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.
- 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).