COMPLEX VARIABLES


MAA 4402, Section 01, Summer Session C 2012

(Reference #01327 in Directory of Classes)

Course page: ON CAMPUS: http://www.math.fsu.edu/~mesterto/ComplexVariables.html (this page)
OFF CAMPUS: http://www.math.fsu.edu.proxy.lib.fsu.edu/~mesterto/ComplexVariables.html (with your FSUID username and password)
Professor:Dr M-G
Office hours: Please check here, where current times are always posted. Although office hours are subject to change—due to unforeseeable circumstances—up to midnight of the previous day (so it is wise to check here first), like a hurricane in Hertford, Hereford or Hampshire, it hardly ever happens. Note that office hours are primarily for personal matters that cannot be addressed in class (as opposed to tutorial help, for which see under Course format and How to study below)
Phone:(850 64) 42580
Main website: Professor M-G's Home Page    Email:
Goal (long version): To introduce the basic theory and techniques of differential and integral calculus over the complex numbers. Topics will include analytic functions, complex integration, Taylor and Laurent series, and the theory of residues with applications. The course will be taught from the perspective of an applied mathematician, i.e., it will focus on developing geometric insight and computational skills (as opposed to rigorous proofs of existence and uniqueness theorems).
Goal (short version): To cause you to understand the text
Class meets: In 102 LOV on Mondays, Tuesdays, Wednesdays, Thursdays and Fridays at 12:30—13:50 (12:30—1:50p.m.)
Text: Brown and Churchill,  Complex Variables and Applications, 8th edition (McGraw-Hill, 2009, ISBN 978-0-07-305194-9), §§1-79 (but not necessarily in that order). Note that you are expected to bring the text to class each day, except on the three test days (unlike, e.g., a calculus text, it does not weigh a ton)
Credit:3 semester hours
Eligibility: You must have the prerequisites listed below
Prerequisites:
(i) C- or better in MAC 2313 (Calculus with Analytic Geometry III) and
(ii) self-motivation and industriousness and
(iii) the patience to believe in yourself—you may not get it right away, but given (ii), if you are patient, then understanding will come
My philosophy of learning is perhaps best expressed by the green curve in the diagram below:
 
