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 develop intuition towards formulating physical phenomena in mathematical language and gain an appreciation of the analytical methods that are most commonly used to solve problems in physics. This course has an in-depth understanding of the basics of mathematics.

**Learning Outcomes**

This course will enable students to understand

- Legendre functions
- Hermite functions
- Laguerre functions
- Special type of functions and its applications to problem solving techniques.
- Fourier series and Fourier Analysis
- Fourier transforms.
- Laplace transform to initial value problems.

**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**

1. Fourier Series:

a) Basic definition and properties of Fourier series

b) Complex Fourier

c) Gibbs Phenomenon

d) Fourier Integral

e) Fourier transforms

f) Discrete Fourier transform

2. Legendre Functions:

a) Generating function

b) Recurrence relations

c) Orthogonality

d) Associated Legendre functions

e) Legendre functions of second kind

3. Laguerre Functions

4. Hermite functions:

5. Laplace transforms:

a) Basic concept of Laplace transform

b) Laplace transforms of different functions

c) Transfer function, initial value problem solving method

d) Inverse Laplace transform

**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 **Msc Physics Semester 2nd (Regular) **on

Monday-Wed: From 1:00 to 02:00

The class for this course will be conducted for **Msc Physics Semester 2nd (SS) **on

Wed to Thr From 2:30 to 03:30

Friday From 3:30 to 04:30

**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.