Numerical solution of algebraic and transcendental equations, Iterative
algorithms, Convergence, Newton Raphson procedure, Solutions of polynomial and
simultaneous linear equations, Gauss method, Relaxation procedure, Error
estimates, Numerical integration, Euler-Maclaurin formula. Newton-Cotes
formulae, Error estimates, Gaussian quadratures, Extensions to multiple
integrals.

Numerical integration of ordinary differential equations: Methods of Euler,
Adams, Runge-Kutta and predictor - corrector procedures, Stability of solution.
Solution of stiff equations.

Solution of boundary value problems: Shooting method with least square
convergence criterion, Quasilinearization method, Parametric differentiation
technique and invariant imbedding technique.

Solution of partial differential equations: Finite-difference techniques,
Stability and convergence of the solution, Method of characteristics. Finite
element and boundary element methods.

Suggested books and references:

Gupta, A. and Bose, S. C., Introduction to Numerical analysis, Academic Publishers, 1989.

Conte, S. D. and Carl de Boor., Elementary Numerical Analysis, McGraw-Hill, 1980.

Hildebrand, F. B., Introduction to Numerical Analysis, Tata McGraw-Hill, 1988.

Froberg, C. E., Introduction to Numerical Analysis, Wiley, 1965.