Part 1: Introduction and Preliminaries (approximately 6 hours)
Some numerical algorithms, interpolation, numerical differentiation and numerical integration.
Part 2: Numerical Methods for ODE's (approximately 15 hours)
Euler, modified Euler, Runge-Kutta methods, multistep methods.
Finite difference method and the shooting method for boundary value problems.
Part 3: Numerical Methods for PDE's (approximately 21 hours)
Basic properties of PDE's, elliptic, parabolic and hyperbolic PDE's. Finite difference,
finite element and finite volume methods. Spectral methods. Multigrid methods. The level set method.
