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Mathematical Methods of Physics


  1. Set Theory - The basic definitions and notations used in set theory is given.
  2. Affine vs. Metric Geometry - Describes difference between affine and metric geometry.
  3. Orthogonal Transformations - Defines and elaborates of orthogonal transformation.
  4. Geodesic Deviation - The relationship for geodesic deviation is provided.
  5. Geodesics - Describes what a geodesics is (path of extremal length) and derives the equations which describe geodesics.
  6. Introduction to Manifolds - An introduction to manifolds is given along with the terminology which goes along with it.
  7. Tensors - The Analytic View - An introductions to tensors in which tensors are defined through their transformation properties
  8. Tensors - The Geometric View - An introductions to tensors in which tensors are defined through their geometric properties
  9. Parallel Transport - The expression for parallel transport is derived. The affine connection is introduced.
  10. Invariance - Defines and analyses the concept of invariance.
  11. Metric Tensor - Defines and describes the metric tensor.
  12. Absolute Derivative - The components of the total derivative are derived in terms of the Christoffel symbols.
  13. Pythagorean theorem - Derivation of the Pythagorean theorem.
 


















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