**Announcements** (reverse chronological order)

*16 Dec:*Final grades are posted. Some explanations:- eCampus does not display meaningful statistics on letter grades. I'll just say that the median grade was a high B.
- The scaled homework grade is 0.52632 times the raw score, to bring it down to the scale stated in the handout and assignments.
- In addition, there were a few points of class participation (mostly from the in-class exercise on metrics of the (...) du dv type) that I added as bonus points. I decided not to count absences; you are grownups.

*9 Dec:*Final exam answers are posted below. Sorry for the bad wording of the hint on the first question (inherited from an old answer key): "2 x 2 matrix" should have been "square matrix". (The matrix is, of course, 6 x 6.)*5 Dec:*Your final graded homework is ready to be picked up at my office (BLOC 620H). On Friday (12/6) I'll be in the vicinity of the office (probably in BLOC 620F) in the morning from 9:30 to 11:00, and in the office in the afternoon approximately from 2:30 to 5:00. As usual, don't hesitate to knock or interrupt.*2 Dec:*Tomorrow (12/3) I'll be in my office from 1 to 4. During the first half of that time you'll have competition from my research students.*2 Dec:*Next Math Club meeting**Tuesday Dec. 3**(Ramanujan movie)*8 Nov:*Next Math Club meeting**Tuesday Nov. 12***20 Oct:*The link to the vanilla TeX macros below has been repaired.*16 Oct:*Due date for the EM paper has been extended to**Monday, Oct. 28**. (Christoffel symbols for static, spherical metric are still due on Oct. 30.)*11 Oct:*Next Math Club meeting**Tuesday Oct. 15***10 Oct:*Due date for the first round of Christoffel symbols has been put off to Monday, 21 Oct. On Monday 14 Oct we will make sure that everybody has a partner for these exercises.*18 Sep:*The grader has provided a solution for Exercise 2.19.*17 Sep (corrected 18 Sep):***IMPORTANT**._. The midterm test will be on**Monday, October 7**, one class day earlier than previously announced. (Oct. 9 is a major religious holiday for some people. Sorry.) ._._. Also, recall that a rough draft of your electromagnetism paper (see instructions below) is due on Oct. 2. Don't worry if you haven't reached the end of the assignment; turn in a copy of whatever you have finished for constructive comments.*12 Aug:*I will be out of town the week of September 2-6.

Course handout (updated with new test day) ._._. Please see my home page for up-to-date office hours.

Corrections to the textbook

Lecture notes
**(subject to further revisions)**

Projector version of the notes
(Printing out is discouraged.)

Chapter on covariant derivatives and non-Abelian gauge
theories with bibliography from *Aspects of Quantum Field Theory
in Curved Space-Time*, S. A, Fulling, Cambridge U. P., 1989.

Electromagnetism paper ._._.
Here's the TeX file,
in case you want to import some of the questions into your own document.
It is in Plain TeX and uses
the vanilla macros.
(LaTeX users will need to make some changes.)

A particularly
impressive format for submitting your paper :-)

**Homework exercises** (subject to change)
(These are not to be turned in except as
announced. Uncollected problems, or questions inspired by them, may show
up later on exams.)

- Chapter 1: 3, 5, 13, 14, 15, 18, 19 (Turn in 18 and 19 on Sept. 4.)
*Also:*Answer the 3 questions on pp. 5-6 of the notes (2 "canards" and one "topic for class discussion"). If you want to use concrete numbers in the Lorentz contraction-dilation discussion, I suggest taking speed 3/5. Turn in these essays on Sept. 9. ("Essay" does not mean a major, multipage production, but it should be a paragraph in intelligible English.) - Chapter 2: 12, 13, 16, 19, 21, 22, 24, 30 (Turn in 19 and 24 on Sept. 11. It may help to do 21 before 19.)
- Chapter 3: 4, 6, 9, 13, 16, 21 (No written homework.)
- Chapter 4: None (We will not cover this chapter in depth, but you will want to read it at least superficially to assure continuity with the later chapters.)
- Chapter 5: 2, 7, 8, 11, 12, 13, 20, 22 (No written homework.)
- Chapter 6: 7, 9, 13, 18, 23, 25, 32, 33

Also: Calculate the Christoffel symbols for the Robertson-Walker metric (12.13). (Work in pairs! One of you should use the geodesic Lagrangian method (see notes, pp. 41-42), and the other should check the results with eq. (5.75). (Trade jobs halfway through.) Turn in one paper (on Christoffel symbols) per pair on Oct. 21.) You will need the results as input into a later assignment. Note that Omega is not a coordinate, but a shorthand for the two angular coordinates collectively (see (10.2)). - Now find the Christoffel symbols for the static, spherically symmetric metric (see Exercise 6.35 of Schutz or p. 77 of notes; note that Omega is not a coordinate, but a shorthand for the two angular coordinates collectively). Work in pairs. Due Oct. 30.
- Chapter 7: 2, 7 [omit (iii)] , 10 (See next line for instructions. Hint on 10(b): There are 4 types of symmetries: space translations, time translation, rotations, Lorentz boosts.)
- Chapter 8: 4, 5, 9, 18 (From Chapters 7 and 8, turn in only Exercises 7.7, 7.10, and 8.18. These are tough, so 2/3 of the points will be "extra credit" -- that is, the actual maximum point value of all homework and class participation, after rescaling, will be something more than 100. I'll accept papers any time before the end of classes (Wednesday, Dec. 4).)
- Chapter 12: 1, 4, 8, 20, 21

Also: For the Robertson-Walker metric, calculate the Riemann tensor (20 independent components), Ricci tensor, Ricci curvature scalar, and Einstein tensor. Check that the last obeys the conservation law (contracted Bianchi identity). (Work in pairs and turn in one paper per pair on Nov. 13.) - Now we need all the same stuff for the static, spherically symmetric metric (Work in pairs; due Nov. 25.)

**Test solutions**

Track your grades on eCampus.

**Supplementary material**

- Solution to Exercise 1.3
- MathCad session on composition of Lorentz transformations
- Solution to Exercises 2.19 and 2.21
- Notes on hyperbolic functions and the twin paradox (from Honors M. 311 notes)
- Notes on div, grad, and curl in curvilinear coordinates (from Honors M. 311 notes)
- Slides on vector calculus and topology (from Honors M. 311 notes)
- Frontiers lectures of Mark Green. (Most relevant are pages 15-28.)
- Recent observational cosmology, with an executive summary by our local expert.
- Nobel Prize scientific background document on the accelerating universe
- Special issues of journals entirely devoted to relativity

Old course home pages: Fall 2017 ._. Fall 2015 ._. Fall 2013 ._. Fall 2011 ._. Fall 2009 ._. Spring 2008 ._. Fall 2005

Go to home pages: Fulling ._._. Calclab ._._. Math Dept ._._. University

e-mail: fulling@math.tamu.edu