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

SYLLABUS

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

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

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

Solutions of algebraic and Transcendental equations, Bisection method, Iteration method, Regula falsi method, Newton-Raphson method.

Solution of simultaneous linear equations:

Guass - elimination method, Guass - Jordan method, Gauss - Siedel method, Crout's method.

Finite differences:

E operators and relation between them, Differences of a polynomial, Factorial polynomials, differences of zero, summation series.

Interpolation with equal intervals:

Newton's forward and backward interpolation formulae. Central differences formulae- Gauss forward and backward formulae, Sterling's formula and Bessel's formula.

Interpolation with unequal intervals:

Divided differences and Newton's divided differences formula for interpolation and Lagrange's formula for interpolation.

Inverse Interpolation - Lagrange's method, Reversion of series 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, S.Chand & Co.