Successive differentiation of various types of functions.
Leibnitz's theorem. Rolle's theorem, Mean value theorem,
Taylor's and Maclaurin's theorems in finite and infinite forms. Lagrange's form of remainders.
Cauchy's form of remainders. Expansion of functions, evaluation of indeterminate forms of L' Hospital's rule. Partial differentiation. Euler's theorem.
Tangent and normal. Subtangent and subnormal in cartesian and polar co-ordinates.
Determination of maximum and minimum values of functions.
Curvature. Asymptotes. Curve tracing.
Integral Calculus:
Integration by the method of substitution. Standard integrals.
Integration by successive reduction.
Definite integrals, its properties and use in summing series. Walli's formulae.
Improper integrals. Beta function and Gamma function.
Area under a plane curve and area of a region enclosed by two curves in cartesian and polar co-ordinates.
Volumes and surface areas of solids of revolution.