SUNY Stony Brook

Office: 4-112 Mathematics Building

Phone: (631)-632-8274

Dept. Phone: (631)-632-8290

FAX: (631)-632-7631

Time and place: TuTh 9:50-11:10, Physics P-124

We will use the text `Function Theory of One Complex Variable' by by Robert Green and Steven Krantz, third edition, published by the AMS, 2006. I hope to cover Chapters 1-9, 12 and 16 with a few sections omitted.

My office hours will be Tu-Th 11:10-12:00 in my office, 4-112 in the Math Building.

This is an introductory course on the theory of one complex variable. We will start with the definition and basic properties of holomorphic functions, the Cauchy integral theorem, residues, maximum principle and the Schwartz lemma. We will then cover more advanced topics such as the Riemann mapping theorem, harmonic functions, infinite series and products, analytic continuation, rational approximation and Hilbert sapces of analytic functions.

Homework problems will be asssigned from the text each week and will be handed in at class each Tuesday.

Although it is not required, you may wish to consider writing up your solution in TeX, since eventually you will probably use this to write your thesis and papers. Here are a sample LaTex file and what the resulting output looks like . You can use the first file as a template to create your own TeX files. Numerous guides exist online that give the basic rules and commands.

The first lecture is Tuesday, Feb 1. The last class meeting is Thursday May 12. There is no class during spring recess: April 18-24 There will be a midterm exam on Thursday March 31 and a final at 11:15am-1:45pm on Thursday, May 19 (in Physics P-124, the usual room). Homework, midterm and final will count for 30%, 30% and 40% of your grade respectively. Weekly Schedule (approximate; this may change depending on our progress)Below is a list of the weeks in the semester. For each week I list the chapter I plan to lecture on and the homework for that chapter that should be turned in on Tuesday of the following week. Also listed are special events, such as exams and holidays. The listed midterm date may change.

Week 1, Jan 31

Chapter 1 --- Fundamental Concepts

Homework (Due Tuesday Feb 8): 7, 10, 30, 39, 45, 52, 55, 57

Week 2, Feb 7

Chapter 2 --- Complex Line Integrals

Homework (Due Thursday, Feb 17 ): 20, 22,25,32, 36, 41, 43, 44

Week 3, Feb 14

Chapter 3 --- Applications of the Cauchy integral

Homework (Due Tuesday, March 1 ): 21, 27, 32, 34, 36, 38, 44,

Week 4, Feb 21

Finish Chapter 3, Start Chapter 4

Week 5, Feb 28

Chapter 4

Homework (Due ) : 8a, 8b, 32, 38, 46, 48, 55, 59

Week 6, Mar 7

Chapter 5

Homework (Due ): 3,5,8,13

Week 7, Mar 14

Chapter 6

Homework (Due Thur March 31 ) : 12,16,20,22,26,27,28,29

Week 8, Mar 21

Finish Chapter 6,

Week 9, Mar 28

MIDTERM Thursday MARCH 31 -- will cover up through Chapter 6

Chapter 7, Homework (Due ): 19,23,28,31,51,64,74

Week 10, Apr 4

Finish Chapter 7

Week 11, April 11

Parts of Chapters 8 and 9.
Homework (Due ): Chapter 8: 12,15,16,17, 20 Chapter 9: 5,6

Week 12, April 18

SPRING RECESS ---- NO CLASS

Week 13, April 25

Chapter 12

Week 14, May 2

Chapter 16

Week 15, May 9

Chapter 16

Week 16, May 16

FINAL EXAM ---- Thursday, May 19, 11:15am-1:45pm In usual room, P-124

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