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.