├── .gitattributes ├── CS345 - Algorithms - II ├── Assignments and solutions │ ├── assgn1_soln.pdf │ ├── assgn2_soln.pdf │ ├── assgn3_soln.pdf │ ├── assgn4_soln.pdf │ ├── assn1 (2).pdf │ ├── assn2 (2).pdf │ ├── assn3 (2).pdf │ └── assn4 (2).pdf ├── Papers │ ├── final_solutions.pdf │ ├── midsem_soln.pdf │ ├── q1_soln.pdf │ └── q2_soln.pdf └── Practice sheets │ ├── Practice_sheet_DFS_SCCgraphs_with_ans.pdf │ ├── Practice_sheet_Greedy_algorithms.pdf │ ├── Practice_sheet_Maximum_Flow.pdf │ ├── Practice_sheet_amortized_analysis.pdf │ └── Practice_sheet_dyn_prog_with_answers.pdf ├── CS646 - Parallel Algorithms └── parallel - all papers.pdf ├── MSO201 - Probability & Statistics ├── 2022-23-Even │ ├── Lecture_notes │ │ ├── lec1-2.pdf │ │ ├── lec10.pdf │ │ ├── lec11.pdf │ │ ├── lec12.pdf │ │ ├── lec13.pdf │ │ ├── lec14.pdf │ │ ├── lec15.pdf │ │ ├── lec16.pdf │ │ ├── lec17.pdf │ │ ├── lec18.pdf │ │ ├── lec19.pdf │ │ ├── lec20.pdf │ │ ├── lec21.pdf │ │ ├── lec22.pdf │ │ ├── lec23.pdf │ │ ├── lec24.pdf │ │ ├── lec25.pdf │ │ ├── lec26.pdf │ │ ├── lec27.pdf │ │ ├── lec28.pdf │ │ ├── lec29.pdf │ │ ├── lec3-5.pdf │ │ ├── lec30.pdf │ │ ├── lec31.pdf │ │ ├── lec32.pdf │ │ ├── lec33.pdf │ │ ├── lec34.pdf │ │ ├── lec35.pdf │ │ ├── lec6.pdf │ │ ├── lec7-8.pdf │ │ └── lec9.pdf │ ├── Quiz-1_solution.pdf │ ├── Quiz-2_solution.pdf │ ├── Quiz-3_solution.pdf │ ├── endsem_solution.pdf │ ├── midsem_solution.pdf │ └── problem___solutions_on_probability___statistics.pdf └── Other PYQs │ ├── 2012.pdf │ ├── 2014 MITRA.pdf │ ├── 2016.pdf │ ├── 2021.pdf │ ├── 2022.pdf │ ├── Endsem_2020 │ ├── Endsem1 2020.pdf │ ├── Endsem1_solution 2020.pdf │ ├── Endsem2 2020.pdf │ ├── Endsem2_solution 2020.pdf │ ├── Endsem3_solution 2020.pdf │ └── Endsems3 2020.pdf │ ├── end sem amit mitra.pdf │ ├── mid sem amit mitra.pdf │ ├── quiz 1 amit mitra 2013.pdf │ └── quiz 2 amit.pdf ├── MTH204A- Abstract Algebra └── 2022-23 - Even │ ├── Problem Sets │ ├── PS-1.pdf │ ├── PS-2.pdf │ ├── PS-3.pdf │ ├── PS-4.pdf │ ├── PS-5.pdf │ ├── PS-6.pdf │ ├── PS-7.pdf │ └── PS-8.pdf │ ├── midsem-23.pdf │ ├── mth204-endsem-23.pdf │ ├── mth204_herstein(Topics in Algebra).pdf │ ├── notes.pdf │ ├── quiz-1-mth204-23.pdf │ └── quiz-2-mth204-23.pdf ├── MTH301A- Analysis ├── 2020-21-Even │ ├── Assignments │ │ ├── 1610939924_Assignment-1.pdf │ │ ├── 1611509453_Assignment-2.pdf │ │ ├── 1612099902_Assignment-3.pdf │ │ ├── 1612813317_Assignment-4a.pdf │ │ ├── 1612813317_Assignment-4b.pdf │ │ ├── 1613418530_Assignment-5.pdf │ │ ├── 1615534320_Assignment-7.pdf │ │ ├── 1615986931_Assignment_8.pdf │ │ ├── 1616653203_Assignment-9.pdf │ │ ├── 1617298203_Assignment-10.pdf │ │ ├── 1617817808_Assignment-11.pdf │ │ ├── 1618769843_Assignment-12.pdf │ │ ├── Assignment-1(discussion).pdf │ │ ├── Assignment-10-discussion.pdf │ │ ├── Assignment-11_discussion.pdf │ │ ├── Assignment-12-hints-solutions.pdf │ │ ├── Assignment-2(Q3-solution).pdf │ │ ├── Assignment-2(discussion).pdf │ │ ├── Assignment-3(discussion).pdf │ │ ├── Assignment-4a (discussion).pdf │ │ ├── Assignment-4b-solution.pdf │ │ ├── Assignment-5-evaluation_solution.pdf │ │ ├── Assignment-5-solution-hint.pdf │ │ ├── Assignment-6.pdf │ │ ├── Assignment-7-solution-hints.pdf │ │ ├── Assignment-9(discussion)pdf.pdf │ │ └── Assignment_8-discussion.pdf │ ├── First-Course-Handout-MTH301A.pdf │ ├── Lectures │ │ ├── Lecture-10.pdf │ │ ├── Lecture-11.pdf │ │ ├── Lecture-12.pdf │ │ ├── Lecture-13.pdf │ │ ├── Lecture-14.pdf │ │ ├── Lecture-15_0.pdf │ │ ├── Lecture-16.pdf │ │ ├── Lecture-17.pdf │ │ ├── Lecture-18.pdf │ │ ├── Lecture-19.pdf │ │ ├── Lecture-20.pdf │ │ ├── Lecture-21.pdf │ │ ├── Lecture-22.pdf │ │ ├── Lecture-23.pdf │ │ ├── Lecture-6.pdf │ │ ├── Lecture-7.pdf │ │ ├── Lecture-8.pdf │ │ ├── Lecture-9.pdf │ │ ├── MTH301-Lecture-1_0.pdf │ │ ├── MTH301-Lecture-2.pdf │ │ ├── MTH301-Lecture-3-update.pdf │ │ └── MTH301-Lectures-4-5.pdf │ ├── Midsem │ │ ├── Midsem 2020.pdf │ │ └── Midsem_sol 2020.pdf │ └── Supplementary_Readings │ │ ├── Cantor-set.pdf │ │ ├── Completion_of_metric_space.pdf │ │ ├── Dini_s_theorem.pdf │ │ └── Interesting-paper-Cantor-set.pdf └── 2021-22-Even │ ├── 301-noteslecture.pdf │ ├── Assgn 1[49325].pdf │ ├── Assgn 2[50446].pdf │ ├── Assgn 3[50869].pdf │ ├── Assgn 4[54239].pdf │ ├── Assgn 5[57238].pdf │ ├── Assgn 6[60011].pdf │ ├── Assgn 7[68621].pdf │ ├── Assgn 8[64455].pdf │ ├── Assgn 9[68203].pdf │ ├── Assignment-5-7-8.pdf │ ├── DocScanner 5 Mar 2022 23-48.pdf │ ├── FCH_2022[48527].pdf │ ├── Limsup and Liminf[50445].pdf │ ├── Metric Space[54242].pdf │ ├── MidSemQ2.pdf │ ├── MidSemQ3.pdf │ ├── MidSemQ4.pdf │ ├── Mid_Sem.pdf │ ├── N. L. Carothers - Real analysis (2000, Cambridge University Press) - libgen.lc.pdf │ ├── NZQ.pdf │ ├── Notes 2-Reals[49324].pdf │ ├── Q1_1.png │ ├── Q1_2.png │ ├── Q1_3.png │ ├── Q1_4.png │ ├── Q1_5.png │ ├── R. Bartle, D. Sherbert - Instructors Manual - Introduction to Real Analysis-John Wiley _ Sons (2010).pdf │ ├── Robert G. Bartle, Donald R. Sherbert - Introduction to real analysis (1999, Wiley) - libgen.lc.pdf │ ├── Terence Tao - Analysis I (Volume 1) -Hindustan Book Agency (2006).pdf │ ├── Walter Rudin - Principles of mathematical analysis-McGraw-Hill (1976).djvu │ ├── Walter Rudin - Solutions Manual to Principles of Mathematical Analysis (1976, McGraw-Hill Science Engineering Math) - libgen.lc.pdf │ └── mth301-remain part.pdf ├── MTH302A- Set theory and logic └── 2021-22-Odd │ ├── Final Exam Solutions.pdf │ ├── Final Exam.pdf │ ├── Homework 1--36.pdf │ ├── Lectures 1-28.pdf │ ├── Midsem solutions.pdf │ ├── Practice Final Solutions.pdf │ ├── Practice Final.pdf │ ├── Practice Midsem solutions.pdf │ └── Solutions 1--36.pdf ├── MTH305A - Several Variable Calculus & Differential Geometry ├── 2022-23-Odd │ ├── (Dover Books on Mathematics) Manfredo P. do Carmo - Differential Geometry of Curves and Surfaces-Dover Publications (2016).pdf │ ├── Adobe Scan Sep 05, 2022.pdf │ ├── Ass-3.pdf │ ├── Assignment 1[102710].pdf │ ├── Assignment 2[106227].pdf │ ├── Assignment 3[109774].pdf │ ├── Assignment 4[113923].pdf │ ├── Assignment 5-sol[116281].pdf │ ├── Assignment 5[116279].pdf │ ├── Assignment 6[122951].pdf │ ├── Assignment 7[123469].pdf │ ├── Assignment 8[124598].pdf │ ├── DocScanner Sep 15, 2022 12-01 AM.pdf │ ├── Elementary Differential Geometry ( PDFDrive ).pdf │ ├── FCH[105836].pdf │ ├── Instructor_s Solutions Manual to Elementary Differential Geometry ( PDFDrive ).pdf │ ├── Jianfei Shen - Calculus on manifolds. A Solution Manual for Spivak-The University of New South Wales (2010).pdf │ ├── Michael Spivak - Calculus On Manifolds_ A Modern Approach To Classical Theorems Of Advanced Calculus-Westview Press (1971).pdf │ ├── Midsem_solution[127045].pdf │ ├── Quiz 1_Sol[110222].pdf │ ├── Quiz 2 notes │ │ ├── 20220908_115817.jpg │ │ ├── 20220908_115819.jpg │ │ ├── 20220908_115823.jpg │ │ ├── 20220908_115827.jpg │ │ ├── 20220908_115830.jpg │ │ ├── 20220908_115832.jpg │ │ ├── 20220908_115835.jpg │ │ ├── 20220908_115838.jpg │ │ ├── 20220908_115841.jpg │ │ ├── 20220908_115845.jpg │ │ ├── 20220908_115848.jpg │ │ ├── 20220908_115851.jpg │ │ ├── 20220908_115854.jpg │ │ ├── 20220908_115856.jpg │ │ ├── 20220908_115858.jpg │ │ ├── 20220908_115900.jpg │ │ ├── 20220908_115903 (1).jpg │ │ ├── 20220908_115903.jpg │ │ ├── 20220908_115905.jpg │ │ ├── 20220908_115908.jpg │ │ ├── 20220908_115912.jpg │ │ └── 20220908_115915.jpg │ ├── Quiz 2[122487].pdf │ ├── Quiz_sol 3[126310].pdf │ ├── Shifrin T. - Differential geometry_ a first course in curves and surfaces (2008).pdf │ ├── Tom M. Apostol - Mathematical Analysis, Second Edition-Addison Wesley (1974).pdf │ ├── assignment 4 sol[115303].pdf │ ├── calculus_on_manifolds_solutions-4-4 (1).pdf │ ├── mth305_1.jpg │ ├── mth305_2.jpg │ ├── mth305_3.jpg │ ├── old │ │ ├── Assignment_1.pdf │ │ ├── Curves_Assignment_1.pdf │ │ ├── Mid_sem_Solution.pdf │ │ └── Quiz_1_New.pdf │ └── spivak-calc-manifolds.pdf └── 2023-24-Odd │ ├── Assignment-3.pdf │ ├── Assignment-4.pdf │ ├── End-Sem_solutions.pdf │ ├── Mid_Sem_Solutions.pdf │ ├── Quiz_III_solutions.pdf │ ├── Quiz_II_solutions.pdf │ └── Quiz_I_solutions.pdf ├── MTH308B-Numerical Analysis and Scientific Computing └── 2023-24-Even │ ├── Lab_Assignments │ ├── Lab Assignment-2 │ │ ├── error1.jpg │ │ ├── error1.m │ │ └── output of error1.pdf │ ├── Lab Assignment-4 │ │ ├── MTH308_and_MTH308B_Lab_Assignment_4.pdf │ │ └── Sample solution code (matlab) of lab assignment-4 │ │ │ ├── Gauss_Jacobi1.m │ │ │ ├── Gauss_Seidal.m │ │ │ ├── SOR.m │ │ │ ├── output of GuassJacobi1.pdf │ │ │ ├── output of GuassSeidal.pdf │ │ │ └── output of SOR.pdf │ ├── Lab Assignment-5 │ │ ├── Bisection.m │ │ ├── MTH308_and_MTH308B_Lab_Assignment_5.pdf │ │ ├── Regula_Falsi.m │ │ ├── output of Bisection.pdf │ │ ├── output of Regula-Falsi.pdf │ │ ├── output of power_method.pdf │ │ └── power_method.m │ ├── Lab assignment -1 │ │ ├── MTH308_and_MTH308B_Lab_assigment_1.pdf │ │ └── Sample solution of lab assignment-1 │ │ │ ├── emach.m │ │ │ └── roots1.m │ ├── Lab assignment -3 │ │ ├── MTH308_and_MTH308B_Lab_Assignment_3.pdf │ │ └── Sample solution code (matlab) of lab assignment-3 │ │ │ ├── LU_Crout.m │ │ │ ├── LU_Doolittle.m │ │ │ ├── gausselim1.m │ │ │ ├── output of LU_Crout-1.pdf │ │ │ ├── output of LU_Crout-2.pdf │ │ │ ├── output of LU_Dolittle-1.pdf │ │ │ ├── output of LU_Dolittle-2.pdf │ │ │ ├── output of gausselim1-1.pdf │ │ │ ├── output of gausselim1-2.pdf │ │ │ └── output of gausselim1-3.pdf │ ├── Lab assignment -7 │ │ ├── Code testing example for Hermite polynomial.pdf │ │ ├── Code testing example for Newton divided difference formula.pdf │ │ ├── Code testing example for Newton method for system.pdf │ │ ├── Code testing example for Spline.pdf │ │ ├── MTH308_and_MTH308B_Lab_Assignment_7.pdf │ │ ├── Newton_divided_1.m │ │ ├── Newton_system_1.m │ │ ├── output of Newton_divided.pdf │ │ └── output of Newton_system.pdf │ ├── Lab assignment-6 │ │ ├── MTH308_and_MTH308B_Lab_Assignment_6.pdf │ │ └── Sample solution code (matlab) of lab assignment-6 │ │ │ ├── Fixed_point.m │ │ │ ├── Newton_Raphson.m │ │ │ ├── Output of Fixed_point.pdf │ │ │ ├── Secant.m │ │ │ ├── output of Newton-Raphson.pdf │ │ │ └── output of Secant.pdf │ ├── Lab assignment-8 │ │ ├── MTH308_and_MTH308B_Lab_Assignment_8.pdf │ │ └── Sample solution code(matlab) of lab assignment-8 │ │ │ ├── Hermite.m │ │ │ ├── Hermite_1.m │ │ │ ├── MTH308_and_MTH308B_Lab_Assignment_8.pdf │ │ │ ├── Spline_cubic_clamped.m │ │ │ ├── Spline_cubic_clamped_1.m │ │ │ ├── Spline_cubic_natural.m │ │ │ ├── Spline_cubic_natural_1.m │ │ │ ├── Spline_linear.m │ │ │ ├── Spline_linear_1.m │ │ │ ├── Spline_linear_graph.jpg │ │ │ ├── Spline_linear_graph_1.jpg │ │ │ ├── output of Hermite.pdf │ │ │ ├── output of Hermite_1.pdf │ │ │ ├── output of Spline_cubic_clamped.pdf │ │ │ ├── output of Spline_cubic_clamped_1.pdf │ │ │ ├── output of Spline_cubic_natural.pdf │ │ │ ├── output of Spline_cubic_natural_1.pdf │ │ │ ├── output of Spline_linear.pdf │ │ │ └── output of Spline_linear_1.pdf │ └── Lab assignment-9 │ │ └── MTH308_and_MTH308B_Lab_Assignment_9.pdf │ ├── Lecture Notes │ ├── First Course Handout │ │ └── MTH308_and_MTH308B_FCH.pdf │ ├── Lecture note 11 │ │ └── MTH308-Lecture-11.pdf │ ├── Lecture note 15 │ │ └── MTH308-Lecture-15.pdf │ ├── Lecture note 2 │ │ └── MTH308_Lecture-2.pdf │ ├── Lecture note 25 │ │ └── MTH308-Lecture-25.pdf │ ├── Lecture note-20 │ │ └── MTH308-Lecture-20.pdf │ ├── Lecture note-24 │ │ └── MTH308-Lecture-24.pdf │ ├── Lecture note-27, Lecture note-28(incomplete) │ │ ├── MTH308-Lecture-27.pdf │ │ └── MTH308-Lecture-28(Incomplete).pdf │ ├── Lecture notes 1-5 │ │ └── MTH308_updated till Lecture-5.pdf │ ├── Lecture notes 12 and 13 │ │ ├── MTH308-Lecture-12.pdf │ │ └── MTH308-Lecture-13.pdf │ ├── Lecture notes-21 │ │ └── MTH308-Lecture-21.pdf │ ├── Lecture notes-6,7 │ │ ├── MTH308-Lecture-6.pdf │ │ └── MTH308-Lecture-7.pdf │ ├── MTH308-Lecture-33.pdf │ ├── MTH308-Lecture-34.pdf │ ├── Practice problems-1 │ │ └── Practice problems1.pdf │ ├── Supplementary Notes on norms and convergence │ │ └── Supplimentary notes on linear lagebra, Kendall Atkinson.pdf │ ├── Supplementary notes for Lecture-25, Lecture-26 │ │ ├── MTH308-Lecture-26.pdf │ │ └── MTH308-Supplementary(Lecture-25).pdf │ ├── Updated lecture note (till lecture-4) │ │ └── MTH308_updated till Lecture-4.pdf │ ├── lecture note 10 │ │ └── MTH308-Lecture-10.pdf │ ├── lecture note 14 │ │ └── MTH308-Lecture-14.pdf │ ├── lecture note 38 (Numerical Differentiation) │ │ └── MTH308-Lecture-38 (Numerical Differentiation).pdf │ ├── lecture note-31-32 │ │ └── MTH308-Lecture-31-32.pdf │ ├── lecture notes 16-17 (single pdf file) │ │ └── MTH308-Lecture-16-17.pdf │ ├── lecture notes 18-19 (single pdf file) │ │ └── MTH308-Lecture-18-19.pdf │ ├── lecture notes 22 │ │ └── MTH308-Lecture-22.pdf │ ├── lecture notes 23 │ │ └── MTH308-Lecture23.pdf │ ├── lecture notes 29-30 │ │ ├── MTH308-Lecture-29.pdf │ │ └── MTH308-Lecture-30.pdf │ ├── lecture notes 31-35 │ │ ├── Lecture-31-32(rough).pdf │ │ ├── Lecture-33(rough).pdf │ │ ├── Lecture-34(rough).pdf │ │ ├── MTH308-Lecture-35(Simpson 1-3rd).pdf │ │ └── MTH308-Lecture-35(Trapozoidal).pdf │ ├── lecture notes 35(remaining), 36, 37 and sample solution code of Lab-9 │ │ ├── MTH308-Lecture-35(Simpson 1-3rd 1).pdf │ │ ├── MTH308-Lecture-36.pdf │ │ ├── MTH308-Lecture-37.pdf │ │ ├── Simpson_1_by_3.m │ │ ├── Trapozoidal.m │ │ └── Trapozoidal_2.m │ └── lecture notes 8-9 │ │ ├── MTH308-Lecture-8.pdf │ │ └── MTH308-Lecture-9.pdf │ ├── Papers │ ├── Sample solution of Quiz-1.pdf │ └── Sample solution of Quiz-2.pdf │ ├── numerical_analysis_atkinson.pdf │ └── scientific-computing-michael-t-heath.pdf ├── MTH403A-Complex Analysis └── 2023-24-Odd │ ├── Complex Analysis_Tarun Goyal.pdf │ ├── Quiz 1 solutions.pdf │ ├── Quiz 2 solutions.pdf │ ├── Solutions for End-Semester Examinations.pdf │ ├── Solutions for Mid-semester Examination.pdf │ └── pathway to complex analysis.pdf ├── MTH421A-Ordinary Differential Equations └── 2023-24-Even │ ├── Papers │ ├── Midsem.jpeg │ └── Quiz-1.jpeg │ ├── assignments │ ├── A31_A32_A33_merged.pdf │ ├── A6_compressed.pdf │ ├── A9.pdf │ ├── Assignment 1o.pdf │ ├── Assignment 4.pdf │ ├── Assignment 8.pdf │ ├── Assignment last.pdf │ ├── Assignment6.pdf │ └── ODE MTH421A A1.pdf │ └── lecture_notes │ ├── FirstCourseHandout.pdf │ ├── Mth421aw2_compressed (1).pdf │ ├── Mth421aw2_compressed.pdf │ ├── Mth421aw3 (1).pdf │ ├── ODE MTH412A_compressed.pdf │ ├── ODE MTH421A (1)_compressed.pdf │ ├── W10C3.pdf │ ├── W10_compressed.pdf │ ├── W12C1-2.pdf │ ├── W12C3.pdf │ ├── W3c2_compressed.pdf │ ├── W4C1_compressed.pdf │ ├── W4C3_compressed.pdf │ ├── W5C1_compressed.pdf │ ├── W5C2_compressed.pdf │ ├── W7C1.pdf │ ├── W7C2-3_compressed.pdf │ ├── W7C2.pdf │ ├── W8 C1_compressed.pdf │ ├── W8C3(1).pdf │ ├── W8C3.pdf │ ├── W9C1-2.pdf │ └── Week 11C1.pdf ├── MTH424 - Partial Differential Equations ├── An Introduction to Partial Differential Equations - Y. Pinchover, J. Rubenstein (Cambridge, 2005) WW.pdf ├── assignments │ ├── Assignment-1-MTH424.pdf │ ├── Assignment-2-MTH424.pdf │ ├── Assignment-3-MTH424.pdf │ ├── Assignment-4-MTH424 (1).pdf │ ├── Assignment-5-MTH424 (2).pdf │ └── Assignment-6-MTH424 (1).pdf ├── partial-differential-equations-by-evans.pdf ├── pde - all papers.pdf ├── quiz-1 solutions.pdf └── quiz-3 solutions.pdf ├── MTH430 - Numerical Analysis and Scientific Computing - II ├── Assignments │ ├── HW1.pdf │ ├── HW2.pdf │ └── HW3.pdf ├── Lab exams │ ├── MTH430_LE2.pdf │ ├── MTH430_LE3.pdf │ └── MTH430_LE4.pdf └── Papers │ └── nasc2- endsem.pdf ├── MTH436 - Basic Algebraic Geometry ├── FCH MTH436.pdf ├── assignments │ ├── MTH 436 PS 2 (1).pdf │ ├── MTH 436 Problem Set 3 (2).pdf │ ├── Problem Set 1.pdf │ ├── Problem Set 4.pdf │ └── Problem Set 5.pdf ├── books │ ├── AtiyahMacdonald.pdf │ ├── CurveBook.pdf │ ├── Hartshorne_engl.pdf │ └── UAG.pdf └── mth436- all papers.pdf ├── MTH442 - Time Series Analysis └── 2023-24-Even │ ├── Excercise │ ├── PS 1.pdf │ ├── PS 2.pdf │ ├── PS 3.pdf │ ├── PS 4.pdf │ ├── PS 5.pdf │ ├── PS 6.pdf │ ├── PS 7.pdf │ ├── Quiz2_sol.pdf │ ├── Solution_Q1.pdf │ ├── endsem_solution_MTH442.pdf │ ├── midsem_solution.pdf │ ├── soln_1.pdf │ ├── soln_2.pdf │ ├── soln_3.pdf │ ├── soln_4.pdf │ ├── soln_5.pdf │ ├── soln_6.pdf │ └── soln_7.pdf │ └── Lectures │ ├── L1,2.pdf │ ├── L10.pdf │ ├── L11.pdf │ ├── L12.pdf │ ├── L13.pdf │ ├── L14.pdf │ ├── L15.pdf │ ├── L16.pdf │ ├── L17.pdf │ ├── L18.pdf │ ├── L19.pdf │ ├── L20.pdf │ ├── L21.pdf │ ├── L22.pdf │ ├── L23.pdf │ ├── L24.pdf │ ├── L25.pdf │ ├── L26.pdf │ ├── L27.pdf │ ├── L28.pdf │ ├── L29.pdf │ ├── L3.pdf │ ├── L30.pdf │ ├── L31.pdf │ ├── L32.pdf │ ├── L33.pdf │ ├── L34.pdf │ ├── L35.pdf │ ├── L36.pdf │ ├── L4.pdf │ ├── L5.pdf │ ├── L6.pdf │ ├── L7.pdf │ ├── L8.pdf │ └── L9.pdf └── README.md /.gitattributes: -------------------------------------------------------------------------------- 1 | *.pdf filter=lfs diff=lfs merge=lfs -text 2 | 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Differential geometry_ a first course in curves and surfaces (2008).pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:64c52208201d403d31713d435d848e16d1e26924bbcb04c60c4ca6690598cea8 3 | size 1456819 4 | -------------------------------------------------------------------------------- /MTH305A - Several Variable Calculus & Differential Geometry/2022-23-Odd/Tom M. Apostol - Mathematical Analysis, Second Edition-Addison Wesley (1974).pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:ba2e63d9f370571ef6f43c99ad94db92497d1f9009c9dadccb64f7cad70207c6 3 | size 8189171 4 | -------------------------------------------------------------------------------- /MTH305A - Several Variable Calculus & Differential Geometry/2022-23-Odd/assignment 4 sol[115303].pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:b2300ac71bd137881fa2f01572e47f0bf2bd0942cc667089f9f206b207dfee6b 3 | size 667707 4 | -------------------------------------------------------------------------------- /MTH305A - Several Variable Calculus & Differential Geometry/2022-23-Odd/calculus_on_manifolds_solutions-4-4 (1).pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:34d358361f67af8b425ddef7e73b71f2f215ed2f0a7117f9e61a5f8c9ad21133 3 | size 534379 4 | -------------------------------------------------------------------------------- /MTH305A - 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Several Variable Calculus & Differential Geometry/2023-24-Odd/Quiz_III_solutions.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:fbf1f47b81d1922459586285ab865012960f9aa8c098935ef585ee0ff997d662 3 | size 383045 4 | -------------------------------------------------------------------------------- /MTH305A - Several Variable Calculus & Differential Geometry/2023-24-Odd/Quiz_II_solutions.