MATH 8150: Complex Variables I, Spring 2003
Instructor: Dr. Shuzhou Wang
Class Time, Location: MWF 1:25-2:15pm, Boyd 326
Office Hours: MWF 2:20-3:20pm, Boyd 506, or by appointment.
Phone, E-mail: (706) 542-0884, szwang at math dot uga dot edu
Text: Analytic Function Theory, Vols I, II, Einar Hille, QA331 .H54
References: 1. L. V. Ahlfors: Complex Analysis, QA331 .A45
2. J. B. Conway: Functions of One Complex Variable, QA331 .C659
3. G. Polya & G. Szego: Problems and Theorems in Analysis, QA301 .P64413 (hard)
4. W. Rudin: Real and Complex Analysis, QA300 .R82 (hard)
5. M. R. Spiegel: Complex Variables, QA331 .S6950 (easy)Prerequisites: Theoretical aspects of calculus: limits, continuity, derivatives and Riemann integrals (math 4100/6100 or equivalent)
Objectives/Topics of the Course: This is a qualifying exam (formerly called prelim) course on the theory of functions of one complex variable. Topics include: Cauchy-Riemann Equations, Cauchy's theorems and its consequences including: Morera's theorem, Taylor and Laurent expansions, maximum principle, residue theorem, argument principle, residue theorem, argument principle, Rouche's theorem and Liouville's theorem. Linear fractional transformations and elementary conformal mappings. Additional topics may be included.
Homework Assignments If you do not have it, download the Adobe® Acrobat® Reader™ to view the them. Late homework will not be accepted (always due during class on the due date).
Collaboration and Academic Honesty: You are encouraged to form study groups to work on homework and discuss the material for the course. However, you must write up your own homework with your own understanding, plagiarism, among other things, is prohibited. Above all, UGA Academic Honesty Policy applies: "All students are responsible for maintaining the highest standards of honesty and integrity in every phase of their academic careers. The penalties for academic dishonesty are severe and ignorance is not an acceptable defense." For more information, visit the web page http://www.uga.edu/ovpi/academic_honesty/culture_honesty.htm
Grading Policy: Course grade will be assigned approximately according to: Homework 40%; Midterm 20%; Final 40%. Exam problems will be comparable to complex analysis problems in the analysis written qualifying exam (formerly called the analysis prelim exam).Midterm Exam (3/5/2003), Midterm Exam Brief Solutions
Final Exam (5/5/2003), Final Exam Hints and Solutions