Module No.

Topic/s

Lectures

1

Polynomial and piecewisepolynomial Interpolation:

• Divided Difference, Lagrange and Newton Form

• Osculatory Interpolation

4

2

2

Numerical Integration:

• Some Basic Rules, Gaussian Integration, Composite Rules

• Adaptive Quadrature, Romberg integration

4

3

3

Numerical Differentiation

2

4

Vector and Matrix Norms

2

5

Solution of System of Linear Equations:

• Gauss Elimination Method, Partial Pivoting

• Jacobi and GaussSeidel Methods

• QR factorization using reflectors

3

3

2

6

Eigenvalue Problem:

• Basic properties:

• Eigenvalue location:

• Power Method and its variants:

3

3

2

7

Initial Value Problems:

• Single step methods such as Euler's Method, RungeKutta
  Methods, Taylor series method

• Multistep methods such as AdamsBashforth method, Milne's method

• PredictorCorrector Formula: AdamMoulton method

3

3

2

8

Boundary value problem:

• Finite Difference method

2

9

Solution of nonlinear system of equations:

3