AAPT - Teaching General Relativity, Syracuse, NY - 07/2006                         Lessons on Teaching Undergraduate GR

Differential Geometry
Linear Algebra
Tangent Vectors
Curves
Fundamental Theorem of Curves
Surfaces
Curvature of Curves and Surfaces
1-Forms
Tensors
Higher Rank Forms
Exterior Derivatives
Hodge * Operator
Frames
Curvilinear Coordinates
Covariant Derivatives
Cartan Equations
Manifolds
Fundamental Forms
Curvature and Einsteins Equation
Prerequisites: Linear Algebra, Multivariate Calculus, Jr-Sr Standing.
Text: G. Lugo, Differential Geometry and Physics, 1995, 1998, 2004; M. Lipschutz , Schaum's
Outline of Differential Geometry, 1969.
Russell L. Herman, University of North Carolina Wilmington, 07/2006
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