Functions of severable variables: 5 hours
Functions, limit and continuity. Partial differentiations, total derivatives, differentiation of implicit functions and transformation of coordinates by Jacobian. Taylor’s series for two variables.
Vector Differentiation: 10 hours
Vector and Scalar Functions, Derivatives, Curves, Tangents, Arc Length, Curves in Mechanics, Velocity and Acceleration, Gradient of a Scalar Field, Directional Derivative, Divergence of a Vector Field, Curl of a Vector Field.
(Sections : 9.4, 9.5, 9.6, 9.9, 9.10, 9.11)
Vector Integration: 15 hours
Line Integral, Line Integrals Independent of Path. (Sections : 10.1, 10.2)
Green’s Theorem in the Plane, Surfaces for Surface Integrals, Surface Integrals, Triple Integrals – Gauss Divergence Theorem, Stoke’s Theorem. (Sections : 10.4, 10.5, 10.6, 10.7, 10.9 )
Lab Practice Problems
Graph of functions of two variables, shifting and scaling of graphs. Vector products. Visualizing different surfaces.