Unit 1

Motion in Space: Lines and Planes in space, Cylinders and Quadric Surfaces, Vector Functions, Arc length and the unit tangent vector, Curvature and the unit normal vector, Torsion and the unit binormal vectors.
Textbook 1: Sections 12.5, 12.6, 13.1, 13.3, 13.4, 13.5

Unit 2

Multivariate Calculus: Functions of Several Variables – Limits and Continuity in Higher Dimensions – Partial Derivatives – The Chain rule, Multiple Integrals – Double Integrals in Cartesian and Polar Coordinates, Triple Integrals in Cartesian, Spherical and Cylindrical Coordinates.
Textbook 1: Sec. Sec. 14.1 to 14.4, 15.1, 15.3, 15.4 and 15.6

Unit 3

Vector Differentiation: Gradient, divergence and curl, identities, invariant scalar and vector fields, invariance of gradient, divergence and curl.
Textbook 2: Chapter 4

Unit 4

Line integrals, Vector Fields, Work, Circulation, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the plane.
Textbook 1: Sec. 16.1,16.2,16.3,16.4.

Unit 5

Surface area, Flux, and surface integrals, Parametrized surfaces, Stokes Theorem, The divergence Theorem and a unified theory.
Textbook 1: Sec. 16.5,16.6,16.7,16.8

Course Outcome
On successful completion of this course, students shall be able to
CO-1: apply the basic concepts of vector valued functions, their limits, derivatives and integrals and its geometrical and physical interpretations to solve problems.
CO-2: apply the concepts of scalar and vector fields, their limits, derivatives and their applications. CO-3: apply the concepts of line integrals and its path independence.
CO-4: apply the concepts of double integrals to various problems including Green’s theorem for plane. CO-5: apply the concepts of surface integrals, divergence theorem and Stoke’s theorem.

1. Maurice D Wier, Joel Hass, Frank R Giordano, Thomas’ Calculus, 11th Edition, Pearson, 2009.
2. Murray R Spiegel, Theory and problems of vector analysis, Schaum’s outline series, McGraw- Hill Book Compnay 1974.