Department of Mathematics
The University of Iowa
The famous 1929
New Yorker cartoon on GR
Syllabus
Notes, part 1 (pdf format): Coordinate systems, vector and covector fields
Notes, part 2 (pdf format): Lie and covariant differentiation of a vector
field
Notes, part 3 (pdf format): Tensor fields
Notes, part 4 (pdf format): Operations on tensors
Notes, part 5 (pdf format): The action of the Riemann curvature
Notes, part 6 (pdf format): Metrics and the empty-space Einstein equation
Notes, part 7 (pdf format): The Schwarzschild solution
Notes, part 8 (pdf format): Conformal change and warped products
Notes, part 9 (pdf format): More on the Schwarzschild solution
Notes, part 10 (pdf format): Differential forms and the Maxwell equations
Notes, part 11 (pdf format): Integral curves, the flow, and the
divergence-free nature of the Einstein and energy-momentum tensors
Notes, part 12 (pdf format): Parallel transport, geodesics, and normal
coordinates
Syllabus