HOMEWORK
MTH 437/537 — Spring 2009
Ground Rules
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Suggested Reading
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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.
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Written Work
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It is your job to explain your work to me clearly and completely. Here are
some guidelines:
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Write legibly, or use a word processor;
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Do not use scratch paper;
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Explain at least briefly what you're trying to do, don't just do it;
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Use complete sentences;
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Equations should (mostly) be contained in sentences;
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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
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Due 6/3/09
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Complete the problems on this page.
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Suggested reading:
Gravity §18.1, §18.4–§18.6 (and skim the rest of
§18).
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Due 5/22/09
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Suggested reading:
Gravity: §21.2 (and skim §21.1), §22.1–§22.3.
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Due 5/20/09
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Compute the curvature of the Schwarzschild geometry two ways.
You should get the same answer!
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1. By hand.
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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.
Your answer should consist of all independent nonzero terms
of either the curvature 2‑form or the Riemann curvature tensor.
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Suggested reading:
My notes;
Gravity: §21.3–§21.4 (and skim §20).
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2. Using computer algebra.
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You may use any package you wish, and any coordinate system you wish.
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Start by verifying your computation by hand from above.
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You should also compute the Ricci tensor and the Ricci scalar (the trace of
the Ricci tensor).
What answer do you expect?
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Suggested reading:
My notes on SHEEP and
other packages for computations in
relativity.
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Due 5/8/09
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No written homework this week.
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Suggested reading:
Gravity: §12.
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Due 4/24/09
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Complete the problems on this page.
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Suggested reading:
Gravity: §8.1–§8.2 (and skim §9.3–§9.4).
(EBH: §3.1–§3.8.)
You may also want to skim Projects B & C in EBH.
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Due 4/15/09
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Complete the problems on this page.
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Suggested reading:
Gravity: §9.1 (and skim §7).
(EBH: §2.4, §2.6–§2.9.)
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Due 4/6/09
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Complete the problems on this page.
(Note that the second problem is optional.)
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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.
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Due 4/1/09
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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.
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If you took MTH 434/534, feel free to include comments about that class.
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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.
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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.
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Suggested reading:
My notes (excerpted from a
book in
progress); Gravity: §2–§4.