In this course, we will study the most fundamental knowledge for understanding vectors and tensors were taught in the traditional way. Prior to our applying vector and tensor analysis to our research area of modern continuum mechanics,  vector and tensor analysis provides a kind of bridge between elementary aspects of linear algebra, geometry and analysis.

Learning Outcomes

At the end of the course the students will be able to:

1. Students will demonstrate that they understand the concept and have learned the basic skills in using vector analysis in solving physics problems.
2. Students will demonstrate that they understand the concept and have learned the basic skills in using linear algebra, vector calculus and tensor analysis in solving physics problems

Course outline

1. Vector Analysis: Gradient.
2. Divergence and curl of point functions.
3. Expansion formulae.
4. Curvilinear coordinates, line, surface and volume integrals.
5. Gauss’s, Green’s and Stoke’s theorems.
6. Proper and improper transformation.
7. Cartesian Tensors: Summation convention.
8. Transformation equations.
9. Orthogonally conditions.
10. Kronecker tensor and Levi-civita tensor.
11. Tensors of different rank.
12. Inner and outer products.
13. Contraction.
14. Quotient theorems.
15. Symmetric and anti-symmetric tensors.
16. Application to Vector Analysis.

Recommended Books

1. Shah, N. A.,Vector and Tenser Analysis, (2015).
2. Spiegel, E.C., Vector and an Introduction to Tensor Analysis, (McGraw Hill, 2016).

Suggested Books

1. Young, E.C., Vector and Tensor Analysis, (Mareel Dekker, Inc, 1993).

Assessment Criteria

Sessional: 20 (Presentation / Assignment 04, Attendance 08, Result Mid-Term 04, Quiz 04)

Mid-Term Exam:  30

Final-Term Exam: 50

Key Dates and Time of Class Meeting

Program: BSPhysics:

class: 4th(self-1)

1.Tuesday(03:00pm-4:00pm)

2. Thursday (02:00pm-03:00pm)

3.Friday(02:00-03:00)

Class: 4th(Self-2)

1. wednesday(12: 00 pm - 1: 00 pm)

2. Thursday(12: 00 pm - 1: 00 pm)

3. Friday(12: 00 pm - 1: 00 pm)

Commencement of Classes                                                   March 23, 2020

Mid Term Examination                                                            April 19-04, 2021

Final Term Examination                                                          June 12-16, 2021

Text Book: https://lms.su.edu.pk/files/6888/Mathematical_Methods_for_Physicists_6th.pdf