COMPUTER BASED NUMERICAL METHODS (JUL

About the Course

This course covers numerical methods such as root finding, interpolation, linear systems of equations and methods for solving them, integration, differential equations and methods for solving them. The programming language used is Python and students are expected to have a beginners level knowledge of the language. If they don't, they are strongly advised to follow any of the basic tutorials available on the Internet.

While there is no real textbook for the course, we will be following the material from the online resource. Any extra material will be suggested in the relevant classes.

Jeffrey R. Chasnov. "Numerical Methods", 2012.

Instructor

Chakravarthy Bhagvati

Classroom and Timings

(effective 23 August 2023)
Wed 2:00 - 3:00 PM: CIS 119
Thu 2:00 - 4:00 PM: LHC1 CR6

CBNM Lab
Wed 3:00 - 5:00 PM: CIS IT Lab

Note: the class and lab on Wednesdays is in the South Campus

Syllabus

The following is the tentative syllabus and it may be fine-tuned during the semester. Links are given for some extra reading or for material not found in the suggested textbook.

Unit Description	Weeks	Links
I. Introduction IEEE floating point representation Accuracy, precision and errors `numpy` module in Python	1 - 2	IEEE Standard for Floating Point Numbers
LAB 1: PRELIMINARIES LAB 1: PROBLEMS	Due: 23/08/2023
II. Root Finding Simple methods: bisection, regula-falsi, Newton-Raphson, Secant, etc. Other methods: Birge-Vieta, Bairstow	3 - 5	Regula falsi Method Birge-Vieta Method Bairstow Method
LAB 2: PROBLEMS	Due: 06/09/2023
III. Solving Systems of Equations Gauss elimination, Gauss-Jordan, Jacobi and Gauss-Siedel methods LU decomposition method Eigenvalue and Eigenvector computations	5 - 8
LAB 3: PRELIMINARIES Gauss Eliminate (C Code) with dynamic arrays Updated Lab Sheet for 27/09/2023 Lab Sheet for 04/10/2023	Due: 27/09/2023
IV. Interpolation and Quadrature Methods Linear, Lagrange, Vandermonde and Cubic-spline interpolations Trapezoidal rule, Simpson's rule for definite integrals Gaussian quadrature	9 - 11
LAB 6: Regression and Least Squares Approximation LAB 7: Interpolation LAB 8: Integration	Due: 11/10/2023
V. Solving Ordinary Differential Equations Euler's and modified Euler's methods Piccard's successive approximation Runge-Kutta methods	11 - 13
LAB 9: Building a Python Package LAB 9: Building a C Library	Due: 01/11/2023
LAB 10: ODE Basics LAB 11: Runge Kutta Methods LAB 12: ODE Problems	Due: 01/11/2023
LAB 9: Building a Python Package (Updated) LAB 9: Building a C Library (Updated)	Due: 16/11/2023

Material for Lab Exam

Practice Problems for Lab Exam