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.

  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. Topological tensor calculus answers
  4. Maxwell’s equations answers
  5. Densities and volumes answers
  6. Bases and coordinates answers
  7. Abstract index notation answers
  8. Metric answers
  9. Metric and volume form answers
  10. Curvature answers
  11. Christoffel symbols answers
  12. Calculus of variations answers
  13. 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

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2019 0559 2016 0823 2019 6919 2019 6927 2019 6921 2017 0862
2019 0274 2017 0683
2019 0734 2017 0246
2019 0334 2019 0163 2018 0272 2018 0896 2018 0935 2018 0933
2019 0420 2018 0493 2019 0667 2018 0223
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2017 0123 2019 6931 2016 0592 2018 0443
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2018 0841 2019 0393
2019 0628 2016 0465
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