Matrix algebra, Systems of linear equations, Eigenvalues and eigenvectors.
Calculus: 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.
Differential equations: First order equations (linear and nonlinear). Higher order linear differential equations with constant coefficients, Method of aviation of parameters, Cauchy's and Euler's equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.
Complex Variables: Analytic functions, Cauchy's integral theorem and integral formula. Taylor 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.
Numerical Methods: Solutions of nonlinear algebraic equations, single and multi-step methods of differential equations.
Transform Theory: Fourier transform, Laplace transform, Z-transform.