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:86cec4fbc6c2fb01fb7b89876e248da1c6b3c660b43fbe79069cebce3dedc134 3 | size 147075 4 | -------------------------------------------------------------------------------- /MTH305A - Several Variable Calculus & Differential Geometry/2023-24-Odd/Quiz_I_solutions.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:312e23251b3b31766fe16dfe67fcd8b013c741497c3b18c2e7d51997b16c5e33 3 | size 141557 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-2/error1.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/mihirm21/mth_iitk/9a3527efeb9ba9afeff1023163db8f8a4f9b8b82/MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-2/error1.jpg -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-2/error1.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | a=input('Enter the point at which the derivative has to be calculated: '); 4 | n=input('Enter the total number of approximations: '); 5 | x=zeros(1,n); 6 | y=zeros(1,n); 7 | z=zeros(1,n); 8 | w=zeros(1,n); 9 | X_r=zeros(1,n); 10 | Y_r=zeros(1,n); 11 | for k=1:n 12 | h=10^(-k); 13 | %h=1/k; 14 | df=cos(a); 15 | df_h=(sin(a+h)-sin(a))/h; 16 | E=abs(df-df_h); 17 | x(k)=h; 18 | z(k)=df; 19 | w(k)=df_h; 20 | y(k)=E; 21 | X_r(n+1-k)=x(k); 22 | Y_r(n+1-k)=y(k); 23 | end 24 | format long 25 | fprintf("\t\t h \t\t\t\t\t f' \t\t\t\t f'_h \t\t\t\t Error \n"); 26 | A=[x ; z; w; y ;]'; 27 | disp(A); 28 | %grid on 29 | loglog(X_r, Y_r,'--ro'); -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-2/output of error1.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:cda806ab785d10892811b07ec40d5c1437b35d04c6787e65f518aa801b44e38c 3 | size 57610 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-4/MTH308_and_MTH308B_Lab_Assignment_4.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:4e86265df0dd5cb191f1122027a1276f3c1fc777ca7f391c5f19118f0d157f2e 3 | size 74893 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-4/Sample solution code (matlab) of lab assignment-4/Gauss_Jacobi1.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Giving all inputs 4 | n=input('\n Enter the numbr of equations: '); 5 | A=input('\n Enter the entries of the coefficient matrix row-wise: '); 6 | b=input('\n Enter the RHS given data of the system (as column vector) : '); 7 | x=input('\n Enter the initial guess (as column vector): '); 8 | m=input('\n Enter the maximum number of iteration: '); 9 | y=zeros(n,1); 10 | % Creating a matrix to store the results of each iteration 11 | X=zeros(n,m+1); 12 | % Storing the initial data in the first column of a matrix X 13 | X(:,1)=x; 14 | % Checking the necessary condition on the diagonal elements of A to run the iteration 15 | w=0; 16 | for i=1:n 17 | if A(i,i)==0 18 | w=w+1; 19 | fprintf("Gauss-Jacobi itereation can not be used. May need to do equations swapping. \n"); 20 | end 21 | end 22 | if w==0 23 | % Starting the iteration 24 | for k=1:m 25 | for i=1:n 26 | z=0; 27 | for j=1:n 28 | if (j~=i) 29 | z=z+A(i,j)*x(j); 30 | end 31 | end 32 | y(i)=(1/A(i,i))*(b(i)-z); 33 | end 34 | x=y; 35 | % Storing the results of each iteration in the matrix X 36 | X(:,k+1)=x; 37 | end 38 | % Printing the outputs 39 | fprintf("\n %d number of Gauss-Jacobi iterations are given as (columnwise):\n\n", m); 40 | % disp(X); 41 | % To get the output in 6 decimal places 42 | disp(cell2mat(compose('%10.6f',X))); 43 | fprintf("\n"); 44 | end -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-4/Sample solution code (matlab) of lab assignment-4/Gauss_Seidal.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Giving all inputs 4 | n=input('\n Enter the numbr of equations: '); 5 | A=input('\n Enter the entries of the coefficient matrix row-wise: '); 6 | b=input('\n Enter the RHS given data of the system (as column vector) : '); 7 | x=input('\n Enter the initial guess (as column vector): '); 8 | m=input('\n Enter the maximum number of iteration: '); 9 | % y=zeros(n,1); 10 | % Creating a matrix to store the results of each iteration 11 | X=zeros(n,m+1); 12 | % Storing the initial data in the first column of a matrix X 13 | X(:,1)=x; 14 | % Checking the necessary condition on the diagonal elements of A to run the iteration 15 | w=0; 16 | for i=1:n 17 | if A(i,i)==0 18 | w=w+1; 19 | fprintf("Gauss-Seidal itereation can not be used. May need to do equations swapping. \n"); 20 | end 21 | end 22 | if w==0 23 | % Starting the iteration 24 | for k=1:m 25 | for i=1:n 26 | z=0; 27 | for j=i+1:n 28 | z=z+A(i,j)*x(j); 29 | end 30 | u=0; 31 | for j=1:i-1 32 | u=u+A(i,j)*x(j); 33 | end 34 | x(i)=(1/A(i,i))*(b(i)-u-z); 35 | end 36 | % y=x; 37 | % Storing the results of each iteration in the matrix X 38 | X(:,k+1)=x; 39 | end 40 | % Printing the outputs 41 | fprintf("\n %d number of Gauss-Seidal iterations are given as (columnwise):\n\n", m); 42 | % disp(X); 43 | % To get the output in 6 decimal places 44 | disp(cell2mat(compose('%10.6f',X))); 45 | fprintf("\n"); 46 | end 47 | 48 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-4/Sample solution code (matlab) of lab assignment-4/SOR.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Giving all inputs 4 | n=input('\n Enter the numbr of equations: '); 5 | A=input('\n Enter the entries of the coefficient matrix row-wise: '); 6 | b=input('\n Enter the RHS given data of the system (as column vector) : '); 7 | x=input('\n Enter the initial guess (as column vector): '); 8 | m=input('\n Enter the maximum number of iteration: '); 9 | w=input('\n Enter a value of the SOR Parameter: '); 10 | y=zeros(n,1); 11 | % Creating a matrix to store the results of each iteration 12 | X=zeros(n,m+1); 13 | % Storing the initial data in the first column of a matrix X 14 | X(:,1)=x; 15 | % Checking the necessary condition for the parameters w of SOR method to run the iteration 16 | p=1; 17 | while (p==1) 18 | if (w > 0) && (w < 2) 19 | p=0; 20 | else 21 | p=1; 22 | fprintf("\n SOR iteration will not converge for this given value of the parameter w,\n" + ... 23 | " please enter another value of w that lies in the interval (0,2). w = "); 24 | w=input(''); 25 | end 26 | end 27 | if p==0 28 | % Checking the necessary condition on the diagonal elements of A to run the iteration 29 | v=0; 30 | for i=1:n 31 | if A(i,i)==0 32 | v=v+1; 33 | fprintf("SOR itereation can not be used. May need to do equations swapping. \n"); 34 | end 35 | end 36 | if v==0 37 | % Starting the iteration 38 | for k=1:m 39 | for i=1:n 40 | u=0; 41 | for j=1:i-1 42 | u=u+A(i,j)*y(j); 43 | end 44 | z=0; 45 | for j=i+1:n 46 | z=z+A(i,j)*x(j); 47 | end 48 | y(i)=(1-w)*x(i)+(w/A(i,i))*(b(i)-u-z); 49 | end 50 | x=y; 51 | % Storing the results of each iteration in the matrix X 52 | X(:,k+1)=x; 53 | end 54 | % Printing the outputs 55 | fprintf("\n %d number of SOR iterations are given as (columnwise):\n\n", m); 56 | % disp(X); 57 | % To get the output in 6 decimal places 58 | disp(cell2mat(compose('%10.6f',X))); 59 | fprintf("\n"); 60 | end 61 | end -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-4/Sample solution code (matlab) of lab assignment-4/output of GuassJacobi1.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:a66f5bcb0831cadbb13ff298bb13d0c83d5a78750c07d682f48e14d17c0b1e3a 3 | size 62941 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-4/Sample solution code (matlab) of lab assignment-4/output of GuassSeidal.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:54050862a62a01d502fe9a2eb8688e307e1f20105c45d18187bf860accb20ce0 3 | size 62636 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-4/Sample solution code (matlab) of lab assignment-4/output of SOR.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:2e276644b3174d1e0ba550d2b3e8335865ffeefae0d59b954a985932b7f8bd0a 3 | size 62862 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-5/Bisection.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Writing the function 4 | f=@(x) sqrt(x)-cos(x); 5 | fprintf("\n The given equation is: sqrt(x) - cos(x)=0. \n"); 6 | %f=@(x) x^3+4*x^2-10; 7 | % Checking the hypothesis of the method 8 | p=0; 9 | while (p==0) 10 | a=input('\n Enter the left end point of the interval: '); 11 | b=input('\n Enter the right end point of the interval: '); 12 | y_0=f(a); 13 | y_1=f(b); 14 | if y_0==0 15 | fprintf("\n A root of the given equation is %10.9f .\n", a); 16 | p=1; 17 | end 18 | if y_1==0 19 | fprintf("\n A root of the given equation is %10.9f .\n", b); 20 | p=1; 21 | end 22 | if y_0*y_1>0 23 | fprintf("\n Bisection method cannot locate any root in the interval [%.2f, %.2f].\n", a,b); 24 | fprintf("\n Restart the method by putting new initial guesses.\n"); 25 | end 26 | if y_0*y_1<0 27 | p=1; 28 | end 29 | end 30 | % Putting stopping criteria 31 | N=input('\n Enter the maximum number of iterations: '); 32 | eps=input('\n Enter the measure of accuracy (tolerance): '); 33 | % Data of iterations storing matrix 34 | X=zeros(1,5); 35 | % Starting iterations 36 | k=1; 37 | while (k<=N && p==1) 38 | x=(a+b)/2; 39 | y=f(x); 40 | X=[k a b x y]; 41 | if k==1 42 | fprintf("\n The Bisection iterations are given as:\n\n"); 43 | D=[' k ' ' a_k ' ' b_k ' ' x_k ' ' f(x_k) ']; 44 | disp(D); 45 | end 46 | disp(cell2mat(compose('%14.9f',X))); 47 | if y==0 48 | fprintf("\n A root of the given equation is %10.9f .