1 Basics of Numerical Methods (3 weeks)
1.1 Interpolation
1.2 Numerical Differentiation
1.3 Numerical Integration

2 Basic Discretization Techniques (3 weeks)
2.1 Finite Difference Method
2.2 Finite Volume Method

3 Analysis of Numerical Schemes (2 weeks)
3.1 Numerical Properties- Consistency, Stability, Convergence
3.2 The Von Neumann Method for Stability Analysis
3.3 The Matrix Method for Stability Analysis

4 Numerical Solution of Ordinary Differential Equations (2 week)
4.1 Simple Explicit Method
4.2 Fully Implicit Method
4.3 Crank-Nicolson Method
4.4 Runge-Kutta Method
4.5 Multi-Step Method

5 Weighted Residual Method (3 weeks)
5.1 Finite Element Method
5.2 Spectral Element Method
5.3 Spectral Method

6 Resolution of Discretized Equations (2 weeks)
6.1 Direct method
6.2 Basic Iterative Methods
6.3 Overrelaxation Methods
6.4 Preconditioning Technique
6.5 Conjugate Gradient Method

7. Application to Parabolic PDE

8. Application to Elliptic PDE