Mathematical Physics

This is a 4 credit course for MSc first semester in Physics.

1. Advanced understanding of mathematical methods used in physics, including but not limited to calculus, differential equations, linear algebra, and probability theory.

2. Knowledge of mathematical techniques used in modern theoretical physics, such as functional analysis, group theory, and topology, as well as their applications to fundamental questions in physics.

3. Ability to apply mathematical methods to problems in physics, including the formulation and analysis of physical models, and the interpretation of experimental data.

4. Understanding of the mathematical foundations of quantum mechanics, classical mechanics, statistical mechanics, and other areas of physics, including the relationship between mathematics and physical concepts such as symmetry and conservation laws.

Syllabus:

Complex Analysis (Brown & Churchill)

Linear Algebra (Gilbert Strang)

Integral Transform (D C Champeney)

Special Functions (Charlie Harper)

Group Theory (Sattinger & Weaver)

Texts:

1. J W Brown and R V Churchill: Complex Variables and Applications [Book]

2. Gilbert Strang: Linear Algebra and its Applications [Book]

3. D C Champeney: Fourier Transforms and their Physical Applications [Book]

4. Charlie Harper: Introduction to Mathematical Physics [Book]

5. Sattinger & Weaver: Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics [Book]

References:

1. Mathews & Walker: Mathematical Methods of Physics [Book]

2. Dennery & Krzywicki: Mathematics for Physicists [Book]

3. Riley, Hobson, Bence: Mathematical Methods for Physics and Engineering [Book]

4. Paul R Halmos: Finite-Dimensional Vector Spaces [Book]

5. Michael Tinkham: Group Theory and Quantum Mechanics [Book]

6. Morton Hamermesh: Group Theory and its Applications to Physical Problems [Book]

7. Arfken, Weber & Harris: Mathematical Methods for Physicists [Book]

8. M R Spiegel: Schaum's Outline of Complex Variables [Book]

9. M L Boas: Mathematical Methods in the Physical Sciences [Book]

10. T L Chow: Mathematical Methods for Physicists [Book]

11. C M Bender & S A Orszag: Advanced Mathematical Methods for Scientists and Engineers [Book]

12. V I Arnold: Mathematical Methods of Classical Mechanics [Book]