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

SYLLABUS

Semester II - Allied I - For B.Sc. Mathematics

Duration of Examination: 3 hrs
Maximum Marks: 100
Credits: 4

Calculus of finite differences and Numerical Analysis - Paper II (135 hrs.)

Numerical differentiation:

Derivatives using Newton's forward and backward difference formulae, Derivatives using Sterling's formula, Derivative using divided difference formula, Maxima and Minima using the above formulae.

Numerical integration:

General quadrature formula, Trapezoidal rule, Simpson's one-third rule, Simpson's three-eigth rule, Weddle's rule, Euler-Maclaurin Summation formula, Sterling's formula for n!.

Difference equations:

Linear homogenous and nonhomogenous difference equation with constant coefficients, particular integrals for a^ux^m, x^{^}m, sinkx, coskx.

Numerical solution of oridinary difference equations (I order only)

Taylor's series method, Picard's method, Euler's method, modified Euler's method, Runge- kutta method fourth order only, Predictor-corrector method- Milne's method and Adams-Bashforth method.

Reference Books:

1. Calculus of finite differences and Numerical Analysis by Gupta-Malik, Krishna prakastan Mandir, Meerut.

2. Numerical methods in Science and Engineering by M.K.venkataraman, National publishing house, Chennai.

3. Numerical Analysis by B.D. Gupta, Konark publishing.

4. Calculus of finite differences and Numerical Analysis by Saxena, Chand & Co.