Methods of Mathematical Physics-I (PHYS-301)

Credit Hours: 03

Objective:

The main objective of this course is to familiarize students with a range of mathematical methods that are essential for solution of advanced problems in theoretical physics.

Learning Outcomes:

After successfull completion of course, students will be able to

• use complex analysis in solving physical problems
• solve ordinary and partial differential equations of second order that are common in the physical sciences
• use Green functions, Beta function and Gamma Function in numerical problems related to real life
• use the orthogonal polynomials

Recommended Books:

• George Arfken and Hans J. Weber, Mathematical Methods for Physicists (6th and onwards editions) Acad Press
• Erwin Kreyszig, Advanced Engineering Mathematics, 9th ed.
• M.R.Spiegel, Schaum’s Outline Series, Complex Variables, McGraw Hill, New York.
• Complex Variables by M.R.Spiegel, Schaum’s Outline Series, McGraw Hill, New York.
• Introduction to Mathematical Physics by C.W. Wong, Oxford University, Press, New York (1991).
• Foundations of Mathematical Physics by Hassani, Prentice Hall International Inc., Singapore (1991).
• Mathematical Physics by ChattopadhyayWiley Eastern Limited, New Delhi, (1990).

Course Contents:

1. Introduction to complex analysis
2. Function of complex variables
3. Analytic functions, Harmonic Functions
4. Cauchy Riemann equations
5. Cauchy's integral formula 
6. Cauchy's integral theorem
7. Calculus of Residues
8. Evaluation of different integral types in Residues
9. Gamma function and its properties
10. Digamma and Poly-gamma Functions
11. Beta functions and its properties
12. Incomplete beta functions
13. Stirling’s Series
14. Eigen Functions and Orthogonal Functions
15. Strum-Liouville Theory
16. Green’s Functions
17. Bessel Functions and its first kind
18. Orthogonality of Bessel Function
19. Generating function and recurrence relations of Bessel function

Evaluation criteria:

Sessional:              20 Marks (Presentations 10 marks and Assignments 10 marks)

Mid term Exam:     30 Marks

Final Exam:           50 Marks

Time Table of Classes:

          The class for this course will be conducted for B.S Physics 5th Semester (Regular) on

          Monday-Tuesday:      From 09:00 to 10:00

          Thursday:                   From 09:00 to 10:00

          The class for this course will be conducted for MSC Physics 1st Semester on  

          Monday-wednesday:      From 12:00 to 1:00

Rules and regulations:

• Assignments must be submitted as per time schedules.
• Students must be punctual and disciplined in the classroom.