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.

  1. Differential topology
    1. Tensors
      1. Vectors and covectors
      2. Exterior algebra
    2. Topological tensor calculus
      1. Tensor fields
      2. Exterior derivative
      3. Integration
    3. Electromagnetism, J.pdf
      1. Maxwell's equations
      2. Spacetime decomposition
      3. Relativistic electrodynamics
    4. Densities and volumes
      1. Volume form and volume element
      2. Divergence
      3. Integration of multivectors
    5. Bases and coordinates
      1. Bases and components
      2. Coordinate bases
  2. Differential geometry
    1. Lengths and angles
      1. Abstract index notation
      2. Metric
      3. Metric and volume form
    2. Tensor calculus
      1. Covariant derivative
      2. Acceleration and geodesics
      3. Covariant partial derivatives
    3. Calculus of variations
      1. Euler-Lagrange equation
      2. Conservation laws
      3. Symmetries and the Lie derivative
      4. 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.

  1. Tensors, answers
  2. Tensor algebra, answers
  3. Maxwell’s equations, answers
  4. Densities and volumes, answers
  5. Bases and coordinates, answers
  6. Abstract index notation, answers
  7. Metric, answers
  8. Metric and volume form, answers
  9. Curvature, 1st due 11/13, 2nd due 11/23
  10. Christoffel symbols, 1st due 11/20, 2nd due 11/30
  11. Calculus of variations, 1st due 11/27, 2nd due 12/7
  12. 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.

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