Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series Vector identities, Directional derivatives
Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems
First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients
Method of variation of parameters, Cauchy's and Euler's equations, Initial and boundary value problems
Partial Differential Equations and variable separable method.
Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent' series, Residue theorem, solution integrals.
Probability and Statistics:
Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.
Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.
Fourier transform, Laplace transform, Z-transform