Physical Mathematics - Fall 2019
- Course
- PH211 - Physical Mathematics
- Instructor
- Ewan Stewart
- Email
- pm.19f @ profstewart.org
- Homepage
- http://profstewart.org/pm/
- Time
- 13:00 - 14:30, Tuesdays and Thursdays
- Space
- Creative 202
- Teaching assistants
- 김재권
- 김혁중
- 김희중
- TA website
- http://klms.kaist.ac.kr/course/view.php?id=107854
- Questions
- Prof: email, before/after class, meeting arranged by email
- TAs: TA website, email, …
- Evaluation
- class participation, homework submission, exam
Course description
This course aims to help you gain a physical understanding of the mathematics used in physics.
Syllabus and lecture notes
The syllabus and lecture notes will be continually revised. Please make sure you have the latest versions.
-
Differential topology
- Tensors
- Vectors and covectors
- Exterior algebra
- Topological tensor calculus
- Tensor fields
- Exterior derivative
- Integration
- Electromagnetism, J.pdf
- Maxwell's equations
- Spacetime decomposition
- Relativistic electrodynamics
- Densities and volumes
- Volume form and volume element
- Divergence
- Integration of multivectors
- Bases and coordinates
- Bases and components
- Coordinate bases
-
Differential geometry
- Lengths and angles
- Abstract index notation
- Metric
- Metric and volume form
- Tensor calculus
- Covariant derivative
- Acceleration and geodesics
- Covariant partial derivatives
- Calculus of variations
- Euler-Lagrange equation
- Conservation laws
- Symmetries and the Lie derivative
- Actions
Problems
You are encouraged to collaborate with one or two other students of similar ability and submit a single joint homework with the names of all collaborators on it.
There will be two submissions for each homework. The teaching assistants will give detailed feedback on each submission.
- Tensors answers
- Tensor algebra answers
- Topological tensor calculus answers
- Maxwell’s equations answers
- Densities and volumes answers
- Bases and coordinates answers
- Abstract index notation answers
- Metric answers
- Metric and volume form answers
- Curvature answers
- Christoffel symbols answers
- Calculus of variations answers
- Symmetry answers
Exam
The exam will be open book and open time (up to 8 hours). The exam will start at 1pm on Sunday 15th December in Creative 311.
Answers
Registration questionnaire
Recommended links
Recommended books
-
- Title
- Geometrical Vectors
- Author
- Gabriel Weinreich
- Publisher
- University of Chicago Press (1998)
Highly recommended. Gives precise and intuitive topological pictures of antisymmetric tensors and their algebra and calculus in three dimensions. Note that the notation used in this book is a compromise between traditional three dimensional vector calculus and the more fundamental tensor notation used in this course.
-
- Title
- Geometry, Topology and Physics
- Author
- M. Nakahara
- Publisher
- Taylor & Francis (2003)
For further study after completing this course.