Anna University 

AFFILIATED INSTITUTIONS

Second Semester 

MA6251 MATHEMATICS – II

UNIT I VECTOR CALCULUS

Gradient, divergence and curl

Green‟s theorem

Stokes‟ theorem

UNIT II ORDINARY DIFFERENTIAL EQUATIONS

Method of variation of parameters

Cauchy‟s and Legendre‟s linear equations

UNIT III LAPLACE TRANSFORM

Transforms of unit step function and impulse functions

Initial and final value theorems

Solution of linear ODE of second order with constant coefficients

UNIT IV ANALYTIC FUNCTIONS

Cauchy-Riemann equations and sufficient conditions

Conformal mapping

Bilinear transformation

UNIT V COMPLEX INTEGRATION

Taylor‟s and Laurent‟s series

Cauchy‟s residue theorem

Evaluation of real definite integrals