Calculus Course Plan :
Calculus Book :
Unit : 01
Partial derivatives and its applications
Function of several variables : Limits, continuity, Partial Differentiation-variable treated as constant, total derivative, partial differentiation of composite functions, and differentiation of an Implicit Function.
Applications of partial derivatives : Euler’s Theorem, Jacobian, Maxima and Minima of Functions of two Variables- with and without constraints, Lagrange’s Method of Undetermined Multipliers
Unit : 02
Multiple Integral
Reduction formula, Curve tracing – Cartesian and polar, Double Integral, Change of order, Change of variables, Triple integral
Unit : 03
Vector Differential Calculus
Vector Differentiation, Directional Derivative, Gradient of a Scalar Function and Conservative Field, Divergence and Curl, Related Properties of Gradient, Sums of Divergence and Curl Curvilinear coordinate system, Cartesian, Spherical and Cylindrical coordinate system
Unit : 04
Vector Integral Calculus
Vector Integration : Integration of a Vector Function of a Scalar Argument
Line Integrals : application to find work done, Potential, Conservative Field and Area Introduction to Surface Integrals, Volume Integrals, Green’s Theorem in Plane, Stokes’ Theorem, Gauss Divergence Theorem