Lectures:

• Lecture 00: Introduction
• Lecture 01: Special Relativity
  Codes
  • [Lorentz Transform]
• Lecture 02: Embedded Curves
  Codes
  • [Frenet Frame]
• Lecture 03: Embedded Surface
• Lecture 04: Gaussian Curvature
• Lecture 05: Connection
• Lecture 06: Riemann Tensor
  Codes
  • [connection, Riemann tensor and Gaussian curvature]
• Lecture 07: Covariant Derivative
  Codes
  • [covariant derivative]
• Lecture 08: Geodesic
• Lecture 09: Four Dimensional Spacetime
• Lecture 10: From Riemann Tensor to Einstein Tensor
• Lecture 11: Action Principle and Einstein Equations
  Codes
  • [Einstein Tensor]
• Lecture 12: Energy Momentum Tensor
• Lecture 13: Observables
• Lecture 14: Spherical Symmetric Metric
  Codes
  • [spherical metric Ricci tensor]
  • [spherical and static metric Einstein tensor]
  • [spherical energy momentum tensor conservation]
• Lecture 15: Test Particle in Schwarzschild metric
• Lecture 16: White Dwarf, Neutron Star and Black Hole
• Lecture 17: Schwarzschild Black Hole
• Lecture 18: Kruskal Coordinates and White Hole
  Codes
  • [Compute and plot W(x)]
  • [Use Kruskal coordinates to compute free fall]
  • [Qiuku problem]
• Lecture 19: General Discussion about Black Holes (Kerr, evaporation)
• Lecture 20: Gravitational Waves
• Lecture 21: Physics of Gravitational Waves
• Lecture 22: Gravitational Radiation (I)
• Lecture 23: Gravitational Radiation (II)
  Codes
  • [TT projection]
  • [GW radiation by a quartic-poential oscillator]
• Lecture 24: Cosmology (FRW metric)
• Lecture 25: Cosmological Pie
  Codes
  • [compute age of a LambdaCDM universe]
• Lecture 26: Cosmological Distances
  Codes
  • [compute cosmological distances]
• Appendix: summary of formulas