### Vectors and tensors analysis, Math-5124

Course Outlines :

Vectors analysis : Gradient, Divergence and Curl of a point function. Expansion formula,  line, surface and volume integrals. Guass 's, Green 's and Stok's theorem. Curvilinear coordinates. Christian tensors. Improper and proper transformation equations, orthogonally conditions, kronecker tensor and Levi -civita tensor, tensors of different ranks, inner and outer products, contraction.Quotient theorem, symmetric and anti symmetric tensor, applications to vector analysis.

Learning outcomes: After the completion of this course, students will be able to

(i) Understand the vectors and its operators.

(ii)  Apply Stoke's, Divergence and Green theorem.

(iii)  Understand the relationship between rectangular and curvilinear coordinates.

(iv)  Basic knowledge of tensor and its applications.

Recomended Book :

(i)  Dr. N. Shah: Vector and Tensor analysis (2015).

(ii)  Spieghel,  M. R.,  Vector and an introduction to tensor analysis (McGraw Hill, 2016.

Suggested Books:

(i)  Young, E. C.,  Vector and Tensor analysis, (Mareel Dekker, Inc, 1993)

(ii) Chorlton, F., Vector and Tensor methods, (Eills Horwood publishers, Chichester, U. K. 1977)

Assignments :

(i)  30 problems on applications of dot, cross product of vectors and gradient, divergence and curl.

(ii) 28 problems on Stokes, Divergence and Green's theorem.

(iii)  Applications of line, surface and volume integral.

(iv)  Relationship rectangular and curvilinear coordinates of cylinderical and spherical coordinates.

Assessment criteria:

Sessional:20(Assignment 10, attandance 05,Quiz 05)

Mid term exam:30

Final term exam:50

Key dates and Time of class meeting :

Wednesday :2pm-3pm.

Thursday :2pm-3pm.

Friday :3pm-4pm.

Commencement of classes:

Jan, 13,2020.

Mid term exam : March  09-13,2020.

Final term exam:May 04-08,2020.

Declaration of results :May19,2020.