**PHYS-301 ****Introduction to Methods of Mathematical Physics-I**

**Credit Hours: 03**

DESCRIPTION & OBJECTIVES

This course provides a wide range of analytical mathematical techniques essential to the solution of

advanced problems in physics. The main objective is to have an in-depth understanding of the basics of complex analysis, residue theorem and its applications to integral solving techniques. This course enables the student to solve for orthogonal functions, Beta functions, Factorial functions, Gamma functions Digamma and Poly-gamma functions and to compute their integral transforms. It also enables the student to apply special functions, their kinds and recurrence relations used in physics problems and to solve the second order differential equations using the concept of Sturm-Liouville theory, Green’s functions and eigen valued problems.

**Learning Outcomes**

This course will enable students to understand

- Complex Variables
- Calculus of Residues
- Gamma Function
- Beta Function
- Eigen Function and Orthogonal Functions
- Green Functions
- Bessel Function

**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.

**Suggested Books**

1 E. Butkov, *Mathematical Physics*, Addison-Wesley London

2. C.W. Wong, *Introduction to Mathematical Physics*, Oxford University, Press, New York (1991).

**Contents**

- Function of complex variables and basic review
- Analytic functions, Harmonic Functions
- Cauchy Riemann equations
- Differentiation and Integration of complex variables
- Sequence and Series in complex numbers
- Calculus of Residues and its basic concept
- Evaluation of different integral types in Residues
- The Gamma function (Definition and its properties)
- Factorial notations
- Digamma and Poly-gamma Functions
- Beta functions and its mathematical notations
- Incomplete beta functions
- Stirling’s Series
- Eigen Functions and Orthogonal Functions
- Strum-Liouville Theory
- Green’s Functions
- Bessel Functions and its first kind
- Orthogonality of Bessel Function
- Generating function and recurrence relations of Bessel function

**System of Evaluation**

Sessional: 20 Marks (Presentation/Assignment 05, Attendance 05, Quiz 10)

Mid term Exam: 30 Marks

Final Exam: 50 Marks

**Key Dates**

Midterm exam will be conducted after eight weeks from the start of course and after sixteen weeks final term exam will be conducted

**Time Table of Classes**

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

Monday-Tuesday: From 11:30 to 01:00

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

Monday-Tuesday: From 2:30 to 4:00

**Rules and regulations:**

Attendance: 80% class attendance is compulsory.

Disciplines: All students must be disciplined in the classroom.

Time bounds: Assignments must be submitted as per time schedules.

Time table: Students must follow the classroom timings as per time table.