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Printed:
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Spr1999: MAA4402 2838...Elem.Complex.Var..MWF5..LIT203

Spr1999: MAA5404 2840..Intro.Complex.Var..MWF5..LIT203

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

26May2000

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 6

Our textbook is
Complex Variables and Applications (7^{th} edition).

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.

Author: | Churchill, Brown | ISBN: | 0072872527 |

Year: | 2003 | Publisher: | McGraw-Hill |

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.

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

(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