Physical Mathematics II

Course description

This course is the second half of a one year introduction to physical mathematics. It aims to help you gain a physical understanding of the mathematics used in physics.

Syllabus and lecture notes

  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

  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

Answers

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