Copies of the classnotes are on the internet in PDF and PostScript.

• Chapter 1: Introduction. Chapter 1 Introduction notes
• Section 1-1: Curves. Section 1-1 notes
• Section 1-2: Gauss Curvature. Section 1-2 notes
• Section 1-3: Surfaces in E³. Section 1-3 notes
• Section 1-4: First Fundamental Form. Section 1-4 notes
• Section 1-5: Second Fundamental Form. Section 1-5 notes
• Section 1-6: The Gauss Curvature in Detail. Section 1-6 notes
• Section 1-7: Geodesics. Section 1-7 notes
• Section 1-8: The Curvature Tensor and the Theorema Egregium. Section 1-8 notes
• Section 1-9: Manifolds. Section 1-9 notes
• Supplement. Equation Sheet for Chapter 1. Equation Sheet notes

• Chapter 2: Special Relativity: The Geometry of Flat Spacetime. Chapter 2 Introduction notes
• Section 2-1: Inertial Frames of Reference. Section 2-1 notes
• Section 2-2: The Michelson Morley Experiment. Section 2-2 notes
• Section 2-3: The Postulates of Relativity. Section 2-3 notes
• Section 2-4: Relativity of Simultaneity. Section 2-4 notes
• Section 2-5: Coordinates. Section 2-5 notes
• Section 2-6: Invariance of the Interval. Section 2-6 notes
• Section 2-7: The Lorentz Transformation. Section 2-7 notes
• Section 2-8: Spacetime Diagrams. Section 2-8 notes
• Section 2-9: Lorentz Geometry. Section 2-9 notes
• Section 2-10: The Twin Paradox. Section 2-10 notes
• Section 2-11: Temporal order and Causality. Section 2-11 notes
• Supplement. Das' The Special Theory of Relativity, A Mathematical Exposition, 1.1. Minkowski Vector Space V₄. Das' Special Theory of Relativity Section 1.1 notes
• Supplement. Das' The Special Theory of Relativity, A Mathematical Exposition, 1.2. Lorentz Mappings of V₄ (partial). Das' Special Theory of Relativity Section 1.2 notes
• Supplement. Das' The Special Theory of Relativity, A Mathematical Exposition, 1.3. The Minkowski Tensors (partial). Das' Special Theory of Relativity Section 1.3 notes

• Supplement: Velocity and Acceleration in Polar Coordinates (This section of Calculus 3 notes includes proofs of Kepler's three laws of planetary motion.) Calculus 3, Section 13.6 notes

• Chapter 3: General Relativity: The Geometry of Curved Spacetime. Chapter 3 Introduction notes
• Section 3-1: The Principle of Equivalence. Section 3-1 notes
• Section 3-2: Gravity as Spacetime Curvature. Section 3-2 notes
• Section 3-3: The Consequences of Einstein's Theory. Section 3-3 notes
• Section 3-6: Geodesics. Section 3-6 notes
• Section 3-7: The Field Equations. Section 3-7 notes
• Section 3-8: The Schwarzschild Solution. Section 3-8 notes
• Section 3-9: Orbits in General Relativity. Section 3-9 notes
• Section 3-10: The Bending of Light. Section 3-10 notes

• Supplement: Based on Foster and Nightingale's A Short Course in General Relativity. Black Holes.Black Holes notes

Other Notes on Differential Geometry and Relativity

Differential Geometry (in preparation)

Differential Geometry (in preparation)

General Relativity (in preparation)

General Relativity (in preparation)

Return to Bob Gardner's home page