**Course Details:**

Linear functional, interpolation by polynomial, error estimation, numerical differentiation and integration.

Solution of a system of linear equations: Gaussian elimination, solution by iteration, pivoting strategy, triangular factorization, ill-conditioning, norms.

Eigenvalue problem, power method, QR method.

Solution of a nonlinear equation by iterative methods like bisection, secant methods and Newton-Raphson method.

Newton’s method, rate of convergence, solution of a system of nonlinear equations.

Numerical solution of ordinary differential equations: Euler and Runge-Kutta methods, multi-step methods, predictor-corrector methods, order of convergence, finite difference methods, numerical solutions of elliptic, parabolic, and hyperbolic partial differential equations.

Exposure to software packages like IMSL subroutines, MATLAB.

**Text Books:**

- S. D. Conte and Carl de Boor, Elementary Numerical Analysis- An Algorithmic Approach (3rd Edition), McGraw-Hill, 1980.
- E. Kreyszig, Advanced engineering mathematics, 10th Edition, John Wiley & sons (2011).