Prof. Kiessling's lecture notes
Working knowledge of basic ODEs and the linear wave equation. Some exposure to analysis at the level of the "baby Rudin," better yet: math 501. Basic knowledge of Euclidean geometry. Curiosity about physics. N.B.: The physics department's mathematical physics course 511 has very little in common with this course. It is not a prerequisite.
Summary: The course introduces the student to a rigorous mathematical treatment of the classical theories of our physical world: "matter made of point particles in space(-)time which interact via gravity and electromagnetism." The emphasis is on both, mathematical rigor and conceptual clarity of the physical theories.
1. The Newtonian universe (Galileian space and time, point particles, Newton's law of motion, Newton's law of gravitational force, Coulomb's law of electrical force; symmetries and conservation laws; other formulations of Newton's mechanics: Hamilton, Hamilton-Jacobi, and Lagrange).
2. Einstein's universe (Minkowski's spacetime, Maxwell's electromagnetic field equations, electromagnetic waves, relativistic energy and momentum; and in *very brief* outline also: Lorentzian manifolds, Einstein's gravitational field equations, geodesics, black holes, gravitational waves)
3. Limits of validity of the classical theories (the joint Cauchy problem for fields and point particles, the problem of self-interactions; energy and momentum laws; the dawn of quantum theory.)