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, Harriman 115
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 Thursday.
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 29. The last class meeting is Thursday May 8. There is no class during spring recess: March 17-22. There will be a midterm exam on TBA and a final at 8:00-10:30am on Thursday, May 15. Weekly Schedule (approximate)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 at recitation on the Tuesday of the following week. Also listed are special events, such as exams and holidays.
Week 1, Jan 28
Chapter 1 --- Fundamental Concepts
Homework (Due Feb 7): 7, 10, 30, 39, 45, 52, 55, 57
Week 2, Feb 4
Chapter 2 --- Complex Line Integrals
Homework (Due Feb 14): 20, 22,25,32, 36, 41, 43, 44
Week 3, Feb 11
Chapter 3 --- Applications of the Cauchy integral
Homework: 21, 27, 32, 34, 36, 38, 44,
Week 4, Feb 18
Chapter 4
Homework: 8a, 8b, 32, 38, 46, 48, 55, 59
Here is a
problem set
from Physics 540 (statistical mechanics) involving
contour integrals. I got these from Prof. McCoy. At the end is integral
whose value is known, but not by a contour method and McCoy says this is
publishable if you can find such a derivation.
Week 5, Feb 25
Finish Chapter 4
Week 6, Mar 3
Chapter 5
Homework: 3,5,8,13
Week 7, Mar 10
Chapter 6
Homework: 12,16,20,22,26,27,28,29
Week 8, Mar 17
SPRING RECESS ---- NO CLASS
Week 9, Mar 24
Finish Chapter 6, NO CLASS THURSDAY
Week 10, Mar 31
MIDTERM TUESDAY
Chapter 7,
Week 11, April 7
Continue Chapter 7, Homework: 19,23,28,31,51,64,74
Week 12, April 14
FInish Chapter 7
Homework:
Week 13, April 21
Chapter 8, 9
Homework: Chapter 8: 12,15,16,17, 20 Chapter 9: 5,6
Week 14, April 28
Chapter 12
Homework:
Week 15, May 5
Chapter 13
Week 15, May 12
FINAL EXAM ----THURSDAY, MAY 15, 8:00am-10:30am
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