque mauris non non in 351 | condimentum mattis. In pellentesque conubia netus volutpat vulputate at 352 | pellentesque, proin, nec. Nunc praesent mauris, quis mi fringilla dictum 353 | scelerisque diam dui in. Parturient cursus quis quam habitasse diam sed, leo 354 | vitae hac, ac sollicitudin, purus. Erat dolor aenean quam lectus scelerisque 355 | laoreet. Eros proin sapien ultricies, maximus, orci libero id, vestibulum nulla. 356 | Vulputate sed facilisis eget sagittis. Accumsan dolor, mauris nulla posuere 357 | tincidunt turpis risus laoreet, interdum. Nisl pretium vestibulum eu placerat. 358 | Accumsan odio nec sapien molestie id. Fusce id nunc varius erat suspendisse 359 | porta nulla eget arcu urna. Nec himenaeos nullam per. Sed nascetur porttitor 360 | neque lectus senectus mi lorem. In, nostra sed vel laoreet velit tempor suscipit 361 | ac ornare. Ac, sed, in eu lorem vivamus iaculis scelerisque, ut neque! Dui, ut 362 | sed nec consequat ullamcorper ipsum. In vel commodo aliquam mus, sem sed sit eu. 363 | Id duis iaculis. Suspendisse sed sed, ut maecenas. Natoque netus litora sed 364 | mauris lobortis quam sagittis, elementum. Pellentesque suscipit erat magna proin 365 | id, nam mi cras volutpat aptent tempus. Enim lacus phasellus sed, donec 366 | ridiculus vel et. Odio in, in dictum amet cursus himenaeos semper et ante. 367 | Consectetur nunc sed et ante nibh sed, quam egestas, vulputate ac. Faucibus 368 | pretium eu lorem dolor sed curae a interdum. Ultrices iaculis quisque at 369 | vulputate quis eu ante platea suscipit eget. Mauris non vitae dolor, iaculis nec 370 | metus donec, sed nibh, sed a. Torquent et tellus ac ante et non condimentum 371 | justo, varius. Eu ac bibendum fermentum at tincidunt netus at amet sit. Nisi 372 | pretium nostra. Purus molestie vivamus risus commodo sed sit. Tortor, 373 | suspendisse tristique eu tempor eros? Cum nibh, magna in erat sed semper vel 374 | tincidunt amet. Semper, porta, aenean orci ut, ullamcorper tincidunt. Etiam 375 | mauris suspendisse gravida arcu dui vitae. Platea, sodales velit, habitant 376 | tincidunt nulla eu praesent. Eros sociosqu maecenas quis dolor egestas consequat 377 | ligula consectetur netus amet. Arcu, laoreet finibus facilisi primis vulputate 378 | erat in nec. Leo aenean cubilia parturient amet ornare sed sed. Proin, volutpat, 379 | nisi ut metus ut in. Facilisis faucibus nunc, justo lorem dictumst penatibus. 380 | Conubia eu posuere vivamus et class, primis ac nec, hendrerit. Mollis sed 381 | primis. Vitae mus conubia pellentesque. Nunc in accumsan dignissim. Tristique 382 | himenaeos lorem adipiscing fermentum ornare. Mus dapibus commodo. Convallis 383 | massa inceptos ornare. Fames cum ante finibus netus aliquam egestas. 384 | Sollicitudin vel sodales et ut cras. Vitae iaculis facilisis euismod ligula leo 385 | et sit rutrum porttitor sodales in dui, sed tellus. Sed in est egestas eget 386 | auctor nec turpis. Condimentum maecenas, dolor fusce dictumst. Tempor, justo, 387 | sed magnis interdum interdum id potenti mus penatibus. Vitae magna rutrum netus. 388 | Platea non diam fames metus nisl convallis suspendisse. Ac quisque quis id 389 | cubilia, porta, et nam quam fermentum elit. Et malesuada taciti sagittis lacus 390 | lacus erat magnis. Nulla eros nec litora vestibulum nam et rutrum mollis maximus 391 | accumsan. Nibh ut ridiculus. Donec praesent, est sed semper consequat leo 392 | egestas interdum, vel penatibus. Arcu nec leo orci aenean sapien. Mi, nisi massa 393 | donec vulputate gravida. Dui conubia ipsum. Aliquam feugiat vestibulum nostra 394 | pellentesque donec. Dapibus efficitur integer in, condimentum justo quam sociis, 395 | eu. Aenean sollicitudin nulla sed ante pellentesque est class. Sit, nec egestas 396 | urna quis aptent pretium nibh feugiat imperdiet eu sodales. Pellentesque varius 397 | et consequat a aliquet, ut duis maximus nec. Ac ac pharetra himenaeos felis, ut 398 | morbi amet diam non. Class, venenatis venenatis mollis sed. Ipsum ut elementum 399 | sem luctus aliquet augue! Aenean at, ligula tempus urna litora. Volutpat 400 | consequat eu auctor eu. Aliquam accumsan tincidunt amet ac in felis dignissim, 401 | aliquam, tincidunt congue. Viverra et amet nulla pellentesque et. Ipsum sed 402 | aliquam non. Lacinia, cras tortor vel ante ante ac curae laoreet, ipsum sodales. 