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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)

Lecture 36 - The Crank-Nicolson Scheme for Two Spatial Dimensions

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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