Linear Algebra | Vector space, basis, linear dependence and independence, matrix algebra, eigenvalues, and eigenvectors, rank, solution of linear equations - existence and uniqueness. |
Differential Equations | First-order equations (linear and nonlinear), higher order linear differential equations, Cauchy's and Euler's equations, methods of solution using a variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems. |
Calculus | Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series |
Complex Analysis | Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, sequences, series, convergence tests, Taylor and Laurent series, residue theorem. |
Vector Analysis | Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss's, Green's and Stokes’ theorems. |
Probability and Statistics | Mean, median, mode, standard deviation, combinatorial probability, probability distributions, binomial distribution, Poisson distribution, exponential distribution, normal distribution, joint and conditional probability. |
