Special and General Relativity, and an Introduction to Mathematical Methods in Physics
Physics 225, Spring 2018
Lecture (50 minutes): Loomis 151, Tuesdays at 4 pm
Discussion sections (110 minutes): Thursdays at 9 am, 11 am, 1 pm, 3 pm, 5 pm in Loomis 64; Fridays at 8 am, 10 am in Loomis 147.
2 credit hours

Unit 1 and homework
Special relativity—time dilation and Lorentz contraction.
Lecture PowerPoint

Unit 2 and homework
Special relativity—nonsimultaneity; the Lorentz transformations.
Lecture PowerPoint

Unit 3 and homework
The origin of the magnetic field as a consequence of special relativity.
Lecture PowerPoint

Unit 4 and homework
Developing the mathematical tools of relativity—scalars, four vectors, Lorentz tensors, the metric tensor, covariant notation.
Lecture PowerPoint

Unit 5 and homework
Doppler shifts, world lines, energymomentum four vector.
Lecture PowerPoint

Unit 6 and homework
Conservation laws, relativistic kinematics, and a start on dynamics.
Lecture PowerPoint

Unit 7 and homework
Massless particles, relativistic dynamics, and the electromagnetic field.
Lecture PowerPoint

Unit 8 and homework
An introduction to General Relativity—nonEuclidean geometry, the metric tensor, spacetime curvature.
Lecture PowerPoint

Unit 9 and homework
The Riemann curvature tensor, the Einstein field equations, and the Schwarzschild metric.
Lecture PowerPoint

Unit 10 and homework
Motion in curved spacetime.
Lecture PowerPoint

Unit 11 and homework
Fields, fluids, line integrals, and curl.
Lecture PowerPoint

Unit 12 and homework
Gradient, divergence, surface integrals, the divergence theorem, and Gauss’s law.
Lecture PowerPoint

Unit 13 and homework
The Maxwell Equations.
Lecture PowerPoint

Unit 14 and homework
A covariant formulation of electrodynamics.
Lecture PowerPoint

Lecture 15, just for fun: black holes, frame dragging, quantum field theory.
Textbooks and so forth
There are no required texts for Physics 225. You should buy the course packet from the university bookstore, which should be available by the start of the semester. You must bring the course packet to all lectures and discussion sections.
If you do want to read about relativity in a text, consider borrowing "Spacetime Physics" by Taylor and Wheeler. I believe Grainger has them on reserve. Some people like "Special Relativity" by A. P. French, but I am not familiar with it. Past Physics 225 instructors have also suggested "Basic Training in Mathematics: A Fitness Program for Science Students" by R. Shankar.
I will post PDFs of my lecture PowerPoints a day or two after giving each lecture. Most weeks I'll post scanned solutions to discussion section by Friday afternoon; I'll have homework solutions posted shortly after the late submission closing date.
Units 1 – 10: Special and General Relativity
Unit 7: inclass midterm, covering Units 1 — 5.
Exam equation sheetUnits 11 – 14: Vector calculus in electrodynamics and fluid dynamics
Unit 12: inclass midterm, covering Units 6 — 10.
Exam equation sheetFinal exam: Friday, May 11
Exam equation sheetSimulating eXtreme Spacetimes [CC BYSA 4.0 (http://creativecommons.org/licenses/bysa/4.0)], via Wikimedia Commons
Unless otherwise noted, all material copyright George Gollin, University of Illinois, 2018.