# Numerical Methods EC Syllabus for NIT Jalandhar

MA-202 Numerical Methods [3 1 0 4]

Department of Electronics and Communication Engineering
Dr B R Ambedkar National Institute of Technology, Jalandhar
15
Approximation and Errors: Accuracy of numbers, Errors in approximations, Order of approximation and Propagation of errors.
Roots of Algebraic and Transcendental Equations: Bisection method, Regula-falsi method, Iteration method, Newton-Raphson method, Bairstow’s method and Graeffe’s root squaring method.
Solution of Simultaneous Algebraic Equations, Matrix Inversion and Eigen-value Problems:
Triangularisation method, Jacobi’s and Gauss-Siedel iteration methods, Newton-Raphson method for nonlinear simultaneous equations, Triangularisation method for matrix inversion, Partition method for matrix inversion, Power method for largest eigen-values and Jacobi’s method for finding all eigen-values.
Finite Differences Interpolations and Numerical Differentiations: Forward, Backward, Central
differences and relations between them, Newton’s forward, backward and divided difference interpolation formulas, Lagrange’s interpolation formula, Stirling’s and Bessel’s central difference interpolation formulas, Numerical differentiations using Newton’s forward and backward difference formulas and Numerical differentiations using Stirling’s and Bessel’s central difference interpolation formulas.
Numerical Integrations: Trapezoidal rule, Simpson’s one-third rule and Numerical double integrations using Trapezoidal rule and Simpson’s one-third rule.
Numerical Solution of Differential Equations
Ordinary Differential Equations: Taylor’s series method, Euler’s and modified Euler’s methods, Runge-
Kutta fourth order methods, methods for solving simultaneous first order differential equations and methods for solving second order differential equations.
Boundary Value Problems: Finite difference methods for Boundary Value Problems
Partial Differential Equations: Finite difference methods for Elliptic, Parabolic and Hyperbolic equations
Books Recommended
1. Ames, W F., Numerical Methods for Partial Differential Equations, 3rd edition, Academic Press,
New York (1992).
2. Dahlquist, G. and Björck, A., “Numerical Methods”, Prentice-Hall, NJ (1974).
3. Jain, M K., Iyengar, S R.K and Jain, R K., “Numerical Methods for Scientific and Engineeing
Computations”, 4th edition New Age International (P) Limited, Publishers, New Delhi, (2003).
4. Shampine, L F, “Numerical Solution of Ordinary Differential Equations”, Chapman and Hall,
New York, (1994).
5. Shampine,L F et al., “Fundamentals of Numerical Computing ”, Wiley, New York, (1996).
6. Stewart, G W, “Introduction to Matrix Computations”, Academic Press, New York, (1973).