ABOUT THE COURSE:In the first two weeks of this course, an introduction to Python is introduced with hands on. In the subsequent weeks, topics will be introduced followed by hands on to write the Python code of the same topic. This course is very useful for the students who want to do research projects using numerical techniques for data science or to solve differential equations.INTENDED AUDIENCE: UG/PG studentsPREREQUISITES: Some knowledge of any programming language
Overview
Syllabus
Week 1: Introduction to Python:- fundamentals, control flow, listing, functions, loops,file handling.Week 2:Introduction to Python:- fundamentals, control flow, listing, functions, loops,file handling.(Cont,..)Week 3:Error estimation and methods of roots finding:- fixed point method, bisection method, Regula-falsi and secant method, Newton Raphson method and their convergence.Week 4:Solving System of Linear Algebraic equations: Gauss elimination, LU decomposition, Gauss Jacobi and Gauss Seidel method and their convergence.Week 5:Solving System of Linear Algebraic equations: Gauss elimination, LU decomposition, Gauss Jacobi and Gauss Seidel method and their convergence.(Cont,..)Week 6:Curve fitting using least square method and Interpolation:- linear and nonlinear curve fitting, Lagrange interpolation, Newton methods for interpolation.Week 7:Curve fitting using least square method and Interpolation:- linear and nonlinear curve fitting, Lagrange interpolation, Newton methods for interpolation.(Cont,..)Week 8:Splines:- derivation for linear and cubic interpolationWeek 9:Numerical differentiation: - based on forward, backward and central finite difference operator, based on interpolation.Week 10:Numerical Integration: Newton-Cotes Quadrature Formula, Romberg’s integration, Method of undetermined coefficients.Week 11:Numerical solution of Initial value problems (IVP) and their convergence:-Picard’s method, Euler’s method, modified Euler’s method, Runge-Kutta method, Predictor-corrector methods and their convergence.Week 12:Numerical solution of Initial value problems (IVP) and their convergence:-Picard’s method, Euler’s method, modified Euler’s method, Runge-Kutta method, Predictor-corrector methods and their convergence.(Cont,..)
Taught by
Prof. Mani Mehra, Prof. Vivek K. Aggarwal
