Course Instructor: Dr. Himanshu Tyagi
(L-T-P-S-C structure; 3-0-0-6-3)
Course Content: Introduction and motivation, Types of solutions, algorithms and programming languages, error analysis, types of errors, Roots of equations, bracketing methods, graphical method, bisection method, false-position method, open methods, Newton-Raphson method, Secant method, convergence & divergence, Interpolation and polynomial approximation, Finite difference approximations, Newton’s forward and backward differences, Lagrange’s interpolation, divided differences, Cubic spline method, Numerical integration and differentiation, Differentiation using finite difference operators, Richardson’s method, differentiation using interpolation, trapezoidal rule, Simpson’s rule, Solutions of systems of linear algebraic equations, Matrix inversion and Eigen value problems, Gaussian elimination method, Gauss-Jordan elimination method, Solutions of ordinary and partial differential equations, Taylor series method, Euler method, Runge-Kutta method, finite difference methods, explicit, implicit, Crank-Nicholson method, alternate direction implicit method, finite volume method.
Steven C. Chapra, and Raymond P. Canale, Numerical Methods for Engineers, 8th ed., McGraw Hill Education India Pvt Ltd, India, 2021.
M.K. Jain, S.R.K. Iyenger, R.K. Jain, Numerical Methods for Scientific and Engineering Computation, 7th Ed., New Age International, New Delhi, 2019.