Module-1:
Evaluation of improper integrals of Type-I and Type-II, Beta and Gamma functions and their properties.
Module-2:
Taylor’s and Maclaurin’s theorem for a function of one variable, Taylor’s and Maclaurin’s series of a function using statement of the theorems; Indeterminate forms and L' Hospital's rule.
Module-3:
Sequence of numbers and its convergence, Infinite series; Tests for convergence (Telescoping series, Geometric series test, Integral test, p- test, comparison test, D’ Alembert’s ratio test, Cauchy’s root test), Alternating series test; Power series, Radius and interval of convergence
Module-4:
Limit, Continuity and Differentiation for function of two or more variables, total derivative, Extreme values for functions of two variables (Maxima, minima and saddle points).
Module-5:
Multiple Integration: Double integrals (Cartesian, Polar), change of order of integration in double integrals, Change of variables (Cartesian to polar), Applications: areas and volumes, Triple integrals (Cartesian).