Differential Calculus

Limit, Continuity and differentiability, Significance of derivatives, Successive differentiation of various types of functions, Leibnitz’s theorem, Rolle’s theorem, Mean value theorem, Taylor’s theorem in finite and infinite forms, Maclaurin’s theorem in finite and infinite forms, Partial differentiation of different multi- variable functions, Evaluation of indeterminate forms, Tangents, Normals, Subtangents and subnormals in cartesian and polar coordinates, Determination of maximum and minimum values of functions, Points of inflection with applications, Curvature and radius of curvature, Asymptotes, Curve tracing.

Integral Calculus

Definitions of integration, Integration by the method of substitution, Integration by parts, Integration by the method of successive reduction, Definite integrals, Definite integral’s properties and use in summing series, Walli’s formulae, Improper integrals, differentiation and integration under sign of integration, Beta function and gamma function, Jacobian, multiple integrals and their applications.