Series Solution of Ordinary Differential Equation (ODE); Special Functions:
Introduction, validity of series solution of an ordinary differential equation, general method to solve equation of the
type: P0y//+P1y/+P2y=0; problems; Bessel’s equation; properties of Bessel’s function; Recurrence formula for Bessel’s
function of first kind (Jn(x)); Equation reducible to Bessel’s equation; Legendre’s equation, Legendre function;
Recurrence formula for Legendre function (Pn(x)); Orthogonality relation.
Calculus of Complex Variable:
Functions, Limits and Continuity, Analytic Functions, Cauchy Riemann Conditions, Analytic Continuation, Complex Integration
and Cauchy's Theorem, Cauchy's Integral Formula, Taylor's and Laurent Series, Zeros of an Analytic Function; Poles, Essential
Singularities, Residue Theorem and its application to evaluation of integral, Introduction to Conformal Mapping, Simple problems.
Partial Differential Equations (PDE) and its Applications:
Introduction, linear and nonlinear equation of first order; examples; homogeneous linear equations with constant
coefficients and variable coefficient of second order, Separation of variables, Formulation and solution of wave
equation; one dimensional heat flow equation and solution; two dimensional heat flow equation and solution.
1. Higher Engineering Mathematics by Dr. B. S. Grewal
2. Linear Programming & Game Theory by Chakraborty & Ghosh
3. Complex Variables by M. R. Spiegel
4. Partial Differential Equation by K. S. Rao
5. Engineering Mathematics, Arumugam, Scitech.