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, Math 4-130 (moved from Physics P-122)

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 up to Chaopter 12.

My office hours will be Tu-Th 9:00-9:50 and 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, Jan 27. The last class meeting is Thursday May 7. There is no class during spring recess: April 6-10 There will be a midterm exam on a day TBA and a final at 8:00-10:30am on Tuesday, May 19 (room TBA). 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 26

Chapter 1 --- Fundamental Concepts

Homework (Due Feb 3): 7, 10, 30, 39, 45, 52, 55, 57

Week 2, Feb 2

Chapter 2 --- Complex Line Integrals

Homework (Due Feb 10): 20, 22,25,32, 36, 41, 43, 44

Week 3, Feb 9

Chapter 3 --- Applications of the Cauchy integral

Homework (Due Feb 17): 21, 27, 32, 34, 36, 38, 44,

Week 4, Feb 16

Chapter 4

Homework (Due Feb 24) : 8a, 8b, 32, 38, 46, 48, 55, 59

Week 5, Feb 23

Finish Chapter 4

Week 6, Mar 2

Chapter 5

Homework: 3,5,8,13

Week 7, Mar 9

Chapter 6

Homework: 12,16,20,22,26,27,28,29

Week 8, Mar 16

Finish Chapter 6, Midterm Thursday

Week 9, Mar 23

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

Week 10, Mar 30

Finish Chapter 7

Week 11, April 6

SPRING RECESS ---- NO CLASS

Week 12, April 13

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

Week 13, April 20

Parts of Chapters 10 and 11.

Week 14, April 27

Chapter 12

Week 15, May 4

Chapter 13

Week 15, May 11

FINAL EXAM ----TUESDAY, MAY 19, 8:00am-10:30am

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University graduate schedule spring 2009

University final exam schedule: spring 2009

Link to history of mathematics