Differential Geometry (and Relativity)

Classnotes from Differential Geometry and Relativity Theory, An Introduction by Richard L. Faber, Marcel Dekker (1983)
Copies of the classnotes are on the internet in PDF and PostScript.
 Chapter 1: Introduction.
PDF.
 Section 11: Curves.
PDF.
 Section 12: Gauss Curvature.
PDF.
 Section 13: Surfaces in E^{3}.
PDF.
 Section 14: First Fundamental Form.
PDF.
 Section 15: Second Fundamental Form.
PDF.
 Section 16: The Gauss Curvature in Detail.
PDF.
 Section 17: Geodesics.
PDF.
 Section 18: The Curvature Tensor and the Theorema Egregium.
PDF.
 Section 19: Manifolds.
PDF.
 Supplement. Equation Sheet for Chapter 1. PDF
 Supplement. Wald's General Relativity Notes webpage.
 Supplement. Hawking and Ellis's The Large Scale Structure of SpaceTime Notes webpage.
 Chapter 2: Special Relativity: The Geometry of Flat Spacetime.
PDF.
 Section 21: Inertial Frames of Reference.
PDF.
 Section 22: The Michelson Morley Experiment.
PDF.
 Section 23: The Postulates of Relativity.
PDF.
 Section 24: Relativity of Simultaneity.
PDF.
 Section 25: Coordinates.
PDF.
 Section 26: Invariance of the Interval.
PDF.
 Section 27: The Lorentz Transformation.
PDF.
 Section 28: Spacetime Diagrams.
PDF.
 Section 29: Lorentz Geometry.
PDF.
 Section 210: The Twin Paradox.
PDF.
 Section 211: Temporal order and Causality.
PDF.
 Supplement. Das' The Special Theory of Relativity, A Mathematical Exposition, 1.1. Minkowski Vector Space V_{4}. PDF.
 Supplement. Das' The Special Theory of Relativity, A Mathematical Exposition, 1.2. Lorentz Mappings of V_{4} (partial). PDF.
 Supplement. Das' The Special Theory of Relativity, A Mathematical Exposition, 1.3. The Minkowski Tensors (partial). PDF
 Supplement: Velocity and Acceleration in Polar Coordinates (This section of Calculus 3 notes includes proofs of Kepler's three laws of planetary motion.) PDF.
 Chapter 3: General Relativity: The Geometry of Curved Spacetime.
PDF.
 Section 31: The Principle of Equivalence.
PDF.
 Section 32: Gravity as Spacetime Curvature.
PDF.
 Section 33: The Consequences of Einstein's Theory.
PDF.
 Section 36: Geodesics.
PDF.
 Section 37: The Field Equations.
PDF.
 Section 38: The Schwarzschild Solution.
PDF.
 Section 39: Orbits in General Relativity.
PDF.
 Section 310: The Bending of Light.
PDF.
 Supplement: Based on Foster and Nightingale's A Short Course in General Relativity.
Black Holes.
PDF.
Other Notes on Differential Geometry and Relativity
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