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)