Physical Mathematics  Fall 2017
 Course
 PH211  Physical Mathematics
 Instructor
 Ewan Stewart
 Email
 pm.17f @ profstewart.org
 Homepage
 http://profstewart.org/pm/
 Time
 13:00  14:30, Tuesdays and Thursdays
 Space
 Creative 202
 Teaching assistants
 안단호
 김재권
 TA website
 http://klms.kaist.ac.kr/course/view.php?id=59762
 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
 EulerLagrange 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
 Maxwell’s equations, answers
 Densities and volumes, answers
 Bases and coordinates, answers
 Abstract index notation, answers
 Metric, answers
 Metric and volume form, answers
 Curvature, 1st due 11/13, 2nd due 11/23
 Christoffel symbols, 1st due 11/20, 2nd due 11/30
 Calculus of variations, 1st due 11/27, 2nd due 12/7
 Symmetry, 1st due 12/4
Exam
The exam will be open book and open time (up to 8 hours). It will start at 1pm on Sunday 10th December in Creative 412.
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.