UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN ELECTRONICS SCIENCE
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)

Semester III - Paper III - Numerical Methods

Duration: 3 hrs
Maximum Marks: 100
Credits: 4

Unit-1

Interpolation : Newton's Forward and Backward formulae - Divided differences and their properties, Stirling's and Bessel's formulae - Lagrange's formula - simple problems.

Unit-2

Numerical integration : General Quadrature formula - Trapizoidal rule, Simpson's 1/3 rule, Euler-Maclaurin's formula, Stirling's formula for factorial n - Summation of series by Euler - Maclaurin' s formula.

Unit-3

Solutions of transcendental and polynomial equations in one variable: Method of iteration Newton-Raphson method - Regula Falsi method - Successive bisection method.
Solution of linear equation : Gauss reduction method - Exchange method - Jacobi iteration method - Gauss-Seidel method.

Unit-4

Solutions of differential equations : Numerical solution of ordinary differential eqiation of first order - Euler's method - Modified Euler's method - Picard's method of successive approximation - Runge-Kutta method (Second and third order only).

Unit-5

Methods of curve fitting : Least square analysis - Matrix inversion - Gauss elimination method - Co-factor method - partition method.

Books for study and reference