Linear Algebra: n-dimensional vectors, addition and scalar multiplication. Linear dependence and independence of set vectors. Matrices, operations of addition, scalar multiplication and product; determinants and their properties; sub-matrices and rank; inverse of a matrix. Theory of a system of linear equations, linear transformation and matrices, Eigen values and Eigen vectors of a matrix; eigen values of Hermitian, skew Hermitian and unitary matrices; bilinear quadratic forms.
Analytical geometry: Plane polar coordinates, coordinate transformation. Solid geometry and spheres and quadric surface. Spherical polar and cylindrical polar coordinates.
Functions of several variables: Mean value theorem for function of several variables, maxima and minima, differentiation under the sign of integration. Jacobians.
Numerical Analysis: Numerical differentiation and quadratic formulae. Analytic and numerical solution of ordinary differential equations. Curve fitting and least squares. Further on linear programming (simplex method).