\n", x); 49 | p=0; 50 | end 51 | if ((b-a)<= eps) 52 | fprintf("\n An approximate root (with tolerance %f) of the given equation is %10.9f .\n", eps, (a+b)/2); 53 | p=0; 54 | end 55 | if (y_0*y >0) 56 | a=x; 57 | y_0=y; 58 | else 59 | b=x; 60 | end 61 | k=k+1; 62 | end 63 | if k==N+1 64 | fprintf("\n Maximum number of iteraton reached. \n An Aapproximate root of the given equation is %10.9f.\n\n", x); 65 | end -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-5/MTH308_and_MTH308B_Lab_Assignment_5.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:d96b6fc98a3f9b984802304687ef03f8142ab7965ca1885019c1d2d06d0aed23 3 | size 116397 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-5/Regula_Falsi.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Writing the function 4 | f=@(x) sqrt(x)-cos(x); 5 | fprintf("\n The given equation is: sqrt(x) - cos(x)=0. \n"); 6 | %f=@(x) x-cos(x); 7 | %f=@(x) exp(x)-2; 8 | %f=@(x) sin(x)+x^2-1 9 | % Checking the hypothesis of the method 10 | p=0; 11 | while (p==0) 12 | a=input('\n Enter the left end point of the interval: '); 13 | b=input('\n Enter the right end point of the interval: '); 14 | y_0=f(a); 15 | y_1=f(b); 16 | if y_0==0 17 | fprintf("\n A root of the given equation is %f .\n", a); 18 | p=1; 19 | end 20 | if y_1==0 21 | fprintf("\n A root of the given equation is %f .\n", b); 22 | p=1; 23 | end 24 | if y_0*y_1>0 25 | fprintf("\n Regula-Falsi method cannot locate any root in the interval [%f, %f].\n", a,b); 26 | fprintf("\n Restart the method by putting new initial guesses.\n"); 27 | end 28 | if y_0*y_1<0 29 | p=1; 30 | end 31 | end 32 | % Putting stopping criteria 33 | N=input('\n Enter the maximum number of iterations: '); 34 | % eps=input('\n Enter the measure of accuracy: '); 35 | % Data of iterations storing matrix 36 | X=zeros(1,5); 37 | % Starting iterations 38 | k=1; 39 | while (k<=N && p==1) 40 | x=a-(y_0*(b-a))/(y_1-y_0); 41 | y=f(x); 42 | X=[k a b x y]; 43 | if k==1 44 | fprintf("\n The Regula-Falsi iterations are given as:\n\n"); 45 | D=[' k ' ' a_k ' ' b_k ' ' x_k ' ' f(x_k) ']; 46 | disp(D); 47 | end 48 | disp(cell2mat(compose('%14.9f',X))); 49 | if y==0 50 | fprintf("\n A root of the given equation is %f .\n", x); 51 | p=0; 52 | end 53 | if (y_0*y >0) 54 | a=x; 55 | y_0=y; 56 | else 57 | b=x; 58 | y_1=y; 59 | end 60 | k=k+1; 61 | end 62 | if k==N+1 63 | fprintf("\n Maximum number of iteraton reached. \n An Aapproximate root of the given equation is %10.9f.\n\n", x); 64 | end -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-5/output of Bisection.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:0c691e6116540dfc9a3030cd5cdd32087c5ff68bc3a1f0e73778ffa352091cee 3 | size 60169 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-5/output of Regula-Falsi.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:2f5ecd6719ab0c633676ab94d5cf638f140d0651702a60d906c4b47f2275c0b3 3 | size 59740 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-5/output of power_method.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:8f40d4856dca2e8bd3ee70268f44ecfe14d0b92d57a175dbdec2e1b36d91ee42 3 | size 59755 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab Assignment-5/power_method.m: -------------------------------------------------------------------------------- 1 | clear; 2 | clc, 3 | n=input('\n Enter the dimension of the square matrix : '); 4 | A=input('\n Enter the entries of the matrix (row-wise) : '); 5 | x=input ('\n Enter an initial guess (as a column vector) : '); 6 | TOL=input('\n Enter the tolerance : '); 7 | N=input('\n Enter the maximum number of iterations : '); 8 | fprintf("\n The given matrix is:\n"); 9 | disp(A); 10 | i=1; 11 | while i<=n 12 | if abs(x(i))==norm(x,"inf") 13 | p=i; 14 | i=n; 15 | end 16 | i=i+1; 17 | end 18 | z=x; 19 | Mu=0; 20 | k=1; 21 | while k<=N 22 | y=A*x; 23 | mu=y(p); 24 | Mu=[Mu mu]; 25 | i=1; 26 | while i<=n 27 | if abs(y(i))==norm(y,"inf") 28 | p=i; 29 | i=n; 30 | end 31 | i=i+1; 32 | end 33 | if y(p)==0 34 | fprintf("An eigen vector is: \n"); 35 | disp(x); 36 | fprintf("0 is an eigen value.\n" ); 37 | k=N; 38 | end 39 | ERR=norm((x-y./y(p)), "inf"); 40 | x=y./y(p); 41 | z=[z x]; 42 | if ERR1) 6 | i=i+1; 7 | d=2^(-i); 8 | x=1+d; 9 | end 10 | 11 | fprintf('\n The machine epsilon is 2^(-%d).', i-1); 12 | fprintf('\n From the theory, we conclude that the manitssa has %d bits in this machine. \n\n', i-1); -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -1/Sample solution of lab assignment-1/roots1.m: -------------------------------------------------------------------------------- 1 | %clc; 2 | %clear; 3 | a=input('Enter the co-efficient of the quadratic term of the equation: '); 4 | while (a==0) 5 | a=input('Re-enter a non number for the co-efficient of the quadratic term of the equation: '); 6 | end 7 | 8 | b=input('Enter the co-efficient of the 1st degree term of the equation: '); 9 | c=input('Enter the co-efficient of the 0th degree term of the equation: '); 10 | while (c==0) 11 | c=input('Re-enter a non number for the the 0th degree term of the equation: '); 12 | end 13 | M=max([abs(a), abs(b), abs(c)]); 14 | a=a/M; 15 | b=b/M; 16 | c=c/M; 17 | if (a~=0 && c~=0 && b^2~=0 && 4*a*c~=0) 18 | if ((b^2-4*a*c)<0) 19 | if b==0 20 | x=0; 21 | else 22 | x=-b^2/(2*a); 23 | end 24 | y=sqrt(4*a*c-b^2)/(2*a); 25 | fprintf('Roots of the given equation are %f +i %f and %f -i %f respectively.\n', x, y, x, y) 26 | else 27 | x_1=(-b+sqrt(b^2-4*a*c))/(2*a); 28 | x_2=(-b-sqrt(b^2-4*a*c))/(2*a); 29 | fprintf('Roots of the given equation are %.5f and %.5f respectively.\n', x_1, x_2); 30 | fprintf('We can also the calculate the roots as:'); 31 | z_1=(2*c)/(-b-sqrt(b^2-4*a*c)); 32 | z_2=(2*c)/(-b+sqrt(b^2-4*a*c)); 33 | fprintf(' %.5f and %.5f respectively.\n', z_1, z_2); 34 | end 35 | else 36 | fprintf('There is and under-flow error for the inputs for either of the coefficients a and c. Please re-run the program with modified input values for the coefficients.\n '); 37 | end 38 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -3/MTH308_and_MTH308B_Lab_Assignment_3.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:772867fe6e022c1f471ca7e13415dd4b484c03922e93848cb8e59a94588d4bcf 3 | size 129124 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -3/Sample solution code (matlab) of lab assignment-3/LU_Crout.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | fprintf('\n'); 4 | n=input('Enter the dimension of the square matrix : '); 5 | a=input('Enter the entries the matrix rowwise: '); 6 | U=diag(ones(n,1)); 7 | L=zeros(n); 8 | fprintf("Given matrix is: \n"); 9 | disp(a); 10 | z=0; 11 | % Step-1 12 | if a(1,1)==0 13 | fprintf("Factorization is not possible. \n"); 14 | else 15 | L(1,1)=a(1,1); 16 | for j=2:n 17 | % Step-2 18 | L(j,1)=a(j,1)/U(1,1); 19 | U(1,j)=a(1,j)/L(1,1); 20 | end 21 | % Step-3 22 | for i=2:n-1 23 | % Step-4 24 | s=0; 25 | for k=1:i-1 26 | s=s+L(i,k)*U(k,i); 27 | end 28 | L(i,i)=(a(i,i)-s)/U(i,i); 29 | if L(i,i)==0 30 | z=1; 31 | fprintf("Factorization is not possible. \n"); 32 | else 33 | % Step-5 34 | for j=i+1:n 35 | t=0; 36 | for k=1:i-1 37 | t=t+L(j,k)*U(k,i); 38 | end 39 | L(j,i)=(a(j,i)-t)/U(i,i); 40 | r=0; 41 | for k=1:i-1 42 | r=r+L(i,k)*U(k,j); 43 | end 44 | U(i,j)=(a(i,j)-r)/L(i,i); 45 | end 46 | end 47 | if z==0 48 | % Step-6 49 | w=0; 50 | for k=1:n-1 51 | w=w+L(n,k)*U(k,n); 52 | end 53 | L(n,n)=(a(n,n)-w)/U(n,n); 54 | end 55 | end 56 | if z==0 57 | fprintf("Crout's LU decomposition of the givem matrix is: \n\n"); 58 | disp([L U]); 59 | % disp(L); 60 | % disp(U); 61 | end 62 | end -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -3/Sample solution code (matlab) of lab assignment-3/LU_Doolittle.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | fprintf('\n'); 4 | n=input('Enter the dimension of the square matrix : '); 5 | a=input('Enter the entries the matrix rowwise: '); 6 | L=diag(ones(n,1)); 7 | U=zeros(n); 8 | fprintf("Given matrix is: \n"); 9 | disp(a); 10 | z=0; 11 | % Step-1 12 | if a(1,1)==0 13 | fprintf("Factorization is not possible. \n"); 14 | else 15 | U(1,1)=a(1,1); 16 | for j=2:n 17 | % Step-2 18 | U(1,j)=a(1,j)/L(1,1); 19 | L(j,1)=a(j,1)/U(1,1); 20 | end 21 | % Step-3 22 | for i=2:n-1 23 | % Step-4 24 | s=0; 25 | for k=1:i-1 26 | s=s+L(i,k)*U(k,i); 27 | end 28 | U(i,i)=(a(i,i)-s)/L(i,i); 29 | if U(i,i)==0 30 | z=1; 31 | fprintf("Factorization is not possible. \n"); 32 | else 33 | % Step-5 34 | for j=i+1:n 35 | r=0; 36 | for k=1:i-1 37 | r=r+L(i,k)*U(k,j); 38 | end 39 | U(i,j)=(a(i,j)-r)/L(i,i); 40 | t=0; 41 | for k=1:i-1 42 | t=t+L(j,k)*U(k,i); 43 | end 44 | L(j,i)=(a(j,i)-t)/U(i,i); 45 | end 46 | end 47 | if z==0 48 | % Step-6 49 | w=0; 50 | for k=1:n-1 51 | w=w+L(n,k)*U(k,n); 52 | end 53 | U(n,n)=(a(n,n)-w)/L(n,n); 54 | end 55 | end 56 | if z==0 57 | fprintf("Dolittle's LU decomposition of the givem matrix is: \n\n"); 58 | disp([L U]); 59 | % disp(L); 60 | % disp(U); 61 | end 62 | end -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -3/Sample solution code (matlab) of lab assignment-3/gausselim1.