Differential Caluculus

SYLLABUS- DIFFERENTIAL CALCULUS,

Unit-I: Limit of a function, Continuous functions and kinds of discontinuities, Differentiability, Chain rule of differentiability, Rolle's theorem, First and second mean value theorems, Successive differentiation and Leibnitz's theorem, Taylor's theorem with Lagrange's and Cauchy's forms of remainders.

Unit-II: Expansion of functions (in Taylor's and Maclaurin's series), Indeterminate forms, Partial differentiation and Euler's theorem, Jacobians, Tangents and normals (polar form only).

Unit-III: Curvature, Envelopes and evolutes, Asymptotes, Tests for concavity and convexity. Points of inflexion, Multiple points, Tracing of curves in Cartesian and polar co-ordinates.

Unit-IV: Definite Integral as the limit of a sum, Reduction formulae, Beta and Gamma functions.

Unit-V: Qudrature, Rectification, Volumes and Surfaces of solids of revolution, Double and triple integrals, Change of order of integration.