MCS 321 Problem Assignments
6. Residues and Poles
Sections
to read
| Topics
| Problems
| Due Date
|
| 62-64
| Cauchy's residue theorem
| p. 230 #1abc, 2abc, 3abc
| W 4/28
|
| 65
| Types of singular points
| p. 233 #1
| W 5/3
|
| 66-67
| Residues at poles
| p. 238 #1, 3
| W 5/3
|
| 68-69, 70
| Zeros and poles
Behavior near isolated singular points
| Work some problems on your own.
|
|
Students are encouraged to discuss course topics with one another.
On assigned work, though, you are expected to do the work on your own.
Your discussion with other students should be confined to matters
related to understanding the problems and general approaches to doing
problems, and you should acknowledge those who help you in this way.
You should not collaborate on problem solutions unless directed otherwise.
- Acknowledge your sources (people and texts).
- In nontrivial problems, show how you get your answers.
- Turn in neat, well-written solutions, not messy first drafts.
Trim "fringes." Staple multiple-page submissions.
- Do not copy collaborative solutions; write up solutions in your own words.
- Turn in homework on time. Each class day late reduces the possible points
by 33%.
- Do extra credit problems entirely on your own.
Honor pledge:
"On my honor, I pledge that I have not given, received, or tolerated
others' use of unauthorized aid in completing this work."
Proofs
- Clearly state the proposition to be proved.
- A proof is a clear, logical argument that convinces the reader
that the proposition is true.
Write your proof in complete sentences.
- Embed mathematical expressions in your sentences
in a grammatically sensible way.
Look at your math texts to see how this is done.
- Every step in a proof is or can be justified by a reason.
Valid reasons include assumptions, definitions, and previously
established results.
Consider the audience (or the professor's instructions)
in deciding to what extent you make explicit
or abbreviate your steps and reasons.