Complex Variables with Applications

Syllabus

Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Textbook

Saff, Edward and Arthur David Snider. Fundamentals of Complex Analysis. 3nd ed. Upper Saddle River: Prentice Hall, 1993. ISBN: 0133274616.

Grading

25% Problem Sets and 25% each of three tests.

Problem Sets: About one a week, due on the recitation lecture of the following week. Answers will be provided for all the problems. The graded homework will be returned by the recitation instructor. NO LATE HOMEWORK accepted. WARNING: THE PROBLEM SETS MAKE 25% of the GRADE! DO THEM ALL! There is no way to pass this course if you do not!

E-mail

Read your e-mail regularly. I will send you lots of IMPORTANT information via e-mail! If you do not get a “test” mail from me by Friday, something is wrong. Warn me at my e-mail address above or at the lecture. If you do not have an e-mail address now, get one and send it to me at my e-mail address above.

General Comments

As you can see from the syllabus, we will cover in this course a fairly large amount of material (a good chunk of the book, plus some extra stuff). This should give you some warning of the fact that this will not be a course to relax at; though this does not mean that you will not be able to enjoy it. Complex variables is not only a rather “beautiful” subject (1); but very useful and powerful in practical applications. It’s also basic for the understanding and development of very many other mathematical theories, some of them also useful (2).

Do not be fooled by the fact things start slow. This is the kind of course where things keep on building up continuously, with new things appearing rather often. Nothing is really very hard, but the total integration can be staggering - and it will \sneak" on you if you do not watch it. Or, to express it in mathematically sounding lingo, this course is “locally easy” but “globally hard”. That means that if you keep up to date with the homework and lectures, and read the book and handouts regularly (3), you should not have any problems (and might even be able to enjoy it). Otherwise, you’ll soon find yourself in deep trouble.

Notes:

1. Math. types have weird ideas about what beauty is.
2. As incredible as this may sound; it is true.
3. You will be EXPECTED TO KNOW ALL the assigned reading material AND the stuff covered in the lectures AND recitations.

Policies regarding homeworks, etc, PLEASE READ THEM:

As you know, from the syllabus, the problem sets will count for 25% of the grade, with about one per week, more or less, except when a test is due.

1. Collaboration: It is OK to exchange information with other students, inthe sense of hints, general ideas, pitfalls to avoid and so on; i.e.:“within reason” (“let me see/copy” your answer is NOT within reason). But, the final answer must be written 100% alone, with understanding of every dot that goes in there. This is an absolute MUST. WARNING:The collaboration policy above applies ONLY to problem sets. For take-home EXAMS (if any), the policy is 100% alone, with the only allowed consultations being with the Lecturer and Rec. Instructors.
2. The assigned problems will be graded. Answers to the problems will be provided (hopefully) very shortly after each set is due.
3. ENGLISH: please, use English to explain your answers. Try to avoid the use of arrows and other funny symbols and supply English words so that the steps in your reasoning can be easily followed. Credit may/will be withdrawn from answers that are not properly and clearly explained and justified. THIS IS IMPORTANT!!! True UNDERSTANDING almost always goes with the ability to explain. If you cannot explain it in plain English, there is a good chance that you actually do not understand things with with enough depth.
4. The “suggested reading”, “suggested problems” and any other “suggested” are for you alone to do or not do. It is (strongly) recommend that you do as much as possible of it. But these are NOT to be handed in!
5. About COMPUTER ASSIGNMENTS (if any):
   1. Use any language or computer you like. Athena accounts are available to all students. You can use MatLab, Mathematica, C, FORTRAN …
   2. Include a BRIEF explanation of how the problem was solved (a printout of a program is really not enough!). WHAT is the IDEA!
   3. Results must be CONDENSED to some COMPREHENSIBLE and CONCISE form:
      • Use plots, tables or graphs. Do not show “raw” numerical output.
      • Make sure one does not have to hunt for the answers all over the place. They must be EASY to find and identify. Put them at the beginning, for example, and then justify them
   4. Include a printout of your program appended (i.e. AT THE END).
   5. Look at your output and make sure it makes sense! That a program “runs” does not mean it does so as intended.

NOTE: sometimes the assigned problems will involve graphical output, that will be require an explanation of why they are so. In these cases you can use the computer to make the drawings, BUT, the pictures/figures MUST STILL be “justified” (i.e.: why are they so?). Use of the computer to substitute for thinking is not allowed.