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**Linear Algebra:**

Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.

**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 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, PartialDifferential Equations, Method of separation of variables

**Complex variables:**

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.

**Numerical Methods:**

Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

**Transform Theory:**

Fourier transform, Laplace transform, Z-transform.