Algebra: Set theory and its simple applications. Basic concepts of groups, fields and vector spaces. Matrices: Rank of a matrix. Existence and uniqueness of solution of a system of linear equation. Eigenvalues and Eigenvectors. Inverse of a matrix by elementary transformations. Differential Calculus: Differentiation, Partial differentiation, Taylor series and approximate calculations. Maxima and minima of functions of one and two variables. Integral Calculus: Single and multiple integration. Definite integrals, Change of order and change of variables. Application to evaluation of area, surface and volume. Differential Equations: First order differential equations, linear differential equations of higher order with constant coefficients. Vector Algebra: Addition, subtraction, dot product, cross product, triple product and their applications. Numerical Analysis: Solution of non-linear equations using iterative methods. Interpolation (Lagrange’s formula and Newton’s formulae for equidistant points). Numerical differentiation and integration (Trapezoidal and Simpson’s rules). Probability: Basic concepts of probability theory. Binomial and Poisson distributions. Linear Programming: Formulation and its graphical solution for two variable problems. |