This course is designed to develop advanced topics of differential and integral calculus. Emphasis is placed on the applications of definite integrals, techniques of integration, indeterminate forms, improper integrals and functions of several variables. The topics to be covered are differentiation of inverse, circular, exponential, logarithmic, hyperbolic and inverse hyperbolic functions.  Leibnitz’s theorem. Application of differentiation to stationary points, asymptotes, graph sketching, differentials, L’Hospital rule.  Integration by substitution, by parts and by use of partial fractions. Reduction formulae. Applications of integration to plane areas, volumes and surfaces of revolution, arc length and moments of inertia.  Functions of several variables, partial derivatives.