(Graduate Level, Spring 2015)

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*Course #: 7634**Class meets:*TuTh 2:45PM - 4:00PM in Sears 354.

*Instructor:*Stanislaw J. Szarek (pronounced "Shareck")*Office:*Yost 332*Office hours:*Currently M 11-12, W 2-3 or by appointment (or by luck - just drop by)*Phone:*368-2913*E-mail:*szarek AT cwru.edu Asking questions by e-mail is particularly encouraged, even at strange hours.*WWW Home Page:*http://www.cwru.edu/artsci/math/szarek/*Class WWW Page (this page):*http://www.cwru.edu/artsci/math/szarek/MATH425/*Prerequisite:*MATH 322 or equivalent

(students taking MATH 322 concurrently will be considered on a case by case basis)*Text:*"Functions of One Complex Variable I" by John B. Conway;

Springer Verlag; Second Edition (1978 ISBN: 0-387-90328-3)

Series: Graduate Texts in Mathematics, Vol. 11

Here is a link to corrections (for printings 1-6; not relevant if you have a more recent printing).

**The course:** This is a graduate level course concerning
theory and applications of functions of a complex variable.
Besides for graduate students (in math or elsewhere), the course
will be suitable for undergraduates who are overqualified
for MATH 324 (i.e., they meet the prerequisite, MATH 322, and
have reasonable familiarity with complex numbers).

*Course Catalog Description :*
Analytic functions. Integration over paths in the complex plane.
Index of a point with respect to a closed path;
Cauchy's theorem and Cauchy's integral formula;
power series representation; open mapping theorem; singularities;
Laurent expansion; residue calculus; harmonic functions;
Poisson's formula; Riemann mapping theorem.
More theoretical and at a higher level than MATH 324.

**Grades:** Your Final Grade in the course will be based on
Attendance/Assignments/Various Forms of Class Participation (50%),
Midterm Exam (20%; the week of February 23) and Final Exam (30%; default time
4/30/2015, 12:30-3:30PM).

Students with special needs should contact
Educational Services for Students.

**Assigments etc:** Regularly updated assignments and other info
will be posted
**here**. Solutions (and handouts etc.) will be posted on
Blackboard.

**Integrity:** It is OK (and indeed encouraged)
to discuss homework assignments with fellow students.
However, **any** submitted work must be your own.
Merely copying someone else's work is unethical,
a waste of time, and may be penalized.
See
CWRU academic integrity policy.

Dr. Szarek's Home Page

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