CE 601 NUMERICAL METHODS

Numerical methods is a mathematical course for engineers and scientists designed to solve various engineering and natural problems. The various scientific phenomena in nature and man-made events can be mathematically modeled using equations and expressions. To engineer these phenomena, one may have to solve these mathematical models by - analytical, graphical, or approximations. Numerical methods is that branch that deals with the approximate solution formations of various mathematical models.

Lecture Schedule                                       Solved Examples

Lecture Presentations/Notes

 Sl.No Lectures Sl.No Lectures 1 Lecture 1 (24/07/2012)  - Introduction to Numerical Methods 2 Lecture 2 (25/07/2012) - System of Linear Equations 3 Lecture 3 (30/07/2012) - System of Linear Equations-2 4 Lecture 4 (31/07/2012) - Gauss Elimination Method 5 Lecture 5 (01/08/2012) - Gauss-Jordan Method 6 Lecture 6 (06/08/2012) - LU Decomposition 7 Lecture 7 (07/08/2012) - Banded Matrices and Thomas Algorithm 8 Lecture 8 (08/08/2012) - Drawbacks of Elimination Methods 9 Lecture 9 (13/08/2012) - Iterative Methods 10 Lecture 10 (14/08/2012) - Successive Over-Relax, Eigen Values & Vectors 11 Lecture 11 (21/08/2012) - To formulate Eigen Problems 12 Lecture 12 (22/08/2012) - Power Method, Inverse Power, Shifted Power 13 Lecture 13 (23/08/2012) - Fadeev-Leverrier Method, Similarity Transformations 14 Lecture 14 (27/08/2012) - Solution of Non-linear Equations 15 Lecture 15 (28/08/2012) - Regula-Falsi, Fixed-point Iteration 16 Lecture 16 (30/08/2012) - Newton's Method, Order of Convergence 17 Lecture 17 (03/09/2012) - Secant Method, Muller's Method, Polynomials as Non-linear functions 18 Lecture 18 (04/09/2012) - Newton's Method for Simple Roots, Multiple Roots 19 Lecture 19 (05/09/2012) - Solution of System of Non-linear Equations 20 Lecture 20 (10/09/2012) - Polynomial Approximations 21 Lecture 21 (11/09/2012) - Divided Difference Polynomial, Newton's Forward Difference Polynomial 22 Lecture 22 (12/09/2012) - Newton's Difference Polynomials, Inverse Interpolation 23 Lecture 23 (24/09/2012) - Multivariate Polynomial Approximation, Cubic Splines. 24 Lecture 24 (26/09/2012) - Cubic Splines. 25 Lecture 25 (28/09/2012) - Method of Least Squares. 26 Lecture 26 (01/10/2012) - Numerical Differentiation using Polynomial Approximations 27 Lecture 27 (03/10/2012) - Difference Formulas using Newton's Polynomials 28 Lecture 28 (04/10/2012) - Difference Formulas 29 Lecture 29 (08/10/2012) - Numerical Integration - Introduction 30 Lecture 30 (09/10/2012) - Numerical Integration - Simpson's Rule 31 Lecture 31 (15/10/2012) - Gaussian Quadrature 32 Lecture 32 (16/10/2012) - Ordinary Differential Equations - Introduction 33 Lecture 33 (17/10/2012) - Finite-Difference Method for Initial Value -ODE (Part-1) 34 Lecture 34 (19/10/2012) - FDM for IV-ODE: Modified Euler Method; Runge-Kutta Method 35 Lecture 35 (29/10/2012) - Runge-Kutta Method; Multi-point Methods 36 Lecture 36 (30/10/2012) - Multi-point Methods; Boundary Value-ODE 37 Lecture 37 (31/10/2012) - BV-ODE: Dirichlet and Neuman BCs 38 Lecture 38 (02/11/2012) - Partial Differential Equations 39 Lecture 39 (03/11/2012) - Elliptic Partial Differential Equations 40 Lecture 40 (05/11/2012) - Parabolic Partial Differential Equations 41 Lecture 41 (06/11/2012) - Hyperbolic Partial Differential Equations 42 Lecture 42 (07/11/2012) - Introduction to FEM 43 Lecture 43 (12/11/2012) - Rayleigh-Ritz; Collocation Methods 44 Lecture 44 (14/11/2012) - Galerkin Weighted Residual; The FEM; Course Conclusion