CALCULUS
SWN | Calculus
Indus University
CSE Section
Calculus
unit-1
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-2
multiple integral: Reduction formula, Curve tracing - Cartesian and polar, Double Integral, Change of order, Change of variables, Triple integral, Application of multiple integrals
unit-3
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-4
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