Fourier Series and Method of Separation of Variables (Boundary Value Problems): Expansion of simple functions in Fourier series, half range series, change of interval, harmonic analysis, application to the solution of wave equation and diffusion equation in one dimension and Laplace's equation in two dimensions by method of separation of variable.

Laplace Transform: Laplace transform with its simple properties, Inverse Laplace transform convolution theorem (without proof) solution of ordinary differential equation with constant coefficient.

Special Functions: Bessel's function of first kind, simple recurrence relations, orthogonal property, Legendre's function of first kind simple recurrence relations, orthogonal property, Rodrigue's formula.

Numerical Analysis: Finite differences, difference operators, forward, backward, central and average operators, Newton's forward and backward interpolation formula, Stirling's central difference formula Lagrange's interpolation formula for unequal interval, Solution of non linear equations in one variable by newton raphson's and regula falsi's method.

Numerical Analysis: Numerical solution of simultaneous algebraic equation by Gauss elimination and Gauss Siedel method, Numerical differentiation, Numerical integration trapezoidal rule, Simpson's one third and three eight rule, Numerical solution of ordinary differential equation of first order, Picard's method, Euler's, and modified Euler's method, Milne's methods and Runga Kutta fourth order method.

**Suggested Readings:**

1. Advanced Engineering Mathematics, Kreyszig E., Wiley Eastern.

2. Advance Mathematics for Engineers, Chandrika Prasad, Prasad Mudranalaya, Allahabad.

3. Advanced Engineering Mathematics, Potter, Goldhers and Aboufadel, Wiley Eastern.

4. Numerical Methods for Scientist And Engineers, Jain and Jain, Iyengar S.R.K., Wiley Eastern

5. A First Course in Numerical Analysis, Ralston A., Rabinowitz P., McGraw Hill