NUMERICAL ANALYSIS
Introduction: Floating point representation of numbers and roundoff errors, Interpolation Numerical integration. Linear systems and matrix theory: Various factorizations of inversion of matrices, Condition number and error analysis. Non-linear systems: Fixed point iteration, Newton-Rapson and other methods, Convergence acceleration. Numerical methods for ODE: Introduction and analysis of Taylor, Runge-kutta and other methods. Numerical methods for PDE: Finite difference method for Laplace, Heat and wave equations.
Books
- Faires, J. D. and Burden, R., Numerical Methods, Brooks/Cole Publishing Co., 1998.
- Conte, S. D. and Carl de Boor., Elementary Numerical Analysis, McGraw-Hill, 1988.
- Stoer, J. and Bilrisch, R., Introducation to Numerical Ana;lysis, Springer- Verlag, 1993.
- Iserlas, A., First course in the numerical analysis of differential equations, Cambridge, 1996.