Mathematics 185A
Complex Variables, Winter Quarter 2008
Time : MWF 1:10-2:00pm
Place: PHYGEO 140
Office Hours: M 2:10-3:00pm, W 2:10-3:00pm, and by Appointment
Office : MSB 2151
e-mail: zhangzh@math.ucdavis.edu
TA: Jing Xia
Office Hours: Tu 2:10-3:00pm, Th 9:10-10:00am
Office : MSB 3202
e-mail: jxia@math.ucdavis.edu
Textbook:
J.E. Marsden, M.J. Hoffman, Basic complex analysis, 3rd edition, ISBN
0-7167-2877-X, published by W. H. Freeman and Company.
Course description
The class is primarily based on Chapters 1-4 of the book by Marsden and
Hoffman.
1. Analytic functions
Introduction to complex numbers, complex powers, topology of the
complex plane, complex functions and limits, elementary functions, and
analyticity.
2. Cauchy's theorem
Contour integration and Cauchy's theorem, harmonic functions
3. Series representation of analytic functions
Convergent series of analytic functions, Laurent and Taylor series,
zeros and poles
4. Calculus of residues
Calculation of residues, residue theorem
Class Web Page:
I will maintain the Web page for this course. All homework assignments
and important announcements
will be posted on these pages. Please check these pages regularly.
You can access the 185A home page at http://www.math.ucdavis.edu/~zhangzh/math185a.html
Homework Assignments and Solutions.
Each Friday, you will be assigned a problem set, which will be due in
class the following Friday. Problem set solutions will be posted on the
course website. No late homeworks will be accepted.
Homework Assignment #1 Due Friday January 18
P9: 1, 13, 16
P23: 4, 5, 8, 19
P39: 2, 4, 6
Solutions by
Jing Xia
Homework Assignment #2 Due Friday January 25
P39: 7, 27
P57: 1, 7
P77: 3, 9, 10, 15
Solutions by
Jing Xia
Homework Assignment #3 Due Friday February 1
P89: 1, 2
P109: 1, 10
Solutions by
Jing Xia
Homework Assignment #4 Due Friday February 8
P122: 1
P143: 9
P161: 1, 7
Solutions by
Jing Xia
Homework Assignment #5 Due Friday February 15
P177: 2, 9(c)
P202: 12
Solutions by
Jing Xia
Homework Assignment #6 Due Friday February 22
P218: 2, 3, 8, 16
Solutions by
Jing Xia
Homework Assignment #7 Due Friday February 29
P234: 1(a)(d), 2, 3, 4
Solutions by
Jing Xia
Homework Assignment #8 Due Friday March 7
P239: 25, 26
P254: 1, 8, 9, 13(a)(d)
Solutions by
Jing Xia
Homework Assignment #9
Due Monday March 17
P268: 3, 5, 7
P301: 1, 3, 5
Solutions by
Jing Xia
Exams
There will be one Midterm Exam is scheduled in class on Monday,
February 11 and a comprehensive Final Exam on March 22. There
will be no make-up exams!
Midterm
Exam and Solutions
Grading Scheme
The final grade will be based on: Problem sets 30%, Midterm 30%, Final
40%