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | fprintf('\n'); 4 | n=input('Enter the number of unknowns (equations): '); 5 | a=input('Enter the entries the coefficient matrix rowwise: '); 6 | b=input('Enter the entries of the right hand side centor: '); 7 | fprintf("The augmented matrix corresponding to the system is givne by: \n"); 8 | A=[a, b]; 9 | disp(A); 10 | x=zeros(n,1); 11 | % fprintf('The system is given as:\n'); 12 | m=eye(n); 13 | % Gaussian Elimination 14 | fprintf("Gaussian elimination steps: \n"); 15 | % Step-1 16 | for i=1:n-1 17 | % Step-2 18 | fprintf("Step- %d \n\n", i); 19 | %fprintf('\t'); 20 | p=0; 21 | for l=i:n 22 | if p==0 && A(l,i)~=0 23 | p=l; 24 | end 25 | end 26 | % Step-3 27 | if p~=0 28 | if p~=i 29 | R=A(i,:); 30 | A(i,:)=A(p,:); 31 | A(p,:)=R; 32 | end 33 | % Step-4 34 | for k=i+1:n 35 | % Step-5 36 | m(k,i)=A(k,i)/A(i,i); 37 | % Step-6 38 | A(k,:)=A(k,:)-m(k,i).*A(i,:); 39 | end 40 | end 41 | disp(A); 42 | end 43 | % Step-7 44 | if p~=0 45 | if A(n,n)==0 46 | if A(n,n+1)==0 47 | fprintf("No unique solution exists.\n"); 48 | else 49 | fprintf("No solution exists.\n"); 50 | end 51 | else 52 | % Backward Substitution 53 | % Step-8 54 | x(n)=A(n,n+1)/A(n,n); 55 | for i=n-1:-1: 1 56 | s=0; 57 | for j=i+1:n 58 | s=s+A(i,j)*x(j); 59 | end 60 | x(i)=(A(i,n+1)-s)/A(i,i); 61 | end 62 | fprintf("Solution of the system is given by: \n"); 63 | disp(x); 64 | end 65 | end 66 | 67 | if p==0 68 | fprintf("No unique solution exists.\n"); 69 | end -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -3/Sample solution code (matlab) of lab assignment-3/output of LU_Crout-1.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:3f23ee442a2434d2bbec55a986f638310980a3a04a0b615a280b6a8bf945023d 3 | size 59229 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -3/Sample solution code (matlab) of lab assignment-3/output of LU_Crout-2.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:91b497fdad958525a9fa666037dc3760c33ef9fb868c070cc53f6c816b151874 3 | size 59253 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -3/Sample solution code (matlab) of lab assignment-3/output of LU_Dolittle-1.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:f5dafe45debab0ce16896198ca1c9567344f143d48abd6c884a37093b1353413 3 | size 59505 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -3/Sample solution code (matlab) of lab assignment-3/output of LU_Dolittle-2.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:3f11449d82f636ab64e01d60be48ae83c7a89ff92ff46b56fc792aa16858c2b4 3 | size 59253 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -3/Sample solution code (matlab) of lab assignment-3/output of gausselim1-1.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:9e0dcb1face933ddcac1a70bb97dd63c9a25c07e6681169a284c34d1d77aa550 3 | size 61808 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -3/Sample solution code (matlab) of lab assignment-3/output of gausselim1-2.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:2929789e5ff7a14387b538961ebdc0f974c3a72e73f55aba474fd31f56644aa6 3 | size 62200 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -3/Sample solution code (matlab) of lab assignment-3/output of gausselim1-3.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:d2aebddd08492bd8edb093b0e89a3154083d8b3ddf99dfabe1cab692ed6b4827 3 | size 61888 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -7/Code testing example for Hermite polynomial.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:4a75a59de892e1af890f8236e6ecccf693e8432679f3da435c1e9334bbc15fac 3 | size 53761 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -7/Code testing example for Newton divided difference formula.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:e91f77fd13fb2df60652fea18d6d478e203bf7c5a90f83e1ea7ee5fe8005b16a 3 | size 57548 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -7/Code testing example for Newton method for system.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:e6bcc17f08d2e53eb167937d5d30fe0838e2cfe5f8bd66800f5f26730b2c483e 3 | size 59040 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -7/Code testing example for Spline.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:8725407b4d9a176b024c104b8ec8b6d9a6b961e8046aadea925efd3080d8ebd5 3 | size 53884 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -7/MTH308_and_MTH308B_Lab_Assignment_7.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:6af2c6569f2258fe635d9bfbd3d97374641d22448f5474a75a016824e64ed27f 3 | size 138587 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -7/Newton_divided_1.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Interpolating polynomial where the data are coming from a known function 4 | y=@(x) sin(x); 5 | % Taking the data inputs 6 | x=input("Enter the x-coordinates of the data points as row vector: "); 7 | f=y(x); 8 | N=length(x); 9 | F=zeros(N); 10 | % constructing the divided difference table 11 | F(:,1)=f'; 12 | for j=2:N 13 | for i=1:N+1-j 14 | F(i,j)=(F(i+1,j-1)-F(i,j-1))/(x(i+j-1)-x(i)); 15 | end 16 | end 17 | fprintf("\n Newton divided difference table is given as: \n\n"); 18 | disp(cell2mat(compose('%14.7f', [x' F]))); 19 | fprintf("\n In the above table the entries of the first rows (from 2nd to %dth columns) \n", N+1); 20 | fprintf("are required to contruct the interpolating polynomial.\n"); 21 | z=input("\n Enter the point at which we want to find the value of the function : "); 22 | v=F(1,1); 23 | for k=2:N 24 | m=1; 25 | for j=1:k-1 26 | m=m*(z-x(j)); 27 | end 28 | v=v+F(1,k)*m; 29 | end 30 | fprintf("\n The value of the interpolating polynomial (of degree less than or equal to %d \n", N-1); 31 | fprintf("for the given data) at %2.2f is :%14.7f \n\n", z, v); 32 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -7/Newton_system_1.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | 4 | % Defining the function 5 | f1=@ (x1, x2) 4*x1^2-20*x1+ (1/4)*x2^2+8; 6 | f2=@ (x1, x2) (1/2)*x1*x2^2+2*x1-5*x2+8; 7 | 8 | % Defining the Jacobian of function 9 | df_11=@ (x1, x2) 8*x1-20; 10 | df_12=@ (x1, x2) (1/2)*x2; 11 | df_21=@ (x1, x2) (1/2)*x2^2+2; 12 | df_22=@ (x1, x2) x1*x2-5; 13 | 14 | fprintf("\n First equation of the given system is:4x_1^2-20x_1+ (1/4)x_2^2+8=0. \n"); 15 | fprintf("\n Second equation of the given system is: (1/2)x_1x_2^2+2x_1-5x_2+8=0. \n"); 16 | % Cheking the hypothis of the iterations 17 | p=0; 18 | while (p==0) 19 | % Putting initial approximations 20 | x=input('\n Enter the first initial approximation (vector in colum format): '); 21 | b=[f1(x(1),x(2)); f2(x(1),x(2))]; 22 | A=[df_11(x(1),x(2)), df_12(x(1),x(2)); df_21(x(1),x(2)), df_22(x(1),x(2))]; 23 | if b(1)==0 && b(2)==0 24 | fprintf("\n A solution of the given system of equations is %f .\n", x_0); 25 | p=2; 26 | end 27 | if det(A)==0 28 | fprintf("\n Newton method cannot locate any root for the given system of equations.\n"); 29 | fprintf("\n Restart the method by putting new initial guesses.\n"); 30 | else 31 | p=1; 32 | end 33 | end 34 | % Putting stopping criteria 35 | N=input('\n Enter the maximum number of iterations: '); 36 | eps=input('\n Enter the measure of accuracy: '); 37 | % Data of iterations storing matrix 38 | X=x; 39 | % Starting iterations 40 | k=1; 41 | while (k<=N && p==1) 42 | x_0=x; 43 | % Solving the system J_F(x_k)y=F(x_k) 44 | y=A\b; 45 | % Calculating the iterations 46 | x=x-y; 47 | % Storing the values of each iterations 48 | X=[X, x]; 49 | b=[f1(x(1),x(2)); f2(x(1),x(2))]; 50 | A=[df_11(x(1),x(2)), df_12(x(1),x(2)); df_21(x(1),x(2)), df_22(x(1),x(2))]; 51 | if b(1)==0 && b(2)==0 52 | fprintf("\n A root of the given equation is %14.10f .\n", x); 53 | p=0; 54 | end 55 | if (norm((x-x_0),Inf)<= eps) 56 | fprintf("\n An approximate root (with tolerance %f) of the given system of equations is:\n", eps); 57 | disp(x); 58 | p=0; 59 | end 60 | k=k+1; 61 | end 62 | if k==N+1 63 | fprintf("\n Maximum number of iteraton reached. The method fail after %d iterations.\n", N); 64 | end 65 | fprintf("The iterations are given as:\n\n"); 66 | % D=[' k ' ; ' x_k ' ]; 67 | % disp(D); 68 | K=1:k; 69 | disp(cell2mat(compose('%14d',K))); 70 | fprintf("\n"); 71 | disp(cell2mat(compose('%14.10f',X))); 72 | 73 | 74 | 75 | 76 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -7/output of Newton_divided.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:f2f86033fd28d4d0f83d20369e5bb7aed652f9a1be8e266f7a5c85c0a7af2bca 3 | size 59692 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment -7/output of Newton_system.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:8493b99ab2f90b21ccef792847bd866314877468ae1ab00be082df81c7f01a75 3 | size 60744 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-6/MTH308_and_MTH308B_Lab_Assignment_6.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:5b9e7bc15898a4f4f26df3f4254cf8336671e45f5114e2a664b7d8a724709d95 3 | size 126833 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-6/Sample solution code (matlab) of lab assignment-6/Fixed_point.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Writing the function 4 | % g=@(x) x-x^3-4*x^2+10 ; 5 | % g=@(x) (10/x - 4*x)^(1/2) ; 6 | % g=@(x) (1/2)*(10-x^3)^(1/2) ; 7 | g=@(x) (10/(4+x))^(1/2) ; 8 | % g=@(x) x- (x^3+4*x^2-10)/(3*x^2+8*x) ; 9 | fprintf("\n The given equation is: x^3+4x^2-10=0. \n"); 10 | % Putting initial approximations 11 | x_0=input('\n Enter the first initial approximation: '); 12 | % Putting stopping criteria 13 | N=input('\n Enter the maximum number of iterations: '); 14 | eps=input('\n Enter the measure of accuracy: '); 15 | % Data of iterations storing matrix 16 | X=zeros(1,3); 17 | fprintf("\n The Fixed-point iterations are given as:\n\n"); 18 | D=[' k ' ' x_k ' ' g(x_k) ']; 19 | disp(D); 20 | X_0=[1 x_0 g(x_0);]; 21 | disp(cell2mat(compose('%14.10f',X_0))); 22 | % Starting iterations 23 | p=1; 24 | k=1; 25 | while (k<=N && p==1) 26 | x=g(x_0); 27 | X=[k x g(x)]; 28 | disp(cell2mat(compose('%14.10f',X))); 29 | if (abs(x-x_0)<= eps) 30 | fprintf("\n An approximate solution (with tolerance %f) of the given equation is %14.10f .