Numerical Analysis

COURSE LAYOUT

Week 1:Errors in Numerical Computations
1. Ch 1 Mod 1:Error in Numerical Computations.
2. Ch 1 Mod 2:Propagation of Errors and Computer Arithmetic.

Week 2:Interpolation - I
3. Ch 1 Mod 3:Operators in Numerical Analysis.
4. Ch 2 Mod 1: Lagrange’s. Interpolation.
5. Ch 2 Mod 2: Newton’s Interpolation Methods.
6. Ch 2 Mod 3: Central Deference Interpolation Formulae.

Week 3:Interpolation - II
7. Ch 2 Mod 4:Aitken’s and Hermite’s Interpolation Methods.
8. Ch 2 Mod 5: Spline Interpolation.
9. Ch 2 Mod 6:Inverse Interpolation.
10. Ch 2 Mod 7:Bivariate Interpolation.

Week 4:Approximation of Functions
11. Ch 3 Mod 1: Least Squares Method.
12. Ch 3 Mod 2:Approximation of Function by Least Squares Method.
13. Ch 3 Mod 3: Approximation of Function by Chebyshev Polynomials.

Week 5:Solution of Algebraic andTranscendental Equation
14. Ch 4 Mod 1:Newton’s Method to Solve Transcendental Equation.
15. Ch 4 Mod 2: Roots of a Polynomial Equation.
16. Ch 4 Mod 3: Solution of System of Non-linear Equations.

Week 6:Solution of System of Linear Equations-I
17. Ch 5 Mod 1:Matrix Inverse Method.
18. Ch 5 Mod 2:Iteration Methods to Solve System of Linear Equations.
19. Ch 5 Mod 3: Methods of Matrix Factorization.

Week 7:Solution of System of Linear Equations-II
20. Ch 5 Mod 4:Gauss Elimination Method and Tri-diagonal Equations.
21. Ch 5 Mod 5: Generalized Inverse of Matrix.
22. Ch 5 Mod 6: Solution of Inconsistent and Ill Conditioned Systems.

Week 8:Assessment

Week 9:Eigen Values and Eigen Function of Matrices
23. Ch 6 Mod 1:Construction of Characteristic Equation of a Matrix.
24. Ch 6 Mod 2:Eigenvalue and Eigenvector of Arbitrary Matrices.
25. Ch 6 Mod 3: Eigenvalues and Eigenvectors of Symmetric Matrices.

Week 10:Differentiation and Integration-I
26. Ch 7 Mod 1:Numerical Differentiation.
27. Ch 7 Mod 2:Newton-Cotes Quadrature.

Week 11:Differentiation and Integration-II
28. Ch 7 Mod 3:Gaussian Quadrature.
29. Ch 7 Mod 4: Monte-Carlo Method and Double Integration.

Week 12:Ordinary Differential Equations-I
30. Ch 8 Mod 1:Runge-Kutta Methods.
31. Ch 8 Mod 2:Predictor-Corrector Methods.

Week 13:Ordinary Differential Equations-II
32. Ch 8 Mod 3:Finite Difference Method and its Stability.
33. Ch 8 Mod 4: Shooting Method and Stability Analysis.

Week 14:Partial Differential Equations
34. Ch 9 Mod 1:Partial Differential Equation: Parabolic.
35. Ch 9 Mod 2:Partial Differential Equations: Hyperbolic.
36. Ch 9 Mod 3:Partial Differential Equations: Elliptic

Week 15:Final examination