Differential Calculus: Limit, Continuity and differentiability; Differentiation of explicit and implicit function and parametric equations, Significance of derivatives, Differentials, Successive differentiation of various types of functions. Leibnitz’s theorem, Rolle’s theorem, Mean value theorems, Taylor’s theorem in finite and infinite forms, Maclaurin’s theorem in finite and infinite forms, Langrange’s form of remainders, Cauchy’s form of remainder, Expansion of functions by differentiation and integretion, Partial differentiation, Euler’s theorem. Tangent, Normal, Subtangent and subnormal in Cartesian and polar coordinates, Determination of maximum and minimum values of functions and points of inflection, Applications, Evaluation of indeterminate forms by L’Hospitals rule, Curvature, Circle of curvature, center of curvature and chord of curvature, Evolute and involute, Asymptotes, Envelopes, Curve tracing.
Integral Calculus: Definitions of integrations, Integration by method of substitution. Integration by parts, Standard integrals, Integration by the method of successive reduction. Definite integrals, its properties and use in summing series; Wallis’s formulae, Improper Integrals, Beta function and Gamma function; Area under a plane curve in Cartesian and Polar co-ordinates, Area of the region enclosed by two curves in Cartesian and Polar co-ordinates, Trapezoidal rule, Simpson’s rule. Arc lengths of curves in Cartesian and Polar co-ordinates, parametric and pedal equations, Intrinsic equation, Volumes of solids of revolution, Volume of hollow solids of revolution by shell method, Area of surface of revolution, Jacobians, Multiple integrals with application.
 M.R. Spiegel, Advanced Calculus, I/e, McGraw-Hill, 1974
 Thomas & Finney, Calculus & Analytic Geometry, 6/e, Norosa pnblishing House, India, 1996
 JR.F. Ayres, Schaum’s outline of Theory and problems of Calculus(Differential & Integral), 2/e, McGraw-Hill, 1974
 Das & Mukharjee, Differential Calculus, 43/e, Dhur & Sons, India, 1997
 Das & Mukharjee, Integral Calculus, 43/e, Dhur & Sons, India, 1997