Sequences & Series and Differential Calculus: Sequences of real numbers, Convergent sequences and series, absolute and conditional convergence. Mean Value Theorem, Taylor’s theorem, Maxima and Minima of functions of a several variables. Partial derivatives, maxima and minima.

Integral Calculus: Integration, Fundamental theorem of calculus, Double and Triple, integrals, Surface Areas and Volumes.

Differential Equations: Ordinary differential equations of the first order of the form y’= f(x.y). Linear Differential Equations of second order with constant coefficients, Euler Cauchy Equation, method of variation of parameters.

Vector Calculus: Gradient, divergence, curl, Laplacian. Green’s, Stokes’ and Gauss’ theorems and their Applications.

Algebra: Groups, sub-groups and normal subgroups, Lagrange’s Theorem on finite groups, group homomorphisms and basic concepts of quotient groups, rings, ideals, quotient rings and fields.

Linear Algebra: Systems of Linear Equations, Matrices, rank, determinant, inverse, Eigenvalues and eigenvectors. Finite Dimensional Vector Spaces over Real and Complex Numbers, Basis, Dimension, Linear Transformations.

Real Analysis: Open and closed sets and limit points, completeness in R, Uniform Continuity, Uniform Convergence, Power Series.