ALTERNATIVE THEORIES OF LEARNING VERSUS PAIN
For further details, please click here.
Communication: I will send email to your FSU email account on a regular basis. It is your responsibility to check it regularly (or arrange to have my messages forwarded, if you prefer to read your email elsewhere)
Your name:
      I don't know who you are, but because everything works so much better when I do, I would like to learn your name as soon as possible. So, please take a sheet of card stock (or even paper), fold it in half, write your name in large letters on one side and stand it up on your desk so that I can see it. (Write what you want me to call you: if you're a William who likes to be called Dubya or a Margaret Jane who likes to be called Dee Dee, write Dubya or Dee Dee, not William or Margaret Jane.) Please bring your nameplate to every class until I have finally learnt your name (which will take significantly longer than it used to take when I started out)
Course format: The course will be based on your reading of Chapters 1—7 of the text together with much interactive problem solving, on which we'll spend most of our time in class (except during the first period); the text is stuffed with exercises, as you can see for yourself. After each period I will set homework for the following period (either at the end of class or soon afterwards by email). This homework will consist of three items:
  1. Problems on the current topic or topics
  2. An assigned reading (not uncommonly the next few sections of the text, but we will sometimes skip sections or combine them in nonsequential order)
  3. A problem or problems associated with the topic or topics of the assigned reading
Although I will occasionally—on randomly chosen days—collect your stab at Item 3 (so always bring it with you), homework will not be graded. Nevertheless, it is essential to complete a significant and representative sample of every problem set (as many as you have time for), as well as at least attempt Item 3. For the sake of illustration, here is your second homework, that is, your homework for Monday, July 02:
  • Do:
    From Exercises 2 (p. 5): ##1, 4 and as many as possible of the other problems (not already done in class)
    From Exercises 3 (p. 8):##1a, 1b and as many as possible of the other problems
    From Exercises 8 (p. 22):##1, 2, 5 and as many as possible of the others
    Obviously, it gets tiresome to keep repeating ``as many as possible ...'' when it is always implied, so in setting homework I will abbreviate ``as many as possible ...'' to a simple ``etc.''
  • Read §§4-5 (pp. 9-14) and if possible §11 (pp. 31-32), as well as §§6-8 (pp. 16-22) if you have not already done so
  • At least seriously attempt #1 of Exercises 4 (p. 12) and #1 of Exercises 5 (p. 14)
At the start of each class, I will always assume that you have both read (not necessarily understood) the assigned reading and at least seriously attempted (not necessarily completed) the associated problem, that is, you have completed Items 2 and 3. I will begin the class by highlighting the key points of Item 2, to jog your memory and perhaps add a bit of perspective. I will work from notes that ultimately get posted here. (With the exception of the notes for July 02, which are primarily for your benefit, these notes are largely to help me remember what I decided to cover; however, to the extent that they are also useful to you, you are welcome to avail yourselves of them.)
    We will then proceed to work on problems, beginning with Item 3. Questions may be asked at any time—and should be, if there's anything you don't understand. (Perhaps you have a question about the assigned reading that you anticipate being answered by one or more of the problems we work together; in which case, it may well be socially minded not to ask your question at the outset. However, if it turns out that you anticipated incorrectly, then be sure to ask your question before the class is over!)
    On days when there is no quiz, we will attempt to end the formal class period after about an hour, so that the last 15-20 minutes or so can be devoted to individual tutorial help.
First homework: Before our first meeting at 12:30 on Monday, July 02: Please read §§1-2 (pp. 1-4) of the text, read as much as possible of §§6-8 (pp. 16-22), and at least seriously attempt #11 of Exercises 2 (p. 5).
Test format: Begin each question (but not subsequent parts of the same question) on a fresh sheet of paper, use one side of the paper only, and have your solutions stapled together in order at the end of the examination. Do not use dog ears. (Not owning a stapler is no excuse: I will bring one to the classroom.) Needless to say, your name must appear on Page 1
Calculator policy: You are allowed to use a Texas Instruments TI-30XA, TI-30XS, TI-30XIIB, TI-30XIIS or TI-36X Scientific Calculator or a four-function calculator for tests and quizzes. The use of any other calculator for a test or a quiz is strictly forbidden.
    Homework, however, is an entirely different matter. For homework, you are not only allowed to use a graphing calculator or mathematical software, you are strongly encouraged to do so. The rationale behind this policy is as follows: You should use a graphing calculator or mathematical software only to speed up tasks you understand so well that you could carry them out flawlessly without the help of a graphing calculator or mathematical software, if you had sufficient time and did not have access to either tool. Tests are designed to assess whether you have attained the requisite level of understanding (and the time allowed will be commensurate).
Grades: Will be based on participation in class (10%) and three quizzes (5% apiece) and tests (25% apiece), for which you must use either a pen or a dark pencil. Note that it is not enough merely to produce an answer. The method by which you obtain it must be sound and clearly demonstrated: Show all necessary steps in your method, with enough comments or diagrams to convince that you thoroughly understand.
    Precise cut-off points for A, B and C will be determined by the distribution of grades at the end of the semester, but are likely be in the vicinity of 90%, 80% and 70%, respectively. In borderline cases, a smaller number of completely correct solutions will carry more weight than a proportionate number of fragmentary answers; later scores will carry more weight than earlier scores; and a record of active participation in class will carry more weight than a record of passive attendance. Plus or minus grades may be assigned in a manner consistent with standard University practice.
    Please note that partial credit will be awarded only when part of a solution is completely correct—not when all of a solution is partially correct, whatever that means, if anything. A score for a question worth 10 points should be interpreted as follows:
10 Practically perfect
9 Still very good, but lacking—or wrong about—a significant detail
8 Still good, but lacking—or wrong about—significant details
7 Minimally satisfactory. You have—just—managed to demonstrate that you basically understand and are at least capable of getting all details correct (although it clearly did not happen this time)
6 A grade that will not be given
5 Half right in some appropriate sense (e.g., there were two parts, each worth 5 points, and your first part was practically perfect)
1-4 Not even half right and showing little understanding, but some degree of positive effort
Also note that a grade of I will not be given to avoid a grade of F or to give additional study time. Failure to process a course drop will result in a course grade of F
Solutions to
homework exercises:

Will be posted here, but only if specifically requested (if you ask in class, be advised to back up your request with an email, otherwise I am likely to forget). I caution you, however: never read the posted solution to a problem until first of all you have seriously attempted the problem yourself. If you have at least made a serious (and I do mean serious) attempt, then—even if you were unable to complete the problem yourself—you will benefit from reading the posted solution; if not, then not (rather, you will merely form a false impression of how well you understand ... as indicated by the green curve in the above learning-versus-pain diagram)
Quiz solutions: Will be posted here
Test solutions: Will likewise be posted here
Attendance policy: You are expected to attend class regularly, and bear the full responsibility for learning anything covered during any class that you miss.
Exam policy: No makeup exams. An absence may be excused given sufficient evidence of extenuating circumstances (in which case, extra weight will be attached to the other exams). But you must either have discussed the matter with me (well) in advance; or, in the case of illness, have brought me a note from a physician explicitly stating that you were too ill to attend class on the day in question. An unexcused absence will result in a grade of zero
Etiquette: You are firmly bound by Florida State University's Academic Honor Code. Briefly, you have the responsibility to uphold the highest standards of academic integrity in your own work, to refuse to tolerate violations of academic integrity in the University community, and to foster a high sense of integrity and social responsibility on the part of the University community. Even more briefly, you must neither cheat nor enable others to cheat. The penalties for violations can be severe. Please carefully read the section in the FSU Student Handbook on the Honor Code and official procedures for dealing with students who violate it. If you are in any doubt at all as to what constitutes acceptable behavior in this regard, you should ask me for clarification.
    You are also bound by the ordinary rules and customs of polite behavior that prevail in a civilized society. I assume that you know these rules and customs, and I expect you to comply with them. (In particular, you are not allowed to use a cell phone or otherwise have private conversations with others during class; and you are not allowed to create disturbances through arriving late or leaving early.)
Quiz dates: Friday, July 06
Friday, July 20
Friday, August 03
Test dates: Friday, July 13
Friday, July 27
Friday, August 10
How to study: It is important to keep up with the course from the very beginning, always attempting as many as possible (preferably all) of the homework exercises. If you get stuck, then send me a question by email. As soon as I possibly can, which might be as soon as within half an hour, but might also be a day or two later (I have a life, too, you know), I will reply—not to you, but rather to the class alias (after carefully concealing your identity, just in case you are inexplicably bashful about being perceived as smart enough to ask a question).
    Note, however, the following. First, you must identify yourself (i.e., you remain anonymous to the other students in the class, but not to me) in the body of your message (because your username does not identify you to me, and I don't reply to anonymous email). Second, you should be as specific as possible in describing your difficulty: the more precisely you identify how you got stuck, the more helpful my reply is likely to be.
Disabilities:If you have a disability requiring academic accommodations, then not only should you register with the Student Disability Resource Center (SDRC), but also you should bring me written confirmation from SDRC during the first week of class. This and other class materials are available in alternative format upon request.

