Lecture Notes: Math 280---Intro to Diff Geom and GR:

  • Introduction
  • Relativistic Fluids
  • Classical Limit of Relativistic Euler and Equipartition of Energy-Short
  • Manifolds
  • Tangent Bundle
  • Cotangent Bundle
  • Tensors in General
  • Special Relativity (Short)
  • Special Relativity I
  • Special Relativity II
  • Special Relativity III
  • Vector Fields and the Lie Bracket
  • Maps Between Manifolds/Lie Derivative
  • Differential Forms I
  • Differential Forms II
  • Geodesics
  • Connection
  • Curvature
  • Schwarzschild Solution
  • Kruskal Coordinates
  • Buchdahl Stability Limit
  • Cosmology
  • Redshift
  • Shock Waves
  • Stress Energy Tensor
  • Covariance for Conservation Laws
  • Relativistic Mechanics