Week 1: Introduction to significant digits and errors, Solution of system of linear Equations (direct methods, Iterative methods, Ill-conditioned systems)
Week 2: Roots of Nonlinear Equations (Bisection method, Regula-Falsi method, Newton-Raphson method, Fixed point iteration method, convergence criteria
Week 3: Eigenvalues and Eigenvectors, Gerschgorin circle theorem , Jacobi method, Power methods
Week 4: Interpolation (Finite difference operators, difference tables, Newton's Forward/Backward difference)
Week 5: Interpolation ( Central difference formula's i.e. Bessel and Stirling’s interpolation formulae, Divided differences, Lagrange interpolation and Newton’s divided difference interpolation)
Week 6: Numerical Differentiation (Using Forward/ Backward/central difference formula) Week:7 Integration (Trapezoidal and Simpson's rules for integration)
Week 8: Solution of first order and second order ordinary differential equations (Euler method, Euler modified method, Runge-Kutta methods, Milne PC method)
BOOKS AND REFERENCES
1. Gerald, C. F. and Wheatly, P. O.," Applied Numerical Analysis", 6th Edition, Wesley.
2. Jain, M. K., Iyengar, S. R. K. and Jain, R. K., "Numerical Methods for Scientific and Engineering Computation", New Age Pvt. Pub, New Delhi.
3. Conte, S. D. and De Boor, C., "Elementary Numerical Analysis", Mc Graw Hill Publisher.
4. Krishnamurthy, E. V. & Sen, S. K., "Applied Numerical Analysis", East West Publication.