Part- A
1. Fourier series: Periodic Functions, Euler’s Formula. Even and odd Functions, Half range expansions,
Fourier series of different waveforms. [4]
2. Laplace transformations: Laplace transforms of various standard functions, properties of Laplace
transform. [4]
3. Partial Differential Equations: Formation of Partial Differential Equations, linear Partial Differential
Equations, Homogeneous Partial Differential Equations with constant coefficients. [5]
4. Functions of complex variables: Limits, continuity and derivatives of the function of complex variables,
Analytic function, Cauchy- Riemann equations, conjugate functions. [5]
Part- B
5. Linear Systems and Eigen- Values: Gauss - elimination method, gauss- Jordan method, Gauss- Seidel
iteration method, Rayleigh’s Power method for Eigen values and Eigenvectors. [4]
6. Differential Equations: Solutions of Initial values problems using Eulers, modified Eulers method and
Runge- kutta (upto fourth order) methods. [4]
7. Probability distribution: Binomial, Poisson and Normal distribution. [4]
8. Sampling Distribution & testing of Hypothesis: Sampling, Distribution of means and variance, ChiSquare
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.