Introduction to Complex Variables Syllabus Instructor: Professor Peter R. Kramer Office: 310 Amos Eaton Hall Telephone:  (518) 276-6896 Email: kramep@rpi.edu Office Hours:  Wednesdays, 2-3 PM (graduate  priority); Wednesdays 4-5 PM (this class priority); Fridays 4-5 PM  (free-for-all)

Resources Course Objectives Attendance Exams/Grading Honesty  Schedule

• James Ward Brown and Ruel V. Churchill, Complex Variables and Applications, Sixth Edition. McGraw-Hill 1996.  Required textbook available at bookstore.
• Murray R. Spiegel, Complex Variables with an Introduction to Conformal Mapping and Its Applications. McGraw-Hill 1964.  Optional textbook available at bookstore.
• Class reserves available online and at Folsom Library.  See Readings on the WebCT site for current reading list.
• Maple and MATLAB may be used for some parts of the course.  You will not be expected to program in either of these packages, and will be given specific instructions for how to use them for the particular purposes of the course.  You are welcome to use mathematical computing packages such as these to assist you in your homework, subject to any explicit restrictions I may state on particular assignments.  Be careful that you are learning the concepts and techniques  though; you will not have access to a computer or calculator during exams!
• WebCT will be used for some aspects of course management.  You can get started by going to http://www.rpi.edu/web/webct/ and consulting the document describing the use of WebCT in this class.

Course Objectives

• To learn how complex variable techniques can be used to solve certain kinds of problems in the applied sciences
• To develop analytical reasoning skills
• To gain some familiarity with how complex variables provide connections between geometry and analysis

• You will be responsible on homework and exams for all material covered in class, and there will be some you won't find in the course readings.  It would therefore behoove you to attend the classes, and if you miss class, I suggest getting notes from a friend.
• If you are absent for a midterm of final, you must let me know as soon as possible, and certainly within 24 hours after the exam.  If I excuse your absence because of a very good reason (like a serious illness), you can take a make-up oral examination.  If your absence is unexcused, you get a zero for that exam and there will be no opportunity for a make-up.  "Forgetting" that a midterm has been scheduled will not be excused.

• Your course grade will be weighted as follows:
• Homework:  25%
• Midterm #1:  20%
• Midterm #2:  25%
• Final exam:  30%

A:  90% +

B:  80-89%

C:   70-79%

D:  50-69%

F:    0-50%

Evaluating student performance is an important part of the service provided by Rensselaer, and for it to be meaningful, it must be based on fair and honest representations.  Acts which violate this trust undermine the educational process.
The general rules governing academic honesty in this course are those found in the Rensselaer Handbook of Student Rights and Responsibilities, with the following clarifications:
• Unless otherwise indicated, you may cooperate in small groups on the solution of problems.  Generally speaking, you should show your work.  It is not permissible for one person to simply copy the solutions of another person, even if they are working together.  If there is evidence for such copying, all people involved will be penalized 10 points for the first such infraction, 20 points for the second, 30 points for the third, and so on in arithmetic progression.  Realize that I am able to detect trivial attempts to conceal a copying operation.  The worst penalty for not making your own independent and serious effort on the homework is, of course, a disappointing performance on the exams.  Several people fall into this trap yearly in my FOAM class, so be warned!  Friends, don't let your friends do your thinking for you!
• You may under no circumstances collaborate on examinations or misrepresent another person's work as your own on examinations.
• You may not bring books, notes, or electronic instruments to examinations outside of those explicitly permitted, and you may not write on or alter examination materials that you submit for regrading.
Students who violate the spirit or letter of these rules are subject to penalties according to the principles outlined in the Rensselaer Handbook, in addition to receiving a zero on any work on which cheating has taken place.  I generally pursue infractions to the full extent indicated in the Rensselaer Handbook.
,Back to top

• The midterm dates are set, but the precise dates of topic coverage are subject to change.

 

Session/ Date	Topics
1.  01/14-01/21	Introduction to complex numbers and complex arithmetic
2.  01/24-02/04	Analytic functions
3.  02/11-02/14	Elementary functions and their mappings
4.  02/21	Midterm 1
5.  02/24-03/07	Integrals
6.  03/18-03/21	Series
7.  03/25-03/28	Residues and Poles
8.  04/01	Midterm 2
9.  04/04-04/15	Applications of Residues
10.    04/18-04/22	Conformal Mapping
11.    04/25-04/29	Applications of Conformal Mapping