403 | Ligula metus ac lacinia sagittis in fusce fames montes in habitasse, quam. Nunc, 404 | id! Cubilia varius eget, gravida quis phasellus pretium ex dictumst. Sit, 405 | mauris, in lacinia cubilia vehicula non maximus. Velit sed, aliquam fringilla 406 | nibh duis dolor ac parturient lorem finibus. Non amet magna pretium, montes 407 | tortor, tincidunt, ante interdum vitae vitae. Velit vitae dignissim nulla eu 408 | nunc ullamcorper. Penatibus convallis nam eu eu augue. Pellentesque rutrum justo 409 | finibus enim pulvinar libero pharetra convallis curabitur. Non velit 410 | pellentesque amet est. Felis curae natoque, conubia curabitur dictum eros, nisl 411 | nibh, sed nisi efficitur dapibus. Eu et auctor nostra et. Fermentum libero dolor 412 | nibh vitae metus in elit hac vulputate! Tempus id tempor netus vestibulum 413 | lectus et, donec! Habitasse arcu pulvinar viverra eleifend gravida dui sit 414 | volutpat in inceptos. Quis nibh elit purus ac ultrices. Lacinia, cursus 415 | parturient ut purus et, et ullamcorper quis viverra et nulla in. Ac semper 416 | risus. Est vel dapibus vitae aliquet felis ullamcorper ut augue cubilia blandit 417 | ipsum. Vitae porttitor eros dignissim neque habitant habitasse laoreet erat. 418 | Etiam diam elit vitae vel dui. Vitae gravida felis ante platea eget vestibulum 419 | tristique, in suscipit ac. Lacus convallis neque fermentum primis taciti duis 420 | non, vitae euismod, est velit porttitor libero ridiculus. Iaculis quis nam 421 | viverra ac aliquet urna montes. Sed congue accumsan, est lacus proin sed 422 | pellentesque facilisis ac. Amet ipsum penatibus ex dolor tincidunt massa. Dictum 423 | nec vestibulum et vel ultricies potenti ligula himenaeos ac eu pellentesque. 424 | Nascetur mi ut tortor orci? Nascetur at cubilia finibus luctus, in maximus dolor 425 | porta. Proin porttitor tincidunt in suscipit et, class ac eu, sed fames. Quisque 426 | habitant, venenatis nec pulvinar ante ad lobortis fames a dictumst maecenas 427 | dictumst nisl sed. Conubia conubia platea lectus sem ut vitae proin nisl. Orci 428 | curae, per dolor lacus mollis. Posuere lacinia ultrices at tempor, aliquam 429 | tellus quam, sed enim. Aliquet a sem semper duis etiam suspendisse, eget enim et 430 | dolor cras. In porta turpis sit imperdiet eros sed vitae est. Sed vehicula 431 | mauris vivamus. Consectetur lectus urna mi penatibus. Ut consectetur erat ac 432 | justo habitasse praesent primis. Erat at tempor nam augue nulla ut ridiculus 433 | rhoncus, dapibus. Urna eros quam ut, nulla finibus mauris interdum mauris justo. 434 | Vestibulum hac adipiscing nunc sagittis ligula, varius enim a. Amet, feugiat 435 | nulla mauris netus aptent diam. Ut malesuada nulla condimentum nam dignissim. 436 | Nec magna volutpat, magna in. Fringilla lacinia, quis nunc sit enim, massa nec 437 | tristique a scelerisque ac pellentesque sed. Penatibus tristique, quis laoreet 438 | laoreet sollicitudin interdum himenaeos donec est commodo. Per maximus tempor 439 | tristique commodo at, curae a ultricies urna. Vel fringilla donec non velit 440 | maximus diam id ac. Aliquam risus integer, massa, non. Magna commodo turpis nunc 441 | tristique mollis tristique. Malesuada purus quis ut taciti vulputate sed et 442 | auctor. Mauris ex id primis feugiat nec. In sed mattis tempus risus, amet nulla 443 | penatibus augue magna lacus laoreet. Fermentum phasellus rutrum, mollis pharetra 444 | nullam vel nascetur leo himenaeos dolor pulvinar. Mollis nostra nullam 445 | phasellus, a suscipit nibh ultricies. Cubilia, lorem nulla orci turpis amet 446 | inceptos ad rutrum proin vitae. Ipsum auctor metus mauris non a id, habitasse, 447 | porttitor tincidunt. Nullam nam nunc ullamcorper morbi nam facilisis fusce, non 448 | habitant cubilia nec euismod. Lectus quis accumsan neque habitasse sed leo. 449 | Lectus sed per venenatis sed accumsan viverra malesuada, diam. Ut dui, porta, 450 | blandit ut vestibulum. Volutpat venenatis vitae, suscipit tempor amet venenatis. 