# InfoCoBuild

## 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 nptel.ac.in)

 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

 References 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.