### Vector Calculus

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.

5.      Discuss gradient, curl and divergence and their applications.

Course structure:
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) [1994], Vector analysis", Encyclopedia of Mathematics, Springer Science$+$Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4