\n", eps, x); 31 | p=0; 32 | end 33 | x_0=x; 34 | k=k+1; 35 | end 36 | if k==N+1 37 | fprintf("\n Maximum number of iteraton reached. The method fail after %d iterations.\n", N); 38 | end -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-6/Sample solution code (matlab) of lab assignment-6/Newton_Raphson.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Writing the function 4 | f=@(x) x-cos(x); 5 | df=@(x) 1+sin(x); 6 | fprintf("\n The given equation is: x - cos(x)=0. \n"); 7 | %f=@(x) x-cos(x); 8 | %f=@(x) exp(x)-2; 9 | %f=@(x) sin(x)+x^2-1 10 | % Cheking the hypothis of the iterations 11 | p=0; 12 | while (p==0) 13 | % Putting initial approximations 14 | x_0=input('\n Enter the first initial approximation: '); 15 | if f(x_0)==0 16 | fprintf("\n A root of the given equation is %f .\n", x_0); 17 | p=2; 18 | end 19 | if df(x_0)==0 20 | fprintf("\n Newton-Raphson method cannot locate any root for the given equation.\n"); 21 | fprintf("\n Restart the method by putting new initial guesses.\n"); 22 | else 23 | p=1; 24 | end 25 | end 26 | % Putting stopping criteria 27 | N=input('\n Enter the maximum number of iterations: '); 28 | eps=input('\n Enter the measure of accuracy: '); 29 | % Data of iterations storing matrix 30 | X=zeros(1,3); 31 | fprintf("\n The Newton-Raphson iterations are given as:\n\n"); 32 | D=[' k ' ' x_k ' ' f(x_k) ']; 33 | disp(D); 34 | X_0=[1 x_0 f(x_0);]; 35 | disp(cell2mat(compose('%14.10f',X_0))); 36 | % Starting iterations 37 | k=1; 38 | while (k<=N && p==1) 39 | x=x_0-f(x_0)/df(x_0); 40 | X=[k x f(x)]; 41 | disp(cell2mat(compose('%14.10f',X))); 42 | if f(x)==0 43 | fprintf("\n A root of the given equation is %14.10f .\n", x); 44 | p=0; 45 | end 46 | if (abs(x-x_0)<= eps) 47 | fprintf("\n An approximate root (with tolerance %f) of the given equation is %14.10f .\n", eps, x); 48 | p=0; 49 | end 50 | x_0=x; 51 | k=k+1; 52 | end 53 | if k==N+1 54 | fprintf("\n Maximum number of iteraton reached. The method fail after %d iterations.\n", N); 55 | end -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-6/Sample solution code (matlab) of lab assignment-6/Output of Fixed_point.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:90033dbc0b99b1043abe6d3c1393edeb3e581ac68af7d6a3ebb3843eab34fac0 3 | size 62430 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-6/Sample solution code (matlab) of lab assignment-6/Secant.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Writing the function 4 | f=@(x) x-cos(x); 5 | fprintf("\n The given equation is: x - cos(x)=0. \n"); 6 | % Cheking the hypothis of the iterations 7 | p=0; 8 | while (p==0) 9 | % Putting initial approximations 10 | x_0=input('\n Enter the first initial approximation: '); 11 | x_1=input('\n Enter the second initial approximation: '); 12 | y_0=f(x_0); 13 | y_1=f(x_1); 14 | if y_0==0 15 | fprintf("\n A root of the given equation is %f .\n", x_0); 16 | p=2; 17 | end 18 | if y_1==0 19 | fprintf("\n A root of the given equation is %f .\n", x_1); 20 | p=2; 21 | end 22 | if p~=2 23 | if y_0==y_1 24 | fprintf("\n Secant method cannot locate any root for the given equation.\n"); 25 | fprintf("\n Restart the method by putting new initial guesses.\n"); 26 | else 27 | p=1; 28 | end 29 | end 30 | end 31 | % Putting stopping criteria 32 | % if p==1 33 | N=input('\n Enter the maximum number of iterations: '); 34 | eps=input('\n Enter the measure of accuracy: '); 35 | % end 36 | % Data of iterations storing matrix 37 | X=zeros(1,3); 38 | fprintf("\n The Secant iterations are given as:\n\n"); 39 | D=[' k ' ' x_k ' ' f(x_k) ']; 40 | disp(D); 41 | X_0=[1 x_0 y_0; 2 x_1 y_1]; 42 | disp(cell2mat(compose('%14.10f',X_0))); 43 | % Starting iterations 44 | k=2; 45 | while (k<=N && p==1) 46 | x=x_1-(y_1*(x_1-x_0))/(y_1-y_0); 47 | y=f(x); 48 | X=[k x y]; 49 | disp(cell2mat(compose('%14.10f',X))); 50 | if y==0 51 | fprintf("\n A root of the given equation is %f .\n", x); 52 | p=0; 53 | end 54 | if (abs(x-x_1)<= eps) 55 | fprintf("\n An approximate root (with tolerance %f) of the given equation is %14.10f .\n", eps, x); 56 | p=0; 57 | end 58 | x_0=x_1; 59 | y_0=y_1; 60 | x_1=x; 61 | y_1=y; 62 | k=k+1; 63 | end 64 | if k==N+1 65 | fprintf("\n Maximum number of iteraton reached. The method fail after %d iterations.", N); 66 | end -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-6/Sample solution code (matlab) of lab assignment-6/output of Newton-Raphson.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:d970745abd724b851aa4da0c9c79a6a22e143fb786432bdb4e3e16657ec8d2ee 3 | size 62690 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-6/Sample solution code (matlab) of lab assignment-6/output of Secant.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:7ee96c7bf41d52913fcfa1e0783190a529764ce96e2e23ab20decb67604c0a3d 3 | size 60564 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/MTH308_and_MTH308B_Lab_Assignment_8.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:4c1466e1bea8d9446c1dd0eaf77b0dc5220994210c77cfa94bb9dac03e6f34c7 3 | size 135539 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Hermite.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Taking the data inputs 4 | x=input("Enter the x-coordinates of the data points as row vector: "); 5 | f=input("Enter the y-coordinates of the data points as row vector: "); 6 | df=input("Enter the derivative of y-coordinates of the function as row vector: "); 7 | N1=length(x); 8 | N2=length(f); 9 | N3=length(df); 10 | p=0; 11 | while (p==0) 12 | if N1~=N2 || N1~=N3 13 | fprintf("Please check the number of data points and re-enter."); 14 | x=input("Enter the x-coordinates of the data points as row vector : "); 15 | f=input("Enter the y-coordinates of the data points as row vector : "); 16 | df=input("Enter the derivative of y-coordinates of the function as row vector : "); 17 | N1=length(x); 18 | N2=length(f); 19 | N3=length(df); 20 | else 21 | N=N1; 22 | p=1; 23 | % Displaying the data points 24 | fprintf("\n The data is given in a table as: \n\n "); 25 | D=[' x ' ' f(x) ' ' df(x) ']; 26 | disp(D); 27 | disp(cell2mat(compose('%14.8f', [x ; f; df]'))); 28 | end 29 | end 30 | z=zeros(1,2*N); 31 | Q=zeros(2*N,2*N); 32 | % constructing the divided difference table 33 | for i=1:N 34 | z(2*i-1)=x(i); 35 | z(2*i)=x(i); 36 | Q(2*i-1,1)=f(i); 37 | Q(2*i,1)=f(i); 38 | Q(2*i-1,2)=df(i); 39 | end 40 | for i=1:N-1 41 | Q(2*i,2)=(Q(2*i+1,1)-Q(2*i,1))/(z(2*i+1)-z(2*i)); 42 | end 43 | for j=3:2*N 44 | for i=1:2*N+1-j 45 | Q(i,j)=(Q(i+1,j-1)-Q(i,j-1))/(z(i+j-1)-z(i)); 46 | end 47 | end 48 | fprintf("\n Hermite divided difference table is given as: \n\n"); 49 | disp(cell2mat(compose('%14.7f', [z' Q]))); 50 | fprintf("\n In the above table the entries of the first rows (from 2nd to %dth columns) \n", 2*N+1); 51 | fprintf("are required to contruct the interpolating polynomial.\n"); 52 | 53 | % Finding values of Hemite polynomial(which approximates the given data) at some point 54 | w=input("\n Enter the point at which we want to find the value of the function : "); 55 | v=Q(1,1); 56 | for k=2:2*N 57 | m=1; 58 | for j=1:k-1 59 | m=m*(w-z(j)); 60 | end 61 | v=v+Q(1,k)*m; 62 | end 63 | fprintf("\n The value of the Hermite interpolating polynomial (of degree less than or equal to %d \n", 2*N-1); 64 | fprintf("for the given data) at %2.2f is :%14.7f \n\n", w, v); 65 | 66 | 67 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Hermite_1.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % The datas are coming from the following known function 4 | % y=@(x) x.*log(x); 5 | % dy=@(x) 1+log(x); 6 | y=@(x) x.*cos(x)-2*x.^2+3*x-1; 7 | dy=@(x) cos(x)-x.*sin(x)-4*x+3; 8 | % Taking the data inputs 9 | x=input("Enter the x-coordinates of the data points as row vector: "); 10 | fprintf("\n Rule of the given function is : f(x)=x*cos(x)-2*x^2+3*x-1.\n"); 11 | f=y(x); 12 | df=dy(x); 13 | % Displaying the data points 14 | fprintf("\n The data is given in a table as: \n\n "); 15 | D=[' x ' ' f(x) ' ' df(x) ']; 16 | disp(D); 17 | disp(cell2mat(compose('%14.8f', [x ; f; df]'))); 18 | N=length(x); 19 | z=zeros(1,2*N); 20 | Q=zeros(2*N,2*N); 21 | % constructing the divided difference table 22 | for i=1:N 23 | z(2*i-1)=x(i); 24 | z(2*i)=x(i); 25 | Q(2*i-1,1)=f(i); 26 | Q(2*i,1)=f(i); 27 | Q(2*i-1,2)=df(i); 28 | end 29 | for i=1:N-1 30 | Q(2*i,2)=(Q(2*i+1,1)-Q(2*i,1))/(z(2*i+1)-z(2*i)); 31 | end 32 | for j=3:2*N 33 | for i=1:2*N+1-j 34 | Q(i,j)=(Q(i+1,j-1)-Q(i,j-1))/(z(i+j-1)-z(i)); 35 | end 36 | end 37 | fprintf("\n Hermite divided difference table is given as: \n\n"); 38 | disp(cell2mat(compose('%14.8f', [z' Q]))); 39 | fprintf("\n In the above table the entries of the first rows (from 2nd to %dth columns) \n", 2*N+1); 40 | fprintf("are required to contruct the interpolating polynomial.