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

SYLLABUS

Semester V - Application Oriented Subject - Numerical Methods

Practical: 40
Record: 10
Total: 50

Unit I

Curve Fitting:

Principle of least squares - fitting a straight line - linear regression - fitting a parabola - fitting an exponential curve.

Unit II

Solution of numerical algebraic, transcendental and differential equations:

Bisection method - method of successive approximations - Regula Falsi method - Newton-Raphson method - Homer's method - Euler's method - modified Euler's method - Runge Kutta method (II & IV).

Unit III

Simultaneous linear algebraic equations:

Gauss elimination method - Gauss-Jordan method - Gauss-Seidel method - computation of inverse of a matrix using Gauss elimination method - method of triangularisation.

Unit IV

Interpolation:

First differences - difference tables - properties of the operator A.E.D.
Linear interpolation: Newton forward interpolation formula and backward interpolation formula - Bessel's Formula.
Interpolation with unequal intervals: Lagrange's interpolation formula.

Unit V

Numerical Integration:

Trapezoidal rule - Simpson's 1/3 rule and 3/8 rule - practical applications - Weddle's rule - Gaussian Quadrature formulae.

Books for Study and Reference:

1. Venkatraman, M.K. (1977) Numerical Methods in Science and Engineering, National publishing Company - Chennai.

2. Shastry, S.S, Introductory methods of numerical methods - Prentice-Hall Ltd.

3. Jam, Iyenfar, S.R.K. and Jam R.K. Numerical methods for Scientific and Engineering Computation - New Age Publishers.