DIFFERENTIAL & INTEGRAL CALCULUS

Limit and Continuity (e and d definition). Types of Discontinuities. Theorems on Limit and Continuity. Differentiability of Functions. Successive Differentiation. Leibnitz's Theorem. 

Unit II

Mean Value Theorem. Rolle's Theorem. Cauchy's Generalised Mean Value Theorem. Lagranges Mean value Theorem. Taylors Theorem with Lagranges & Cauchy's form of remainder. Maclaurin's Series & Taylor's Series of sin x, cos x, ex, log(1+x), (1+x)m.

Unit III 

Improper integrals, Gamma function, Properties of Gamma function. Beta function. Properties of Beta function. Indeterminate forms L. Hospitals Rule.

Unit IV

Double Integration. Properties of Double Integration. Iterated Integral. Change of order Integration. Transformation of Double Integral in Polar Form.