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SF State
MATH 380

Functions of a Complex Variable

Fall 2007

A complex picture from Halun's collection

Lecture: MWF 11:10-12:00 HSS 302
Prerequisites: MATH 228 (Calculus III) & MATH 325 (Linear Algebra) with grades of C or better or consent of the instructor

Instructor: Matthias Beck
Office: Thornton Hall 933
Office hours:
M 2:10-3:00
W 1:10-2:00
F 10:10-11:00
& by appointment
Phone: +1 415 405 3473

Our goal is to study the calculus of functions in one complex variable. That is, we will look at concepts of real-variable functions and see which of these concepts and their accompanying theorems can be transferred into the complex realm, which have to be modified, and which don't exist in the world of complex numbers. We will see that there are concepts and theorems in all of these three categories. Topics we will study include complex numbers and functions, differentiation, integration, Cauchy's theorem and its consequences, harmonic functions, power and Laurent series, and residues.

Texts: M. Beck, G. Marchesi, and D. Pixton, A First Course in Complex Analysis.

Grading system & exam dates:
40% Homework
20% Quizzes
20% Midterm (Nov 5)
20% Final exam (Dec 19 10:45-1:15)
Grades will be assigned according to the following scheme:

I want to ensure that each of you accomplishes the goals of this course as comfortably and successfully as possible. At any time you feel overwhelmed or lost, please come and talk with me.

Homework: I will assign homework problems as we go through the material. We can discuss the homework problems at any time during class. I will assign certain problems to be handed in; they will be due on the beginning of the Friday classes. You may hand problems in early to be able to correct your mistakes. Although you may (and should) work together with your class mates, the solutions you hand in have to be your own. I expect well composed solutions; you may want to experiment with Math typesetting programs.

Quizzes: I will frequently check your progress through unannounced quizzes given at the beginning of class. A quiz will typically test your concept of a certain definition or concept. There will be no make-up quizzes. At the end of the semester, I will drop the lowest of your quiz grades.

The way to learn math is through doing math. It is vital and expected that you attend every lecture. You will get a good feel for the math from there, but it is even more crucial that you do the homework. Working in groups is not only allowed but strongly recommended. The iLearn system allows you to send emails to anybody in your class. iLearn also features an online discussion board. Contact each other and work together.

Some more general fine print:
SFSU academic calender
Math typesetting programs
CR/NCR grading
Incomplete grades
Late and retroactive withdrawals
Students with disabilities
Religious holidays

This syllabus is subject to change. All assignments, as well as other announcements on tests, policies, etc., are given in class. If you miss a class, it is your responsibility to find out what's going on. I will try to keep this course web page as updated as possible, however, the most recent information will always be given in class. Always ask lots of questions in class; my courses are interactive. You are always encouraged to see me in my office.

"I believe that numbers and functions of Analysis are not the arbitrary result of our minds; I think that they exist outside of us, with the same character of necessity as the things of objective reality, and we meet them or discover them, and study them, as do the physicists, the chemists and the zoologists."
David Hilbert (1862-1943)

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