This course has detailed explanation of following Topics:

Partial Derivatives : Partial and Total Derivatives ( Chain rule), Homogeneous functions, Euler's Theorem, Maxima and Minima for a function of One variable, Two variables and Three variables.

Mean value theorems : Continuity of a function at a particular value and in a closed interval, Differentiability of a function in an open interval, Roll's theorem, Legrange's Mean value theorem, Cauchy's Mean value theorem , Taylor's theorem ( Generalized Mean value theorem.

Definite and Improper Definite Integrals: Properties of Definite Integrals, Convergence and Divergence, Comparison Test, P-Series Test, Integral test, Gamma and Beta functions.

Limits : Limits definition, Indeterminate forms of Limits.

Vector Calculus : Basics of Vector Algebra, Dot ( Scalar ) Product , Cross ( Vector )Product , Scalar Triple Product, Vector Triple Product, Application of Partial Derivatives on Vectors :Gradient, Directional Derivative( d,d ), Unit normal, Divergence, Solenoidal vector, Curl or Rotation, Irrotational or Conservative Force Field.

Multiple Integrals : Line integrals, Work done, Surface Integrals, Double Integrals evaluation Techniques, Volume Integrals, Triple Integrals evaluation techniques.

Vector Integral Theorems : Green's Theorem, Stoke's Theorem and Gauss - Divergence Theorem