Numerical Methods

This course is a basic course offered to UG student of Engineering/Science background. It contains solution of system of linear equations, roots of non-linear equations, interpolation, numerical differentiation and integration. It plays an important role for solving various engineering sciences problems. Therefore, it has tremendous applications in diverse fields in engineering sciences.INTENDED AUDIENCE: UG students of technical universities/colleges.PREREQUISITES: NILINDUSTRY SUPPORT: TCS, Intel, General Electric, General Motors, ABB, Nuclear Industries, etc.

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)