## Syllabus For The Subject MATHEMATICAL AND NUMERICAL METHODS

UNIT - 01

DIFFERENTIAL EQUATIONS AND SPATIAL FUNCTION - SECOND ORDER DIFFERENTIAL

EQUATION - SERIES SOLUTION - GENERATING FUNCTIONS - RODRIGUE`S FORMULA

UNIT - 02

RECURRENCE RELATION AND ORTHOGONALLY PROPERTY FOR BESSEL - LEGENDRE

UNIT - 03

COMPLEX VARIABLE: FUNCTIONS OF A COMPLEX VARIABLE - ANALYTIC FUNCTIONS -

CAUCHY REIMANN CONDITIONS MULTI VALUED FUNCTIONS AND BRANCH POINTS

UNIT - 04

CACHY`S INTEGRAL THEOREM AND FORMULA

UNIT - 05

LAPLACE AND FOURIER TRANSFORMS - LAPLACE TRANSFORMS - INVERSE LAPLACE

TRANSFORM APPLICATION TO DIFFERENTIAL AND INTEGRAL EQUATION.

UNIT - 06

FOURIER TRANSFORM AND INTEGRAL THEOREM - CONVOLUTION THEOREM

UNIT - 07

CURVE FITTING - PRINCIPLES OF LEST SQUARES - FITTING A STRAIGHT LINE - PARA

BELL - EXPONENTIAL CURVE - CURVE OF A FORM Y=AXB AND Y=ABX.

UNIT - 08

THEORETICAL DISTRIBUTION - BINOMIAL DISTRIBUTION - FORMULA FOR MEANS -

STANDARD DEVIATION - POISSON DISTRIBUTION

UNIT - 09

FORMULA FOR MEAN - STANDARD DEVIATION MOMENTS NORMAL DISTRIBUTION -

FORMULA FOR MEAN - STANDARD DEVIATION

UNIT - 10

SOLUTIONS OF NUMERICAL - ALGEBRA - TRANSCENDENTAL AND DIFFERENTIAL

EQUATION - PICARD`S METHOD OF SUCCESSIVE APPROXIMATIONS - NEWTON -

REPHSON METHOD.

UNIT - 11

EULER`S METHOD - MODIFIED EULER`S METHOD - RUNGE - KUTTA METHOD (SECOND

AND THIRD ORDER ONLY) - GAUSS ELIMINATION METHOD

UNIT - 12

LAGRANGE`S INTERPRETATION FORMULA FOR UNEQUAL INTERVALS TRAPEZOIDAL

RULE - SIMPSON`S (1/3) AND (1/8) RULES

Vinayaka Missions University,Directorate of Distance Education

Salem India

MASTER OF SCIENCE IN PHYSICS

1 Yr.

MATHEMATICAL AND NUMERICAL METHODS(2030505)