Venue: Emmy Noether Seminar Room

Class Timings: Tuesdays & Thursdays from 9:45 AM - 11:15 AM

First Meeting: 13 August 2024

Course Syllabus:

Unit 1: Linear vector spaces, linear operators and matrices, systems of linear equations. Eigenvalues and eigenvectors, singular value decomposition, classical orthogonal polynomials

Unit 2: Linear ordinary differential equations, exact and series methods of solution, special functions; some nonlinear equations, Complex variable theory; analytic functions; Taylor and Laurent expansions, classification of singularities, analytic continuation, contour integration.

Unit 3: Linear partial differential equations of physics, separation of variables method of solution, Green’s function methods;  Dispersion relations; Fourier and Laplace transforms. Asymptotic analysis, introduction to singular perturbation theory

Course Outcomes:
 

1. Gain a good understanding of the mathematical methods that are useful for several advanced physics courses.
2. Develop analytical and numerical problem solving skills.

Textbooks and reading material:
We will follow a variety of texts as we proceed through the course, which will change depending on the topic. There will also often be pre-class readings from these texts (or others) that you will be expected to do before class. I will share these on the Moodle page.

1. GB Arfken, HJ Weber and FE Harris: Mathematical Methods for Physicists, 7e
2. KF Riley, MP Hobson, and SJ Bence: Mathematical Methods for physics and engineering, 3e
3. GF Simmons: Differential equations with applications and historical notes, 3e
4. P Dennery and A Krzywicki: Mathematics for physicists, Dover Inc.
5. RV Brown and JW Churchill : Complex Variables and Applications, 8e
6. T Needham: Visual Complex Analysis, 25e 2023
7. CM Bender and SA Orszag: Asymptotic Methods and perturbation theory

Course evaluation:
Pre-class readings and questions, or in-class quizzes (20%)
Problem sets (40%)
Final exam (40%)

TAs:
Nitesh Kumar Patro
Naveen Kumar D

Credit Score: 4