Media Storage Type : DVD-ROM
NPTEL Course Name : Advanced Numerical Analysis
NPTEL Subject Matter Expert : Prof. Sachin C. Patwardhan
NPTEL Co-ordinating Institute : IIT Bombay
NPTEL Lecture Count : 51
Lecture Titles:
Module 1 - Overview of the Course
Module 1 - Section 1 : Introductions
Module 1 - Section 2 : Lumped Parameter Models and Abstract Equation Formss
Module 1 - Section 3 : Distributed Parameter Models and Abstract Equation Formss
Module 2 - Section 1 : Introduction
Module 2 - Section 2 : Vector Spaces
Module 2 - Section 3 : Normed Linear Spaces and Banach Spaces
Module 2 - Section 4 : Inner Product Spaces and Hilbert Spaces
Module 2 - Section 5 : Gram-Schmidt Process and Orthogonal Polynomials
Module 2 - Section 6 : Induced Matrix Norms
Module 2 - Section 7 : Summary
Module 3 - Section 1 : Unified Problem Representation
Module 3 - Section 2 : Polynomial Approximation [3]
Module 3 - Section 3 : Discretization using Taylor Series Approximation
Module 3 - Section 4 : Discretization using Polynomial Interpolation
Module 3 - Section 5 : Least Square Approximations
Module 3 - Section 6 : Errors in Discretization and Computations [4]
Module 3 - Section 7 : Summary and Conclusions
Module 3 - Section 8 : Appendix: Necessary and Sufficient Conditions for Unconstrained Optimality
Module 4 - Section 1 : Introduction
Module 4 - Section 2 : Existence of Solutions
Module 4 - Section 3 : Direct Solution Techniques
Module 4 - Section 4 : Direct Methods for Solving Sparse Linear Systems
Module 4 - Section 5 : Iterative Solution Techniques
Module 4 - Section 6 : Optimization Based Methods
Module 4 - Section 7 : Matrix Conditioning and Behavior of Solutions
Module 4 - Section 8 : Summary
Module 4 - Section 9 : Appendix A: Behavior of Solutions of Linear Difference Equations
Module 4 - Section 10 : Appendix B: Theorems on Convergence of Iterative Schemes
Module 4 - Section 11 : Appendix C: Steepest Descent / Gradient Search Method
Module 5 - Section 1 : Introduction
Module 5 - Section 2 : Method of Successive Substitutions [4]
Module 5 - Section 3 : Newtonï¾’s Method
Module 5 - Section 4 : Solutions of Nonlinear Algebraic Equations Using Optimization
Module 5 - Section 5 : Condition Number of Nonlinear Set of Equations [7]
Module 5 - Section 6 : Existence of Solutions and Convergence of Iterative Methods [12]
Module 5 - Section 7 : Summary
Module 6 - Section 1 : Introduction
Module 6 - Section 2 : Existence, Uniqueness and Continuity of Solutions [1]
Module 6 - Section 3 : Analytical Solutions of Linear ODE-IVPs
Module 6 - Section 4 : Numerical Solution Schemes: Basic Concepts
Module 6 - Section 5 : Numerical Methods Based On Taylor Series Expansion [2]
Module 6 - Section 6 : Numerical Methods Based on Polynomial Interpolation [2]
Module 6 - Section 7 : Convergence Analysis and Selection of Integration Interval
Module 6 - Section 8 : Solutions of Differential Algebraic System of Equations
Module 6 - Section 9 : Solution of ODE-BVP using Shooting Method [3]
Module 6 - Section 10 : Summary
Module 6 - Section 11 : Exercise
Module 4 - Section 12 : Excercise
Module 2 - Section 8 : Excercise
Module 1 - Section 4 : Summary