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

SYLLABUS

Semester IV - Allied IV - Numerical Methods

UNIT - 1:

Finite differences - forward and backward differences operators E and A, and their basic properties - interpolation with equal intervals - Newton's forward and backward differences formulae - simple problems.

UNIT - 2:

Interpolation with unequal intervals - divided differences and their properties - Newton's divided difference formula - Lagrange's formula - simple problems.

UNIT - 3:

Central difference interpolation formula - Gauss forward and backward differences formulae - Stirling , Bessel's Everett's central difference formula.

UNIT - 4:

Inverse interpolation - Lagrange's method - iteration of successive approximation method - simple - problems. Numerical differentiation - Numerical differentiation upto 2^nd order only - simple problems.

UNIT - 5:

Numerical integration - Trepezoidal rule - Simpsons 1/3 and 3/8^th rules - Weddle's rule - Euler's summation formula. Numerical method of solution of ordinary differential equations - Taylor's series method - Euler method and Runga Kutta upto second order - simple problems only.

Books for Study:

Gupta P.P. & Malik G.S.: Calculus of finite differences and numerical analysis.

BOOKS FOR REFERENCE:

Whittakar and Robinson: Calculus of observations, Blackie and sons.
Scarborough, B.: Numerical Mathematical Analysis, OUP.
Sastry, S.S.: Introductory method of numerical analysis, P.H.L.
Ramasamy, M.M. & Palaniappan, K.: Numerical mathematics.
Balasubramanian: Numerical mathematics, Vol. II & I.