Lagrangian, metric and coordinates.

Orbital motion from the Lagrangian. Tensor
transformation rules.

Legendre transform and the Hamiltonian.

Canonical (infinitesimal) transformations and constants
of the motion.

Solution for Newtonian orbits using the Hamiltonian.

Tensor transformation and the derivative.

Parallel transport on a sphere.

Relativistic Lagrangian(s) and parametrization.

Infinitesimal transformations, and a relativistic
Hamiltonian.

Forces in special relativity, examples and issues.

Newtonian gravity and E&M, comparison.

The Riemann tensor and curvature.

Curvature for curves and spacetimes.

Einstein's equation.

Scalar fields and action.

Coordinates and densities.

Energy momentum tensor and conservation.

Particle stress tensors. First order form for the
action.

Use with package from "Course Resources"

Vector field theory: Electricity and Magnetism.

E&M and source coupling.

A scalar source for E&M.

Field theory model building.

Second rank tensor fields.

Second rank self-coupling and the Einstein-Hilbert
action.

Matter coupling and variation.

Linearized gravity and metric interpretation.

Schwarzschild geodesics: precession.