\n"); 41 | 42 | % Finding values of Hemite polynomial(which approximates the given data) at some point 43 | w=input("\n Enter the point at which we want to find the value of the function : "); 44 | v=Q(1,1); 45 | for k=2:2*N 46 | m=1; 47 | for j=1:k-1 48 | m=m*(w-z(j)); 49 | end 50 | v=v+Q(1,k)*m; 51 | end 52 | fprintf("\n The value of the Hermite interpolating polynomial (of degree less than or equal to %d \n", 2*N-1); 53 | fprintf("for the given data) at %2.2f is :%14.8f \n\n", w, v); -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/MTH308_and_MTH308B_Lab_Assignment_8.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:18b56152ec056fc28d1f83914254c6694b7ea022a23d5baae13207c40b0a73a7 3 | size 135536 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Spline_cubic_clamped.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Taking the data inputs 4 | x=input("Enter the x-coordinates of the data points as row vector: "); 5 | f=input("Enter the y-coordinates of the data points as row vector: "); 6 | L=input("Enter value of derivative of f at left end point : "); 7 | R=input("Enter value of derivative of f at right end point : "); 8 | N1=length(x); 9 | N2=length(f); 10 | p=0; 11 | while (p==0) 12 | if N1~=N2 13 | fprintf("Please check the number of data points and re-enter."); 14 | x=input("Enter the x-coordinates of the data points as row vector : "); 15 | f=input("Enter the y-coordinates of the data points as row vector : "); 16 | L=input("Enter value of derivative of f at left end point : "); 17 | R=input("Enter value of derivative of f at right end point : "); 18 | N1=length(x); 19 | N2=length(f); 20 | else 21 | N=N1; 22 | p=1; 23 | fprintf("\n The data is given in a table as: \n\n "); 24 | D=[' x ' ' f(x) ']; 25 | disp(D); 26 | disp(cell2mat(compose('%14.8f', [x ; f]'))); 27 | end 28 | end 29 | a=zeros(1,N-1); 30 | b=zeros(1,N-1); 31 | c=zeros(1,N-1); 32 | d=zeros(1,N-1); 33 | h=zeros(1,N-1); 34 | v=zeros(1,N-2); 35 | l=zeros(1,N-1); 36 | u=zeros(1,N-1); 37 | z=zeros(1,N-1); 38 | for j=1:N-1 39 | a(j)=f(j); 40 | h(j)=(x(j+1)-x(j)); 41 | end 42 | a(N)=f(N); 43 | % Solving tridiagonal system 44 | v(1)=3*(a(2)-a(1))/h(1)-3*L; 45 | v(N)=3*R-3*(a(N)-a(N-1))/h(N-1); 46 | for i=2:N-1 47 | v(i)=3*(a(i+1)-a(i))/h(i)- 3*(a(i)-a(i-1))/h(i-1); 48 | end 49 | l(1)=2*h(1); 50 | u(1)=0.5; 51 | z(1)=v(1)/l(1); 52 | for i=2:N-1 53 | l(i)=2*(h(i-1)+h(i))- h(i-1)*u(i-1); 54 | u(i)=h(i)/l(i); 55 | z(i)=(v(i)-h(i-1)*z(i-1))/l(i); 56 | end 57 | l(N)=h(N-1)*(2-u(N-1)); 58 | z(N)=(v(N)-h(N-1)*z(N-1))/l(N); 59 | c(N)=z(N); 60 | for j=N-1:-1:1 61 | c(j)=z(j)-u(j)*c(j+1); 62 | b(j)=(a(j+1)-a(j))/h(j)- h(j)*(c(j+1)+2*c(j))/3; 63 | d(j)=(c(j+1)-c(j))/(3*h(j)); 64 | end 65 | a(N)=[]; 66 | c(N)=[]; 67 | k=1:N-1; 68 | S=[k; a ; b; c ;d]'; 69 | fprintf("\n The coefficients a_j, b_j, c_j, d_j of the sub-spline S_j are given in a table as: \n\n "); 70 | D=[' j ' ' a_j ' ' b_j ' ' c_j ' ' d_j ']; 71 | disp(D); 72 | disp(cell2mat(compose('%14.8f', S))); 73 | 74 | % Finding values of Spline (which approximates the given data) at some point 75 | w=input("\n Enter the point at which we want to find the values of the function and its derivative. : "); 76 | i=1; 77 | while i<= N-1 78 | if (w-x(i)>=0) && (w-x(i+1)<=0) 79 | k=i; 80 | i=N; 81 | end 82 | i=i+1; 83 | end 84 | v=a(k)+b(k)*(w-x(k))+c(k)*(w-x(k))^2+d(k)*(w-x(k))^3; 85 | fprintf("\n The value of the natural cubic Spline at %2.2f is : %14.8f \n", w, v); 86 | dv=b(k)+2*c(k)*(w-x(k))+3*d(k)*(w-x(k))^2; 87 | fprintf("\n The value of the derivative of the natural cubic Spline at %2.2f is : %14.8f \n\n", w, dv); -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Spline_cubic_clamped_1.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % The datas are coming from the following known function 4 | % y=@(x) x.*log(x); 5 | % dy=@(x) 1+log(x); 6 | y=@(x) sin(exp(x)-2); 7 | dy=@(x) cos(exp(x)-2).*exp(x); 8 | % y=@(x) x.*cos(x)-2*x.^2+3*x-1; 9 | % dy=@(x) cos(x)-x.*sin(x)-4*x+3; 10 | % Taking the data inputs 11 | x=input("Enter the x-coordinates of the data points as row vector: "); 12 | fprintf("\n Rule of the given function is : f(x)=sin(e^x-2).\n"); 13 | f=y(x); 14 | L=dy(x(1)); 15 | R=dy(x(end)); 16 | % Displaying the data points 17 | fprintf("\n The data is given in a table as: \n\n "); 18 | D=[' x ' ' f(x) ']; 19 | disp(D); 20 | disp(cell2mat(compose('%14.8f', [x ; f]'))); 21 | N=length(x); 22 | a=zeros(1,N-1); 23 | b=zeros(1,N-1); 24 | c=zeros(1,N-1); 25 | d=zeros(1,N-1); 26 | h=zeros(1,N-1); 27 | v=zeros(1,N-2); 28 | l=zeros(1,N-1); 29 | u=zeros(1,N-1); 30 | z=zeros(1,N-1); 31 | for j=1:N-1 32 | a(j)=f(j); 33 | h(j)=(x(j+1)-x(j)); 34 | end 35 | a(N)=f(N); 36 | % Solving tridiagonal system 37 | v(1)=3*(a(2)-a(1))/h(1)-3*L; 38 | v(N)=3*R-3*(a(N)-a(N-1))/h(N-1); 39 | for i=2:N-1 40 | v(i)=3*(a(i+1)-a(i))/h(i)- 3*(a(i)-a(i-1))/h(i-1); 41 | end 42 | l(1)=2*h(1); 43 | u(1)=0.5; 44 | z(1)=v(1)/l(1); 45 | for i=2:N-1 46 | l(i)=2*(h(i-1)+h(i))- h(i-1)*u(i-1); 47 | u(i)=h(i)/l(i); 48 | z(i)=(v(i)-h(i-1)*z(i-1))/l(i); 49 | end 50 | l(N)=h(N-1)*(2-u(N-1)); 51 | z(N)=(v(N)-h(N-1)*z(N-1))/l(N); 52 | c(N)=z(N); 53 | for j=N-1:-1:1 54 | c(j)=z(j)-u(j)*c(j+1); 55 | b(j)=(a(j+1)-a(j))/h(j)- h(j)*(c(j+1)+2*c(j))/3; 56 | d(j)=(c(j+1)-c(j))/(3*h(j)); 57 | end 58 | a(N)=[]; 59 | c(N)=[]; 60 | k=1:N-1; 61 | S=[k; a ; b; c ;d]'; 62 | fprintf("\n The coefficients a_j, b_j, c_j, d_j of the sub-spline S_j are given in a table as: \n\n "); 63 | D=[' j ' ' a_j ' ' b_j ' ' c_j ' ' d_j ']; 64 | disp(D); 65 | disp(cell2mat(compose('%14.8f', S))); 66 | 67 | % Finding values of Spline (which approximates the given data) at some point 68 | w=input("\n Enter the point at which we want to find the values of the function and its derivative. : "); 69 | i=1; 70 | while i<= N-1 71 | if (w-x(i)>=0) && (w-x(i+1)<=0) 72 | k=i; 73 | i=N; 74 | end 75 | i=i+1; 76 | end 77 | v=a(k)+b(k)*(w-x(k))+c(k)*(w-x(k))^2+d(k)*(w-x(k))^3; 78 | fprintf("\n The value of the natural cubic Spline at %2.2f is : %14.8f \n", w, v); 79 | dv=b(k)+2*c(k)*(w-x(k))+3*d(k)*(w-x(k))^2; 80 | fprintf("\n The value of the derivative of the natural cubic Spline at %2.2f is : %14.8f \n\n", w, dv); -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Spline_cubic_natural.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Taking the data inputs 4 | x=input("Enter the x-coordinates of the data points as row vector: "); 5 | f=input("Enter the y-coordinates of the data points as row vector: "); 6 | N1=length(x); 7 | N2=length(f); 8 | p=0; 9 | while (p==0) 10 | if N1~=N2 11 | fprintf("Please check the number of data points and re-enter."); 12 | x=input("Enter the x-coordinates of the data points as row vector: "); 13 | f=input("Enter the y-coordinates of the data points as row vector: "); 14 | N1=length(x); 15 | N2=length(f); 16 | else 17 | N=N1; 18 | p=1; 19 | fprintf("\n The data is given in a table as: \n\n "); 20 | D=[' x ' ' f(x) ']; 21 | disp(D); 22 | disp(cell2mat(compose('%14.8f', [x ; f]'))); 23 | end 24 | end 25 | a=zeros(1,N-1); 26 | b=zeros(1,N-1); 27 | c=zeros(1,N-1); 28 | d=zeros(1,N-1); 29 | h=zeros(1,N-1); 30 | v=zeros(1,N-2); 31 | l=zeros(1,N-1); 32 | u=zeros(1,N-1); 33 | z=zeros(1,N-1); 34 | for j=1:N-1 35 | a(j)=f(j); 36 | h(j)=(x(j+1)-x(j)); 37 | end 38 | a(N)=f(N); 39 | % Solving tridiagonal system 40 | for i=2:N-1 41 | v(i)=3*(a(i+1)-a(i))/h(i)- 3*(a(i)-a(i-1))/h(i-1); 42 | end 43 | l(1)=1; 44 | for i=2:N-1 45 | l(i)=2*(h(i-1)+h(i))- h(i-1)*u(i-1); 46 | u(i)=h(i)/l(i); 47 | z(i)=(v(i)-h(i-1)*z(i-1))/l(i); 48 | end 49 | l(N)=1; 50 | z(N)=0; 51 | c(N)=0; 52 | for j=N-1:-1:1 53 | c(j)=z(j)-u(j)*c(j+1); 54 | b(j)=(a(j+1)-a(j))/h(j)- h(j)*(c(j+1)+2*c(j))/3; 55 | d(j)=(c(j+1)-c(j))/(3*h(j)); 56 | end 57 | a(N)=[]; 58 | c(N)=[]; 59 | k=1:N-1; 60 | S=[k; a ; b; c ;d]'; 61 | fprintf("\n The coefficients a_j, b_j, c_j, d_j of the sub-spline S_j are given in a table as: \n\n "); 62 | D=[' j ' ' a_j ' ' b_j ' ' c_j ' ' d_j ']; 63 | disp(D); 64 | disp(cell2mat(compose('%14.8f', S))); 65 | 66 | % Finding values of Spline (which approximates the given data) at some point 67 | w=input("\n Enter the point at which we want to find the values of the function and its derivative. : "); 68 | i=1; 69 | while i<= N-1 70 | if (w-x(i)>=0) && (w-x(i+1)<=0) 71 | k=i; 72 | i=N; 73 | end 74 | i=i+1; 75 | end 76 | v=a(k)+b(k)*(w-x(k))+c(k)*(w-x(k))^2+d(k)*(w-x(k))^3; 77 | fprintf("\n The value of the natural cubic Spline at %2.2f is : %14.8f \n", w, v); 78 | dv=b(k)+2*c(k)*(w-x(k))+3*d(k)*(w-x(k))^2; 79 | fprintf("\n The value of the derivative of the natural cubic Spline at %2.2f is : %14.8f \n\n", w, dv); -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Spline_cubic_natural_1.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % The datas are coming from the following known function 4 | y=@(x) x.*log(x); 5 | % y=@(x) sin(exp(x)-2); 6 | % Taking the data inputs 7 | x=input("Enter the x-coordinates of the data points as row vector: "); 8 | fprintf("\n Rule of the given function is : f(x)=xlog(x).