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Elementary Numerical Analysis. Instructor: Prof. Rekha P. Kulkarni, Department of Mathematics, IIT Bombay.
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Description
This course introduces the implementation and analysis of numerical algorithms for finding an approximate solution to a mathematical problem. The important topics covered in this course are polynomial and piecewise polynomial (spline) interpolation, numerical integration and numerical differentiation, approximate solutions of differential equations, direct and iterative solution of a system of linear equations and eigenvalue problems. The theory behind various methods is rigorously discussed. Emphasis is on comparison of various methods and their implementation using a computer. (from nptel.ac.in)
Course content
- Lecture 01 – Introduction Unlimited
- Lecture 02 – Polynomial Approximation Unlimited
- Lecture 03 – Interpolating Polynomials Unlimited
- Lecture 04 – Properties of Divided Difference Unlimited
- Lecture 05 – Error in the Interpolating Polynomial Unlimited
- Lecture 06 – Cubic Hermite Interpolation Unlimited
- Lecture 07 – Piecewise Polynomial Approximation Unlimited
- Lecture 08 – Cubic Spline Interpolation Unlimited
- Lecture 09 – Tutorial 1 Unlimited
- Lecture 10 – Numerical Integration: Basic Rules Unlimited
- Lecture 11 – Composite Numerical Integration Unlimited
- Lecture 12 – Gauss 2-point Rule: Construction Unlimited
- Lecture 13 – Gauss 2-point Rule: Error Unlimited
- Lecture 14 – Convergence of Gaussian Integration Unlimited
- Lecture 15 – Tutorial 2 Unlimited
- Lecture 16 – Numerical Differentiation Unlimited
- Lecture 17 – Gauss Elimination Unlimited
- Lecture 18 – LU Decomposition Unlimited
- Lecture 19 – Cholesky Decomposition Unlimited
- Lecture 20 – Gauss Elimination with Partial Pivoting Unlimited
- Lecture 21 – Vector and Matrix Norms Unlimited
- Lecture 22 – Perturbed Linear System Unlimited
- Lecture 23 – Ill-Conditioned Linear System Unlimited
- Lecture 24 – Tutorial 3 Unlimited
- Lecture 25 – Effect of Small Pivots Unlimited
- Lecture 26 – Solution of Nonlinear Equations Unlimited
- Lecture 27 – Quadratic Convergence of Newton’s Method Unlimited
- Lecture 28 – Jacobi Method Unlimited
- Lecture 29 – Gauss-Seidel Method Unlimited
- Lecture 30 – Tutorial 4 Unlimited
- Lecture 31 – Initial Value Problem Unlimited
- Lecture 32 – Multi-Step Methods Unlimited
- Lecture 33 – Predictor-Corrector Formula Unlimited
- Lecture 34 – Boundary Value Problems Unlimited
- Lecture 35 – Eigenvalues and Eigenvectors Unlimited
- Lecture 36 – Spectral Theorem Unlimited
- Lecture 37 – Power Method Unlimited
- Lecture 38 – Inverse Power Method Unlimited
- Lecture 39 – QR Decomposition Unlimited
- Lecture 40 – QR Method Unlimited
Instructor
