# PHY405 Geometrical Methods in Physics

# S. G. Rajeev

### I will be using Blackboard to post lecture notes and homework sets in the Spring of 2015.

### Classes will meet Tue and Thur 9:40-1055 MOREY 501

#### Please come to the first class on Thursday Jan 14 if you need my permission to sign up for the course.

- If you know linear algebra, and have taken junior level Electricity & Magnetism and Quantum Mechanics
(e.g., Shankar's book), you will know enough.
- There will be no examinations in the course; instead there will be some homework assignments.
- No required textbook. I will post lecture notes.
- The course will be graded on a Pass/Fail basis for Graduate Students.
- The first part of the course will be accessible to undergraduates and
to experimental physics graduate students.
- The later parts will aim to bring the subject up
to the level of modern research papers in mathematical physics.

### Syllabus

- Review of Linear Vector algebra; tensors; wedge products.
- Index notation for tensors
- Curvilinear Co-ordinates in flat space.
- The Sphere; geodesics on the sphere.
- Differential Manifolds.
- Vector Fields and Differential Forms
- Thermodynamics: Caratheodory's form of the second law of thermodynamics.
- Mechanics; Special Relativity.
- Riemannian Geometry; Geodesics.
- Parallel Transport and Curvature.
- Geometrical Optics.
- Electrodynamics.
- General Relativity.
- Fluid Mechanics
- Quantum Mechanics in Curvilinear Co-ordinates