Math 364 - Complex Analysis

Fall Semester, 1998-99

Go straight to the course syllabus.

Calculus and real analysis are the study of real-valued functions of a real variable. Not surprisingly then, complex analysis is the study of complex-valued functions of a complex variable. The calculus of complex-valued functions has some similarities to the calculus of real-valued functions, but there are striking differences. In particular, the amazing relationship between differentiation, integration, and infinite series in complex calculus is much more intimate and complete than it is in real calculus.

The above picture is a plot of the reciprocal of the absolute value of the Riemann zeta function. The spikes correspond to the nontrivial zeros. The Riemann Hypothesis, one of the most important unsolved problems in mathematics, asserts that all the nontrivial zeros of the Riemann zeta function lie along the line Re(z)=1/2. The Riemann Hypothesis is known to be true for at least the first billion and a half zeros.

CLASS INFORMATION:

• Meeting time: TTh 8:30-9:45
• Meeting room: Glatfelter 203

OFFICE AND OFFICE HOURS:

• Office: Glatfelter 215A
• Office hours: MTWF 10:00-11:50 and by appointment

TELEPHONE NUMBER AND E-MAIL:

• Telephone: 337-6630
• E-mail: jfink@gettysburg.edu
• WWW page: http://www.gettysburg.edu/~jfink/courses/ma364.html
• Class e-mail alias: math-364-a@gettysburg.edu

EXAM DATES:

• Exam 1: Tuesday, September 29
• Exam 2: Tuesday, November 10
• Final Exam: Saturday, December 12, 8:30-11:30 AM

PREREQUISITES:

• Multivariable calculus (Math 211) with a C grade or better

TEXTBOOK:

• Complex Variables with Applications by A. David Wunsch, second edition

COURSE CONTENT:

• Topics from Chapters 1, 2, 3, 4, 5, and 6
• Detailed syllabus

GRADING POLICY:

• Your grade will be determined by your scores on the following:
  • homework (15%);
  • two exams (15% each);
  • project (15%);
  • final exam (30%);
  • class attendance and participation; attendance at three or more department colloquia and other designated special events (10%).
• ***There will be no make-up exams, and late work will not be accepted.***

DAILY READINGS:

• Assigned readings should be done before class, and you should also attempt a problem or two from the textbook.
• Working problems is essential for an understanding of the material, and there are plenty of problems in the textbook. A representative selection of problems is given on the course syllabus.

HOMEWORK:

• Homework will be assigned, collected, and graded.
• Assignments may include material that will not be discussed in class. You are expected to learn this material on your own and to make use of the resources available to you to complete the assignments.
• Grading will be based both on mathematical content and on the quality of your write-up. NEATNESS COUNTS! Show all work necessary to justify your solutions. Answers alone are not sufficient.
• You may work with other students on the homework; in fact, I encourage that. However, your write-up should be your own.

TEAM PROJECT:

• The project will be a team effort on a topic of your own choice involving an application of complex analysis.
• The project is not intended to take an unreasonable amount of time, but it is unlikely that you will complete a project in a single sitting. Thus, your team should begin work on the project well in advance of the due date. You will probably find that shorter work sessions spread over several days are the best way to attack the project.
• To get you started early on the project, a written proposal is a required first step. The proposal is due on Tuesday, November 3.
• Projects will be presented in class after Thanksgiving.