\n"); 9 | f=y(x); 10 | % Displaying the data points 11 | fprintf("\n The data is given in a table as: \n\n "); 12 | D=[' x ' ' f(x) ']; 13 | disp(D); 14 | disp(cell2mat(compose('%14.8f', [x ; f]'))); 15 | N=length(x); 16 | a=zeros(1,N-1); 17 | b=zeros(1,N-1); 18 | c=zeros(1,N-1); 19 | d=zeros(1,N-1); 20 | h=zeros(1,N-1); 21 | v=zeros(1,N-2); 22 | l=zeros(1,N-1); 23 | u=zeros(1,N-1); 24 | z=zeros(1,N-1); 25 | for j=1:N-1 26 | a(j)=f(j); 27 | h(j)=(x(j+1)-x(j)); 28 | end 29 | a(N)=f(N); 30 | % Solving tridiagonal system 31 | for i=2:N-1 32 | v(i)=3*(a(i+1)-a(i))/h(i)- 3*(a(i)-a(i-1))/h(i-1); 33 | end 34 | l(1)=1; 35 | for i=2:N-1 36 | l(i)=2*(h(i-1)+h(i))- h(i-1)*u(i-1); 37 | u(i)=h(i)/l(i); 38 | z(i)=(v(i)-h(i-1)*z(i-1))/l(i); 39 | end 40 | l(N)=1; 41 | z(N)=0; 42 | c(N)=0; 43 | for j=N-1:-1:1 44 | c(j)=z(j)-u(j)*c(j+1); 45 | b(j)=(a(j+1)-a(j))/h(j)- h(j)*(c(j+1)+2*c(j))/3; 46 | d(j)=(c(j+1)-c(j))/(3*h(j)); 47 | end 48 | a(N)=[]; 49 | c(N)=[]; 50 | k=1:N-1; 51 | S=[k; a ; b; c ;d]'; 52 | fprintf("\n The coefficients a_j, b_j, c_j, d_j of the sub-spline S_j are given in a table as: \n\n "); 53 | D=[' j ' ' a_j ' ' b_j ' ' c_j ' ' d_j ']; 54 | disp(D); 55 | disp(cell2mat(compose('%14.8f', S))); 56 | 57 | % Finding values of Spline (which approximates the given data) at some point 58 | w=input("\n Enter the point at which we want to find the values of the function and its derivative. : "); 59 | i=1; 60 | while i<= N-1 61 | if (w-x(i)>=0) && (w-x(i+1)<=0) 62 | k=i; 63 | i=N; 64 | end 65 | i=i+1; 66 | end 67 | v=a(k)+b(k)*(w-x(k))+c(k)*(w-x(k))^2+d(k)*(w-x(k))^3; 68 | fprintf("\n The value of the natural cubic Spline at %2.2f is : %14.8f \n", w, v); 69 | dv=b(k)+2*c(k)*(w-x(k))+3*d(k)*(w-x(k))^2; 70 | fprintf("\n The value of the derivative of the natural cubic Spline at %2.2f is : %14.8f \n\n", w, dv); 71 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Spline_linear.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Taking the data inputs 4 | x=input("Enter the x-coordinates of the data points as row vector : "); 5 | f=input("Enter the y-coordinates of the data points as row vector : "); 6 | N1=length(x); 7 | N2=length(f); 8 | p=0; 9 | while (p==0) 10 | if N1~=N2 11 | fprintf("Please check the number of data points and re-enter."); 12 | x=input("Enter the x-coordinates of the data points as row vector : "); 13 | f=input("Enter the y-coordinates of the data points as row vector : "); 14 | N1=length(x); 15 | N2=length(f); 16 | else 17 | N=N1; 18 | p=1; 19 | fprintf("\n The data is given in a table as: \n\n "); 20 | D=[' x ' ' f(x) ']; 21 | disp(D); 22 | disp(cell2mat(compose('%14.8f', [x ; f]'))); 23 | end 24 | end 25 | a=zeros(1,N-1); 26 | b=zeros(1,N-1); 27 | for j=1:N-1 28 | a(j)=f(j); 29 | b(j)=(f(j+1)-f(j))/(x(j+1)-x(j)); 30 | end 31 | k=1:N-1; 32 | fprintf("\n The coefficients of a_j, b_j of the sub-spline S_j are given in a table as: \n\n "); 33 | D=[' j ' ' a_j ' ' b_j ']; 34 | disp(D); 35 | disp(cell2mat(compose('%14.8f', [k; a ; b]'))); 36 | 37 | % Finding values of Spline (which approximates the given data) at some point 38 | w=input("\n Enter the point at which we want to find the value of the function : "); 39 | i=1; 40 | while i<= N-1 41 | if (w-x(i)>=0) && (w-x(i+1)<=0) 42 | k=i; 43 | i=N; 44 | end 45 | i=i+1; 46 | end 47 | v=a(k)+b(k)*(w-x(k)); 48 | fprintf("\n The value of the Spline at %2.2f is : %14.8f \n\n", w, v); 49 | 50 | % Later part is optional 51 | % Printing the graph of linear Spline 52 | grid on 53 | plot(x,f, '-b*'); 54 | xlabel('x-axis (x-->)') 55 | ylabel('y-axis (f(x)-->)') 56 | legend('Linear spline', 'Location', 'northwest') -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Spline_linear_1.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % The datas are coming from the following known function 4 | y=@(x) x.^3+4.001.*x.^2+4.002.*x+1.101; 5 | % Taking the data inputs 6 | x=input("Enter the x-coordinates of the data points as row vector: "); 7 | fprintf("\n Rule of the given function is : f(x)=x^3+4.001x^2+4.002x+1.101.\n"); 8 | f=y(x); 9 | % Displaying the data points 10 | fprintf("\n The data is given in a table as: \n\n "); 11 | D=[' x ' ' f(x) ']; 12 | disp(D); 13 | disp(cell2mat(compose('%14.8f', [x ; f]'))); 14 | N=length(x); 15 | a=zeros(1,N-1); 16 | b=zeros(1,N-1); 17 | for j=1:N-1 18 | a(j)=f(j); 19 | b(j)=(f(j+1)-f(j))/(x(j+1)-x(j)); 20 | end 21 | k=1:N-1; 22 | fprintf("\n The coefficients of a_j, b_j of the sub-spline S_j are given in a table as: \n\n "); 23 | D=[' j ' ' a_j ' ' b_j ']; 24 | disp(D); 25 | S=[k; a ; b]'; 26 | disp(cell2mat(compose('%14.8f', S))); 27 | 28 | % Finding values of Spline (which approximates the given data) at some point 29 | w=input("\n Enter the point at which we want to find the value of the function : "); 30 | i=1; 31 | while i<= N-1 32 | if (w-x(i)>=0) && (w-x(i+1)<=0) 33 | k=i; 34 | i=N; 35 | end 36 | i=i+1; 37 | end 38 | v=a(k)+b(k)*(w-x(k)); 39 | fprintf("\n The value of the Spline at %2.2f is : %14.8f \n\n", w, v); 40 | 41 | % Later part is optional 42 | % Printing the graph of original function 43 | fplot(@(x) x.^3+4.001.*x.^2+4.002.*x+1.101, [x(1) x(N)], ':m'); 44 | hold on 45 | 46 | % Printing the graph of linear Spline 47 | grid on 48 | plot(x,f, '-b*'); 49 | xlabel('x-axis (x-->)') 50 | ylabel('y-axis (f(x)-->)') 51 | legend('x^3+4.001x^2+4.002x+1.101', 'Linear spline', 'Location', 'northwest') -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Spline_linear_graph.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/mihirm21/mth_iitk/9a3527efeb9ba9afeff1023163db8f8a4f9b8b82/MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Spline_linear_graph.jpg -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Spline_linear_graph_1.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/mihirm21/mth_iitk/9a3527efeb9ba9afeff1023163db8f8a4f9b8b82/MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/Spline_linear_graph_1.jpg -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/output of Hermite.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:54dbc3b40913121e939d95725aea851b3e75008b2d12be79394062ccc05a29ba 3 | size 60029 4 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lab_Assignments/Lab assignment-8/Sample solution code(matlab) of lab assignment-8/output of Hermite_1.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:f59d92a77a9d9e8b239b0b56c02acc341c0f4c7fbeccd0f3cb6b34bfca24e1ea 3 | size 61430 4 | 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| fprintf("\n Rule of the given function is : f(x)=x^2log(x^2+1).\n"); 9 | % Taking the data inputs 10 | a=input("Enter the left end point of the interval of integration: "); 11 | b=input("Enter the right end point of the interval of integration: "); 12 | h=input("Enter the lenth of the partition(lenth of the equally spaced sub intervals): "); 13 | % N=input("Enter the number of the partitions of the interval: "); 14 | N=(b-a)/(2*h); 15 | % h=(b-a)/(2*N); 16 | T=f(a)+f(b); 17 | for i=1:N-1 18 | T=T+2*f(a+2*i*h); 19 | end 20 | for i=1:N 21 | T=T+4*f(a+(2*i-1)*h); 22 | end 23 | fprintf("The value of the integration is : %10.7f.\n\n", (h*T)/3); 24 | -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lecture Notes/lecture notes 35(remaining), 36, 37 and sample solution code of Lab-9/Trapozoidal.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % Taking the data inputs 4 | x=input("Enter the x-coordinates of the data points as row vector: "); 5 | f=input("Enter the y-coordinates of the data points as row vector: "); 6 | N1=length(x); 7 | N2=length(f); 8 | p=0; 9 | while (p==0) 10 | if N1~=N2 11 | fprintf("Please check the number of data points and re-enter."); 12 | x=input("Enter the x-coordinates of the data points as row vector: "); 13 | f=input("Enter the y-coordinates of the data points as row vector: "); 14 | N1=length(x); 15 | N2=length(f); 16 | else 17 | N=N1; 18 | p=1; 19 | fprintf("\n The data is given in a table as: \n\n "); 20 | D=[' x ' ' f(x) ']; 21 | disp(D); 22 | disp(cell2mat(compose('%14.8f', [x ; f]'))); 23 | end 24 | end 25 | T=0; 26 | for i=1:N-1 27 | T=T+(f(i)+f(i+1))*(x(i+1)-x(i)); 28 | end 29 | fprintf("\n The value of the integration is : %10.6f.\n\n", T/2); -------------------------------------------------------------------------------- /MTH308B-Numerical Analysis and Scientific Computing/2023-24-Even/Lecture Notes/lecture notes 35(remaining), 36, 37 and sample solution code of Lab-9/Trapozoidal_2.m: -------------------------------------------------------------------------------- 1 | clc; 2 | clear; 3 | % The datas are coming from the following known function 4 | % f=@(x) x*log(x); 5 | f=@(x) x^3*exp(x); 6 | % f=@(x) sin(exp(x)-2); 7 | % f=@(x) sqrt(x)-x^2; 8 | fprintf("\n Rule of the given function is : f(x)=x^3e^x.\n"); 9 | % Taking the data inputs 10 | a=input("Enter the left end point of the interval of integration: "); 11 | b=input("Enter the right end point of the interval of integration: "); 12 | h=input("Enter the lenth of the partition(lenth of the equally spaced sub intervals): "); 13 | % N=input("Enter the number of the partitions of the interval: "); 14 | N=(b-a)/h; 15 | % h=(b-a)/N; 16 | T=(f(a)+f(b))/2; 17 | for i=1:N-1 18 | T=T+f(a+i*h); 19 | end 20 | fprintf("The value of the integration is : %10.6f.\n\n", h*T); 21 | 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Time Series Analysis/2023-24-Even/Lectures/L9.pdf: -------------------------------------------------------------------------------- 1 | version https://git-lfs.github.com/spec/v1 2 | oid sha256:9d99827a469a8437b92af848dd2b16a3fdef80e86be585ac6f979076c81a7fc7 3 | size 1336734 4 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # IIT Kanpur - MTH courses PYQs 2 | 3 | Dumping the resources for MTH departmental courses. 4 | 5 | Pull requests for more dumping :) are welcome. --------------------------------------------------------------------------------