1. Fourier series: Periodic Functions, Euler’s Formula. Even and odd Functions, Half range

expansions, Fourier series of different waveforms.

2. Laplace transformations: Laplace transforms of various standard functions, properties of

Laplace transform 

3. Partial Differential Equations: Formation of Partial Differential Equations, linear Partial

Differential Equations, Homogeneous Partial Differential Equations with constant coefficients. 

4. Functions of complex variables: Limits, continuity and derivatives of the function of complex

variables, Analytic function, Cauchy- Riemann equations, conjugate functions. 

5. Linear Systems and Eigen- Values: Gauss – elimination method, gauss- Jordan method, GaussSeidel

iteration method, Rayleigh’s Power method for Eigen values and Eigenvectors. 

6. Differential Equations: Solutions of Initial values problems using Eulers, modified Eulers

method and Runge- kutta (upto fourth order) methods.

7. Probability distribution: Binomial, Poisson and Normal distribution.

8. Sampling Distribution & testing of Hypothesis: Sampling, Distribution of means and

variance, Chi- Square distribution, t- distribution, F- distribution. General concepts of hypothesis,

Testing a statistical Hypothesis, One and two tailed tests, critical region, Confidence interval

estimation. Single and two sample tests on proportion, mean and variance.