HOMEWORK
MTH 437/537 - Spring 2007

Ground Rules

Suggested Reading

It is to your advantage to skim suggested readings as soon as possible. However, do not expect to master this material the first time around. Don't worry; we'll cover it in class, after which the readings should make more sense. But be warned: we will not always cover the material the same way it is presented in the text. The bottom line is that you are only responsible for material covered in class.

Written Work

It is your job to explain your work to me clearly and completely. Here are some guidelines:

• Write legibly, or use a word processor;
• Do not use scratch paper;
• Explain at least briefly what you're trying to do, don't just do it;
• Use complete sentences;
• Equations should (mostly) be contained in sentences;
• Feel free to use technology when appropriate, but this must be clearly documented. If possible, attach a printout of your session, together with a brief explanation of what you did.

You may discuss homework problems with anyone you like, and you may use any reference materials you like. However, you must write up the solutions in your own words, and you must indicate what help you used. Late homework will be corrected as a courtesy to you, but can earn at most half credit.

Assignments

Due 6/8/07

No homework this week.

Suggested reading: Gravity: §18.1 (and skim the rest of §18).

Due 6/4/07

Complete the problems on this page.

Suggested reading: Gravity: §22.1–§22.3.

Due 5/28/07

Compute the curvature of the Schwarzschild geometry using computer algebra.

• You may use any package you wish, and any coordinate system you wish.
• You should start by verifying your computation by hand from the previous assignment.
• You should also compute the Ricci tensor and the Ricci scalar (the trace of the Ricci tensor).
  What answer do you expect?

You do not need to turn anything in, but do make sure you agree with all factors and signs.

Suggested reading: My notes on SHEEP and other packages for computations in relativity.

Due 5/21/07

Compute the curvature of the Schwarzschild geometry by hand.

You may use any formalism you wish, and any coordinate system you wish. However, the results discussed in class will emphasize computations using differential forms in an orthornormal Schwarzschild ("shell") basis. While the use of computer algebra is permitted, you are strongly discouraged this once from using a preprogrammed algorithm (except to verify your results). Your answer should consist of all independent nonzero terms of either the curvature 2-form or the Riemann curvature tensor.

Suggested reading: My notes; Gravity: §21.3–§21.4 (and skim §20).

Due 5/11/07 Due 5/14/07

Rework any midterm problem on which you received fewer than 15 points.

You may use any references you wish, but please do not seek help from anyone other than me; you should complete this assignment by yourself.

Due 5/4/07

No homework this week.

Suggested reading: EBH: Project B (and skim §4.2, §4.7, Project C); Gravity: §12.3 (and skim §9.3–§9.4).

Due 4/27/07

Complete the problems on this page.

These problems are closely related to EBH: §3:7,8 and EBH: §3:Sample Problem 2.

Suggested reading: Gravity: §8.1–§8.2; EBH: §3.1–§3.8.

Due 4/18/07

Complete the problems on this page.

These problems are alternate versions of EBH: §2:1,4,9. You may do either version.

Suggested reading: EBH: §2.4, §2.7–§2.13; Gravity: §9.1.

Due 4/9/07

Complete the problems on this page.

You may also want to test your understanding of special relativity by considering these paradoxes.
Do not turn these in, but feel free to ask me about them.

Due 4/4/07

Please send an email message to me at tevian@math.oregonstate.edu. Please include some information about yourself, such as your math/physics background and your motivation for taking this class.

If you took MTH 434/534, feel free to include comments about that class.

• I will assume that email is a reliable way to reach you unless you tell me otherwise. If you don't check your email regularly, please let me know.
• It is to your advantage to provide me with a campus email address, as there are some things (such as grades) which I will not send elsewhere.

Suggested reading: My notes (excerpted from a book in progress); Gravity: §2–§4.

I would not recommend using EBH as a reference for special relativity...