HOMEWORK
MTH 434/534 - Winter 2004

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 texts. 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;
• 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 3/8/04

Please complete the assignment sheet.

Suggested reading (skim these only): Bishop & Goldberg §4.7-§4.9, Flanders §3.3.

Due 3/1/04

Please complete the assignment sheet.

Suggested reading: Flanders §3.4, §3.6-§3.8; Bishop & Goldberg § 4.5.

Due 2/23/04

Please complete the assignment sheet.

Suggested reading: Flanders §4.6, §4.5 (in that order).

Due 2/16/04

No homework this week

Due 2/9/04 (PDF version available here.)

Choose any orthogonal coordinate system in 3-dimensional Euclidean space other than rectangular, cylindrical, or spherical coordinates. (You may see me for suggestions, or look at the list of some orthogonal coordinate systems posted on the announcement page.) Working in an orthonormal basis, compute the gradient and Laplacian of an arbitrary function f, and the curl and divergence of an arbitrary "vector field" F (really a 1-form), using the expressions:

• grad f = df
• curl F = *dF
• div F = *d*F

and the fact that the Laplacian is the divergence of the gradient. (You may check your answer in standard reference books, but you should use exterior differentiation and Hodge duality in your computation.)

Suggested reading: Bishop & Goldberg §4.2-§4.3; Flanders §3.1-§3.2.

Due 2/2/04

Please complete the assignment sheet.

Suggested reading: My notes, Bishop & Goldberg §2.22; Flanders §2.7.

WARNING: These readings use different conventions!

Due 1/26/04

Please complete the assignment sheet.

Suggested reading: Bishop & Goldberg §2.20-§2.21; Flanders §2.5-§2.6.

Due 1/16/04

Please complete the assignment sheet.

Suggested reading: Bishop & Goldberg §2.19; Flanders §2.2-§2.3.

Due 1/12/04

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.

• 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: Bishop & Goldberg §2.1; Flanders §2.1.