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 up to Chapter 12 with some omissions.
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 26. The last class meeting is Thursday May 6. There is no class during spring recess: March 29 - April 4 There will be a midterm exam on a day TBA and a final at 11:15am-1:45pm on Thursday, May 13 (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 25
Chapter 1 --- Fundamental Concepts
Homework (Due Tuesday Feb 2): 7, 10, 30, 39, 45, 52, 55, 57
Week 2, Feb 1
Chapter 2 --- Complex Line Integrals
Homework (Due Thursday, Feb 11): 20, 22,25,32, 36, 41, 43, 44
CLASSES CAMCELED THURSDAY DUE TO SNOW
Week 3, Feb 8
Finish Chapter 2, Start Chapter 3 --- Applications of the Cauchy integral
Homework (Due Tuesday Feb 23): 21, 27, 32, 34, 36, 38, 44,
Week 4, Feb 15
Finish Chapter 3
Week 5, Feb 22
Chapter 4
Homework (Due March 2) : 8a, 8b, 32, 38, 46, 48, 55, 59
Week 6, Mar 1
Chapter 5
Homework (Due ??): 3,5,8,13
Week 7, Mar 8
Chapter 6
Homework (Due March 25) : 12,16,20,22,26,27,28,29
Week 8, Mar 15
Finish Chapter 6,
Week 9, Mar 22
MIDTERM TUESDAY MARCH 23 -- will cover up through Chapter 6
Chapter 7, Homework (Due ): 19,23,28,31,51,64,74
Week 10, Mar 29
SPRING RECESS ---- NO CLASS
Week 11, April 5
Finish Chapter 7
Week 12, April 12
Parts of Chapters 8 and 9.
Homework (Due ??): Chapter 8: 12,15,16,17, 20 Chapter 9: 5,6
Week 13, April 19
Parts of Chapters 10 and 11.
Week 14, April 26
Chapter 12
Week 15, May 3
Chapter 16
Week 16, May 10
FINAL EXAM ---- Thursday, May 13, 11:15am-1:45pm
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