Function, Domain, and range. Graphical representation of a function. Limit, continuity and differentiability, Differentiation of explicit and implicit functions and parametric equations, Significance of derivatives, Differentials,
# Successive differentiation:
Successive differentiation of various types of functions, Leibnitz's theorem, Rolle's Theorem, Mean value theorem, Taylor's theorem in finite and infinite forms, LaGrange's form of remainders, Cauche's form of remainders, Expansion of functions by differentiation and integration, partial differentiation, Euler's theorem, Tangent Normal, subtangent and subnormal in Cartesian and Polar co-ordinates, differentiation of maximum and minimum values of function and point of inflection, Application, Evaluation of indeterminate forms by L'Hospital's rule, Curvature, center of curvature, Evaluate and inviolate, Asymptotes, Envelopes, Curve tracing.
Definitions of integration, Integration by methods of substitution, Integration by parts, Standard integrals, Integration by methods of successive reduction.
# Definite Integrals:
Definite Integrals, its properties and use in summing series, Wallis's formulae, Improper Integrals, Beta function and Gamma function.
#Area under a plain curve:
Area under a plain curve in Cartesian and polar co-ordinates, area of the region enclosed by two carves in Cartesian and polar co-ordinates, Trapezoidal rule, Simpson's rule, length of curves in Cartesian and polar co-ordinates, parametric and pedal equations, Intrinsic equation, Volumes of solids of revolutions, Volume of hollow solid of revolution. Volume of hollow solid of revolution by shell method, Area of structure of revolution.