Numerical Analysis and Computer Programing

Numerical Analysis and Computer Programing. Instructor: Prof. P. B. Sunil Kumar, Department of Physics, IIT Madras. This course covers some of the basic aspects of programming and algorithms. Topics covered in this course include Approximations and round off errors, Truncation errors and Taylor Series, Determination of roots of polynomials and transcendental equations by Newton-Raphson, Secant and Bairstow's method; Solutions of linear simultaneous linear algebraic equations by Gauss Elimination and Gauss-Seidel iteration methods; Curve fitting - linear and nonlinear regression analysis; Backward, Forward and Central difference relations and their uses in Numerical differentiation and integration, Application of difference relations in the solution of partial differential equations; Numerical solution of ordinary differential equations by Euler, Modified Euler, Runge-Kutta and Predictor-Corrector method. (from

Programming: Basics

Lecture 01 - Programming: Basics
Lecture 02 - Introduction to Pointers
Lecture 03 - Pointers and Arrays
Lecture 04 - External Functions and Argument Passing
Lecture 05 - Representation of Numbers
Lecture 06 - Numerical Error
Lecture 07 - Error Propagation and Stability
Lecture 08 - Polynomial Interpolation
Lecture 09 - Polynomial Interpolation (cont.)
Lecture 10 - Error in Interpolation Polynomial
Lecture 11 - Piecewise Polynomial Interpolation
Lecture 12 - Cubic Spline Interpolation
Lecture 13 - Data Fitting: Linear Fit
Lecture 14 - Data Fitting: Linear Fit (cont.)
Lecture 15 - Data Fitting: Nonlinear Fit
Lecture 16 - Matrix Elimination and Solution to Linear Equations
Lecture 17 - Solution to Linear Equations: LU Decomposition Number
Lecture 18 - Matrix Elimination with Pivoting and the Condition Number
Lecture 19 - Eigenvalues of a Matrix
Lecture 20 - Eigenvalues and Eigenvectors
Lecture 21 - Solving Nonlinear Equations
Lecture 22 - Solving Nonlinear Equations: Newton-Raphson Method
Lecture 23 - Methods for Solving Nonlinear Equations: Newton-Raphson Iterative Method
Lecture 24 - Systems of Nonlinear Equations
Lecture 25 - Numerical Derivations
Lecture 26 - Higher Order Derivatives from Difference Formula
Lecture 27 - Numerical Integration: Basic Rules
Lecture 28 - Numerical Integration: Comparison of Different Basic Rules
Lecture 29 - Numerical Integration: Gaussian Rules
Lecture 30 - Numerical Integration: Comparison of Gaussian Rules
Lecture 31 - Solving Ordinary Differential Equations: Euler's Method
Lecture 32 - Solving Ordinary Differential Equations: Runge-Kutta Method
Lecture 33 - Adaptive Step Size Runge-Kutta Scheme
Lecture 34 - Partial Differential Equations
Lecture 35 - Explicit and Implicit Methods for Partial Differential Equations
Lecture 36 - The Crank-Nicolson Scheme for Two Spatial Dimensions
Lecture 37 - Fourier Transforms
Lecture 38 - Fast Fourier Transforms

Numerical Analysis and Computer Programing
Instructor: Prof. P. B. Sunil Kumar, Department of Physics, IIT Madras. This course covers some of the basic aspects of programming and algorithms.