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Complex Analysis

We are sorry, but the number you have dialed is imaginary. Please rotate your phone by 90 degrees and try again.
-David Grabiner


I was chairman of the Complex Analysis Ph.D Exam committee this past year. (Other members are Prof.s Rao, Shen and Walsh.) Here is a copy of the Ph.D exam of 25May2000 (pdf).

We used the 6th edition for our text, but I have updated the below reference.
Our textbook is Complex Variables and Applications (7th edition).
Author: Churchill, Brown ISBN: 0072872527
Year: 2003 Publisher: McGraw-Hill
At Marsden Science Library I have put on reserve Ahlfor's text and Marsden's text. I recommend that you look at these often. Ahlfor's has a nice section on stereographic projection, and on Moebius transformations.

My intention is to treat the subject from a geometric point of view, and to give a number of applications both within and outside of mathematics. On my Teaching Page you will find important information for students in all of my classes. A syllabus is available.

[Image: Coffee cup] Homework and reading, so far…

Periodically, I update our list of E-problems. You should look at it once a week or so. (BTWay, E stands for Extra.)

Below, I list problems from our textbook. I use P and Pgs to abbreviate Page(s) and Sec to abbr. Section(s). Problems with an asterisk are either more important, or are problems that I am more likely to ask you to solve at the blackboard.

Please hand-in problems listed as GRADED. I will put comments on them and hand them back to you. These are not counted towards your course grade other than indirectly.

You should write up solutions for the other homework problems, but you should only hand them in if you are in doubt about the correctness of your solution.

DateDue HaveRead DoTheseProblems ________________________________________________________________ 08Jan P05: 4-6,11,(12,14)*. P11: 4,9,10,11 11Jan Pgs.1-23 P11: 12,13,(14,16,18)*. 13Jan Pgs.23-33 15Jan Pgs.33-45 P17: 2,5,9,(10,13,16)*. 20Jan Pgs.45-57 P22: 4,6,(7,8)*. P25: 1-10. 22Jan Pgs.57-63 P31: 4-8. Start reading/reviewing the basic facts on CONVERGENCE OF A SERIES e.g, the Ratio, Root, Comparison and Alternating Series tests; geometric series, absolute and conditional convergence (etc.) and TAYLOR SERIES (Power Series) e.g, radius and interval of convergence, multiplication of power series (etc.). One good reference for this is Calculus, by Tom Apostle. Also, most any book entitled Advanced Calculus will have a treatment of Power Series which is suitable for our needs. 29Jan Pgs.63-71 P42: 1,3,(4,7,10-12)*. P47: 4,(6-8)*. P54: 1-6. Extra Class, Feb01Mon., periods 10-11, in LIT 125. 05Feb Pgs.71-85 P62: 2,5,7*,9,10,(11,14,15)*. P67: 3,6,10,11,12,13,15. P74: 2,6,11,14. Extra Class, Feb08Mon., periods 10-11, in LIT 125. 08Feb Sec. 29-32 12Feb Pgs.85-109 03Mar GRADED: E8 and P93:1,2,5,12. Spring Break, March 6-14. Class CANCELED, Mar15Mon. 17Mar Sec. 38-41. DRILL:P102:3,4,7,16. P128:3,4. 19Mar GRADED: P103:13,15,18. P121:9. P129:5 [Consider the difference of the integrands, then use the Quotient Rule for differentiation]. E8. 24Mar GRADED: E9, using Cauchy's Inequality. 26Mar P62: 7. Contrast the book's method with the solution that I showed in class. 14Apr Hand in E11. End Homework

[Image: Steaming coffee cup] Exams and Projects (Complex Analysis)

StudyGuides ExamText When(1999) Alpha Study Exam Alpha Feb15Mon., 17:20-19:05, LIT125 Beta Study Exam Beta Mar29Mon., 17:15-19:05, LIT125 Gamma Study Exam Gamma Apr26Mon., 5:30PM-7:30PM, LIT203 Solutions to Gamma

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____End: Complex Analysis Page