Objectives of the course :
The aim of this course is to learn the concept of vector differentiation and integration. Also we discuss several properties of vector algebra.
Objective 1 : Students will learn the fundamentals of vector algebra.
Objective 2 : Students will study the properties of vector differentiation.
Objective 3 : Students will have the knowledge about line integral, surface integral and volume integral.
Course learning outcome:Upon completion of this course, the student will be able to:
1. Understand basic concepts of vector algebra.
2. Classify the vector equations and its applications.
3. Characterize the vector differentiation.
4. Know about vector integration.
5. Discuss gradient, curl and divergence and their applications.
Basic operations on vectors, collinear and coplanar vectors, center of mass, centroid of area,
scalar and vector products of vectors and their properties, Vector equations of a straight line,
plane and sphere and related results, Derivative of a vector and its properties,
derivative of triple product, partial derivative of vectors, Serret-Fernet formula,
directional derivative, application of vector differentiation, Line integrals,
conservative field, surface integral, volume integral, Gradient, divergence, curl,
Green’s theorem, stokes’ theorem and their applications.Books:
J. G. Chakravorty, P. R. Ghosh, Vector Analysis, 12th Edition, U. N. Dhur $\&$ Sons Pvt. Ltd.
Hazewinkel, Michiel, ed. (2001) , ``Vector analysis", Encyclopedia of Mathematics, Springer Science$+$Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
- Teacher: Soumen Kundu