ALL SYLLABI MUST INCLUDE THE FOLLOWING STATEMENTS

University Attendance Policy:
Excused absences include documented illness, deaths in the family and other documented crises, call to active military duty or jury duty, religious holy days, and official University activities. These absences will be accommodated in a way that does not arbitrarily penalize students who have a valid excuse. Consideration will also be given to students whose dependent children experience serious illness.

Academic Honor Policy:
The Florida State University Academic Honor Policy outlines the University's expectations for the integrity of students' academic work, the procedures for resolving alleged violations of those expectations, and the rights and responsibilities of students and faculty members throughout the process. Students are responsible for reading the Academic Honor Policy and for living up to their pledge to ". . . be honest and truthful and . . . [to] strive for personal and institutional integrity at Florida State University.'' (Florida State University Academic Honor Policy, found at http://dof.fsu.edu/honorpolicy.htm.)

Americans With Disabilities Act:
Students with disabilities needing academic accommodation should:
(1) register with and provide documentation to the Student Disability Resource Center; and
(2) bring a letter to the instructor indicating the need for accommodation and what type. This should be done during the first week of class.

This syllabus and other class materials are available in alternative format upon request.

For more information about services available to FSU students with disabilities, contact the:

Student Disability Resource Center
874 Traditions Way
108 Student Services Building
Florida State University
Tallahassee, FL 32306-4167
(850) 644-9566 (voice)
(850) 644-8504 (TDD)
sdrc@admin.fsu.edu
http://www.disabilitycenter.fsu.edu/

Syllabus Change Policy

"Except for changes that substantially affect implementation of the evaluation (grading) statement, this syllabus is a guide for the course and is subject to change with advance notice.''


Notes

Monday, July 02 (§§01-02, 06-08)
Tuesday, July 03 (§§04-05, 11)
Thursday, July 05 (§§09-10, 12)
Friday, July 06 (§§13-14)
       Monday, July 09 (§§15-18)
Tuesday, July 10 (§§19-21, 23)
Wednesday, July 11 (§§24-26)
Thursday, July 12 (§§29, 34)
       Monday, July 16 (§§30-33)
Tuesday, July 17 (§§37-42)
Wednesday, July 18 (§§43-44, 46, 48-49)
Thursday, July 19 (§§40-46)
Friday, July 20 (§§50-51)
       Monday, July 23 (§§52-54)
Tuesday, July 24 (§§55-59)
Wednesday, July 25 (§§59-60)
Thursday, July 26 (§62)
       Monday, July 30 (§§63-67)
Tuesday, July 31 (§§68-69)
Wednesday, August 01 (§§70-71)
Thursday, August 02 (§§72-74)
Friday, August 03 (§§67, 74)
       Monday, August 06 (§§75-76)
Tuesday, August 07 (§§78-79)

Solutions to Homework Exercises

Page 14, Exercise 1
Page 22, Exercise 1b
Page 55, Exercise 2c
Page 56, Exercise 8
       Page 71, Exercise 3b
Page 92, Exercise 4
Page 140, Exercise 3*
Page 149, Exercise 4
       Page 172, Exercise 9
Page 197, Exercise 10
Page 205, Exercises 5 & 6

Solutions to Quizzes and Tests

Friday, July 06        Friday, July 13        Friday, July 20        Friday, July 27        Friday, August 03        Thursday, August 09        Friday, August 10

Supplementary Material

The complex cubing function
The derivative of the cubing function
A contour integration problem: Question Answer
       An example of uniform but not absolute convergence       

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