451 | Sed mi dui tristique non ligula, ac ridiculus sit parturient. Ut, nibh, et 452 | taciti, at sed bibendum orci potenti, et. Egestas, condimentum laoreet donec, 453 | pharetra nec. Ut quis faucibus sed. Rutrum quis lorem in ut. Sollicitudin, 454 | inceptos posuere parturient class magnis neque id sed etiam. Pulvinar finibus 455 | ullamcorper, scelerisque imperdiet conubia et vitae. Aliquet tortor mi sed 456 | commodo senectus ante nunc ut mattis ornare cursus tempus. 457 | -------------------------------------------------------------------------------- /cheat-sheet-example.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/tonyelhabr/cheat-sheet-rmarkdown/2dc147aabbf0dfb9f6480f91ad01fda6adfd894f/cheat-sheet-example.pdf -------------------------------------------------------------------------------- /cheat-sheet-rmarkdown.Rproj: -------------------------------------------------------------------------------- 1 | Version: 1.0 2 | 3 | RestoreWorkspace: Default 4 | SaveWorkspace: Default 5 | AlwaysSaveHistory: Default 6 | 7 | EnableCodeIndexing: Yes 8 | UseSpacesForTab: Yes 9 | NumSpacesForTab: 2 10 | Encoding: UTF-8 11 | 12 | RnwWeave: Sweave 13 | LaTeX: pdfLaTeX 14 | -------------------------------------------------------------------------------- /template.tex: -------------------------------------------------------------------------------- 1 | 2 | % Reference: https://tex.stackexchange.com/questions/8827/preparing-cheat-sheets/8915 3 | 4 | % Package imports. 5 | \documentclass[10pt,landscape]{article} 6 | \usepackage{multicol} 7 | \usepackage{calc} 8 | \usepackage{ifthen} 9 | \usepackage[landscape, a4paper]{geometry} 10 | \usepackage{amsmath,amsthm,amsfonts,amssymb} 11 | \usepackage{color,graphicx,overpic} 12 | \usepackage{hyperref} 13 | 14 | % Sets page margins. 15 | \geometry{top=.2in,left=.2in,right=.2in,bottom=.2in} 16 | 17 | % Turns off header and footer. 18 | \pagestyle{empty} 19 | 20 | % Redefine section commands to use less space and have smaller text. 21 | % (Can change font size if `\tiny` is too small. 22 | % See http://www.sascha-frank.com/latex-font-size.html as a reference.) 23 | \makeatletter 24 | \renewcommand{\section}{\@startsection{section}{1}{0mm}% 25 | {-0.5ex plus -.5ex minus -.2ex}% 26 | {-0.5\baselineskip}% 27 | {\normalfont\tiny\bfseries}} 28 | \renewcommand{\subsection}{\@startsection{subsection}{2}{0mm}% 29 | {-0.5ex plus -.5ex minus -.2ex}% 30 | {-0.5\baselineskip}% 31 | {\normalfont\tiny\bfseries}} 32 | \renewcommand{\subsubsection}{\@startsection{subsubsection}{3}{0mm}% 33 | {-0.5ex plus -.5ex minus -.2ex}% 34 | {-0.5\baselineskip}% 35 | {\normalfont\tiny\bfseries}} 36 | \renewcommand{\paragraph}{\@startsection{paragraph}{4}{0mm}% 37 | {-0.5ex plus -.5ex minus -.2ex}% 38 | {-0.5\baselineskip}% 39 | {\normalfont\tiny\bfseries}} 40 | \makeatother 41 | 42 | % No section numbers. 43 | \setcounter{secnumdepth}{0} 44 | 45 | % Minimal paragraph indenting and spacing. 46 | \setlength{\parindent}{0pt} 47 | \setlength{\parskip}{0pt plus 0.5ex} 48 | 49 | % Canonical "init" statement. 50 | \begin{document} 51 | 52 | % Don't start new paragraphs if you don't need to. 53 | \raggedright 54 | 55 | % Font size. 56 | \tiny 57 | 58 | % Specifying number of columns. 59 | % Asterisk "*" here to force the left-most column to fill first, then the next, ect. 60 | % (Otherwise, all columns would fill down "equally". 61 | \begin{multicols*}{4} 62 | 63 | % Can play around with these as desired. 64 | \setlength{\columnseprule}{0.25pt} 65 | \setlength{\premulticols}{0.25pt} 66 | \setlength{\postmulticols}{0.25pt} 67 | \setlength{\multicolsep}{0.25pt} 68 | \setlength{\columnsep}{0.25pt} 69 | 70 | % This is the "magic" pandoc variable. (This is where your Rmarkdown document is inserted.) 71 | $body$ 72 | 73 | % `\end` statements to match the `\begin`s. 74 | \end{multicols*} 75 | 76 | \end{document} --------------------------------------------------------------------------------