Mathematics 185A
Complex Variables, Winter Quarter 2008
Time : MWF at 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:
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,
analyticity and the Cauchy Riemann relations
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,
zeroes and singularities
4. Calculus of residues
calculation of residues, residue theorem
Each Friday, you will be assigned a problem set, which will be due in class the following Frideay. Problem set solutions will be posted on the course website. No late homeworks will be accepted.
Exams
There will be one Midterm held in class on February 8 and a comprehensive Final Exam
on March 22.
There will be no make-up exams!
Grading
The final grade will be based on:
Problem sets 30%, Midterm 30%, Final 40% |