Specific Objectives of course:
This course is designed to teach the students about numerical methods and their theoretical bases. The course aims at inculcating in the students the skill to apply various techniques in numerical analysis, understand and do calculations about errors that can occur in numerical methods and understand and be able to use the basics of matrix analysis.
Floating point arithmetic, approximations and errors.
Methods for the solution of nonlinear equations:
Bisection method, regula-falsi method, fixed point iteration method, Newton-Raphson method, secant method, error analysis for iterative methods.
Interpolation and polynomial approximation:
Lagrange interpolation, Newton’s divided difference formula, forward, backward and centered difference formulae, interpolation with a cubic spline, Hermite interpolation, least squares approximation.
Forward, backward and central difference formulae, Richardson’s extrapolation.
Rectangular rule, trapezoidal rule, Simpson’s 1/3 and 3/8 rules, Boole’s and Weddle’s rules, Newton-Cotes formulae, Gaussian quadrature.
Numerical solution of a system of linear equations:
Direct methods: Gaussian elimination method, Gauss-Jordan method; matrix inversion; LU-factorization; Doolittle’s, Crout’s and Cholesky’s methods, Iterative methods: Jacobi, Gauss-Seidel and SOR. The use of software packages/programming languages for above mentioned topics is recommended.