Numerical Analysis & Computer programming

Credits: 4 (3 lectures and 2 lab hours weekly)

Prerequisites: None. Not open for undergraduates.

Overview: This course takes up the problems of practical computation that arise in various areas of mathematics such as solving algebraic or differential equations. The focus is on algorithms for obtaining approximate solutions, and almost half of the course will be devoted to their implementation by computer programs in MATLAB.

Detailed Syllabus:

1. Solving equations: Iterative methods, Bisection method, Secant method, and Newton-Raphson method.
2. Solving Linear systems: Gaussian Elimination and pivoting
3. Computing eigenvalue and eigenvector: Jacobi method
4. Curve fitting
5. Solution of ODEs and systems: Runge-Kutta method, Boundary value problems, Finite Difference Method
6. Solutions of PDEs

References:

1. Numerical Methods using Matlab, by John H. Mathews and Kurtis D. Fink, 4^th edition, PHI, 2009.
2. An Introduction to Numerical Analysis, by E. Suli and D. Mayers, Cambridge University Press.
3. Numerical Analysis, by Rainer Kress, Springer, 2010.
4. Introduction to Numerical Analysis, by J. Stoer and R. Bulirsch, 3^rd edition, Springer, 2009.