This is a 4 credit course that is offered to students of the 5th and 7th semesters at IISER Pune. It is taught by Dr Prasad Subramanian.

As the name suggests, this is a course that gives an overview of the mathematical tools commonly used in physics. Together with the basics of these methods, we will have opportunities to examine the applications of these methods to problems in physics.

It will be assumed that students are familiar with elementary calculus, complex algebra, determinants and matrices, and the basics of ordinary differential equations and Fourier series. This would correspond (roughly) to familiarity with Chapters 1 - 7 of the book Mathematical Tools for Physics, by James Nearing. Students unfamiliar with these topics are (strongly) advised to read them up on their own.

The course will be organized into the following modules: the approximate number of classes to be spent on each topic is indicated. We will discuss applications of the mathematical tools (to situations encountered in physics) in the tutorial classes.

1)Complex variables (approx 4 classes, 1 tutorial)

2)Fourier Series and Fourier transforms (approx 4 classes, 1 tutorial)

Problem set 1

Quiz 1 with solutions

3)Brief review of ordinary differential equations, introduction to Sturm-Liouville theory (approx 10 classes, 1 tutorial)

Problem set 2

Problem set 3

Mid term exam

4)Partial Differential equations (approx 5 classes, 2 tutorials)

Problem set 4

Quiz 2 with solutions

5)Introduction to tensors (approx 9 classes, 1 tutorial)

Problem set 5

Final exam

Grading: End-sem examination 40 %, Mid-sem examination 30 %, Quiz 30 % Attendance is mandatory, and will be recorded. The first quiz will take place after modules 1 and 2. The midterm will take place after module 4, and will cover modules 1, 2, 3 and 4. The final exam will cover the entire course.

The following books will be used during the course:

Mathematical Tools for Physics, by James Nearing. Available at this weblink.

Mathematical Methods for Physicists, by Arfken and Weber, 5th edition, Academic Press.