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.