Special and General Relativity, and an Introduction to Mathematical Methods in Physics


Physics 225, Summer 2017

Lecture (50 minutes): Loomis 222, Mondays, Thursdays at 10 am

Discussion section (110 minutes): Loomis 222, Mondays, Thursdays at 1 pm

2 credit hours

    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 exercises the next day; I'll have homework solutions posted shortly after the late submission closing date.

    Units 1 – 10: Special and General Relativity


  • Unit 1 and homework

    Special relativity—time dilation and Lorentz contraction.
    Lecture PowerPoint

  • Unit 2 and homework

    Special relativity—non-simultaneity; 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, energy-momentum four vector.
    Lecture PowerPoint

  • Unit 6 and homework

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

    • Unit 7: in-class midterm, covering Units 1 — 5.

    Exam equation sheet

  • Unit 7 and homework

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

  • Unit 8 and homework

    An introduction to General Relativity—non-Euclidean 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

    • Units 11 – 14: Vector calculus in electrodynamics and fluid dynamics


  • Unit 11 and homework

    Fields, fluids, line integrals, and curl.
    Lecture PowerPoint

    • Unit 12: in-class midterm, covering Units 6 — 10.

    Exam equation sheet

  • 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

    • Final exam: Monday, July 31

    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, 2017.