1. Introduction
2. Polynomial Approximation
3. Interpolating Polynomials
4. Properties of Divided Difference
5. Error in the Interpolating Polynomial
6. Cubic Hermite Interpolation
7. Piecewise Polynomial Approximation
8. Cubic Spline Interpolation
9. Tutorial 1
10. Numerical Integration: Basic Rules
11. Composite Numerical Integration
12. Gauss 2-point Rule: Construction
13. Gauss 2-point Rule: Error
14. Convergence of Gaussian Integration
15. Tutorial 2
16. Numerical Differentiation
17. Gaussian Elimination
18. LU Decomposition
19. Cholesky Decomposition
20. Gauss Elimination with Partial Pivoting
21. Vector and Matrix Norms
22. Perturbed Linear Systems
23. ILL-conditioned Linear System
24. Tutorial 3
25. Effect of Small Pivots
26. Solution of Non-linear Equations
27. Quadratic Convergence of Newton's Method
28. Jacobi Method
29. Gauss-Seidel Method
30. Tutorial 4
31. Initial Value Problem
32. Multi-step Methods
33. Predictor-Corrector Formulae
34. Boundary Value Problems
35. Eigenvalues and Eigenvectors
36. Spectral Theorem
37. Power Method
38. Inverse Power Method
39. QR Decomposition
40. QR Method

The important topics covered in this course are polynomial and piecewise polynomial (spline) interpolation, numerical integration and numerical differentiation, approximate solutions of differential equations, direct and iterative solution of a system of linear equations and eigenvalue problems. The theory behind various methods is rigorously discussed. Emphasis is on comparison of various methods and their implementation using a computer.