MATH 420 – Complex Analysis
Carl Toews
Spring 2010
Welcome to Complex Analysis! The subject you are about to study has evolved slowly over roughly the
last two centuries, having originally emerged from the ideas of Euler, Gauss, Cauchy, and Riemann. While
the subject is often viewed as a part of “pure” mathematics, it has numerous applications to physics and
engineering, and forms as essential a part of the “applied” curriculum as it does of the pure.
Our goal in this course is to master the first seven chapters of the text Complex Analysis by Theodore
Gamelin. While this material hardly exhausts the subject, it will provide a solid grounding for future work,
and will leave you well positioned to understand a range of related issues in the sciences.
Text: Complex Analysis, by Theodore W. Gamelin.
Class Hours: TTh, 3:05-4:20, College Hall 220
Web Page: http://www.mathcs.duq.edu/~toews/teaching/spring10/complex/
Course/Topic Agenda
Week
Week 1-2
Weeks 3-4
Weeks 5-6
Weeks 7-8
Weeks 9-10
Weeks 11-12
Weeks 13-14
Topic(s)
The Complex Plane and Elementary Functions
Analytic Functions
Line Integrals and Harmonic Functions
Complex Integrals and Analyticity
Power Series
Laurent Series
The Residue Calculus
The prerequisites for this course are solid coursework in calculus, and a degree of mathematical maturity.
Homework (20%)
Homework will be due every two weeks. Barring exceptional circumstances, late homework will not be
accepted. Grading will be purely cursury, so it will be easy to get all the points, but since homework will
form the basis for tests, it behooves you to complete the homework conscientiously.
Participation (10%)
For each homework assignment, one student will be in charge of writing up their solutions in an intelligible
manner, scanning them, and sending them to me electronically. These solutions will form the basis for a
“homework key” that other students can leverage to study for exams. Your participation grade will be based
on how well you perform these dutues, as well as on how well you contribute to the life of the class.
Exams (40%)
There will be two cumulative in-class exams, spaced at roughly equal intervals throughout the semester. The
best preparation is to thoroughly understand the homework. Tentatively, the exams will be on February 16
and March 23.
Final (30%)
A comprehensive closed-book exam to be administered Wednesday, May 5th, from 11:00 a.m. to 1:00 p.m.
in 220 College Hall.
Grading
Final grades will be weighted as per above, with letter grades roughly as follows:
A
B
C
D
F
90-100
80-89
70-79
60-69
< 60.
Getting Help
Since this is a rather high level class, finding tutors is not easy. But your peers are a good substitute: a group
of minds is generally a better problem solver than a mind working alone. You are encouraged to discuss the
material with your classmates, and to work on the homework in groups. (Caveat: homework can be solved
in groups, but should be written up independently.) You should also feel free to drop by my office, even if
it’s just to say hello or ask a quick question. If my office hours don’t work for you, drop in some other time,
shoot me an email, or give me a call. (Contact information below.)
Statement on Disabilities
Students with documented disabilities are entitled to reasonable accommodations if needed. If you need
accommodations, please contact the Office of Freshman Development and Special Student Services in 309
Duquesne Union (412-396-6657) as soon as possible.
Contact Information
Carl Toews
College Hall 418
Tel: (412) 396-4851
toewsc@duq.edu
Office Hours : TBA, but meawhile, you can always email me to make an appointment
“A scientist worthy of his name, above all a mathematician, experiences in his work the same impression
as an artist; his pleasure is as great and of the same nature.” –Henri Poincaré