Special and General Relativity, and an Introduction to Mathematical Methods in Physics
Physics 225, Summer 2018
Lecture (50 minutes): Loomis 222, Mondays, Thursdays at 10 am
Discussion section (110 minutes): Loomis 222, Mondays, Thursdays at 1 pm
2 credit hours
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Unit 1 and homework
Special relativity—time dilation and Lorentz contraction.
Lecture PowerPoint
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Unit 2 and homework
Special relativity—non-simultaneity; the Lorentz transformations.
Lecture PowerPoint
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Unit 3 and homework
The origin of the magnetic field as a consequence of special relativity.
Lecture PowerPoint
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Unit 4 and homework
Developing the mathematical tools of relativity—scalars, four vectors, Lorentz tensors, the metric tensor, covariant notation.
Lecture PowerPoint
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Unit 5 and homework
Doppler shifts, world lines, energy-momentum four vector.
Lecture PowerPoint
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Unit 6 and homework
Conservation laws, relativistic kinematics, and a start on dynamics.
Lecture PowerPoint
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Unit 7 and homework
Massless particles, relativistic dynamics, and the electromagnetic field.
Lecture PowerPoint
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Unit 8 and homework
An introduction to General Relativity—non-Euclidean geometry, the metric tensor, spacetime curvature.
Lecture PowerPoint
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Unit 9 and homework
The Riemann curvature tensor, the Einstein field equations, and the Schwarzschild metric.
Lecture PowerPoint
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Unit 10 and homework
Motion in curved spacetime.
Lecture PowerPoint
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Unit 11 and homework
Fields, fluids, line integrals, and curl.
Lecture PowerPoint
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Unit 12 and homework
Gradient, divergence, surface integrals, the divergence theorem, and Gauss’s law.
Lecture PowerPoint
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Unit 13 and homework
The Maxwell Equations.
Lecture PowerPoint
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Unit 14 and homework
A covariant formulation of electrodynamics.
Lecture PowerPoint
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Lecture 15, just for fun: black holes, frame dragging, quantum field theory.
Click here to download the 2016, 2017 midterm exams that are printed in the course packet
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: in-class midterm, covering Units 1 — 5.
Exam equation sheetUnits 11 – 14: Vector calculus in electrodynamics and fluid dynamics
Unit 12: in-class midterm, covering Units 6 — 10.
Exam equation sheetFinal exam: Monday, July 30
Exam equation sheet
Simulating eXtreme Spacetimes [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Unless otherwise noted, all material copyright George Gollin, University of Illinois, 2018.
