MTH 425: Complex Analysis

COURSE SYLLABUS

Fall Semester, 2000

CLASS MEETINGS: 1:50-2:40 M W F (C113 Wells Hall (WH))

INSTRUCTOR: Alex Voronov

OFFICE: D326 WH

PHONE: 353-6330

E-MAIL ADDRESS: voronov@math.msu.edu. You are welcome to use e-mail to send questions to me.

INTERNET: All class announcements and assignments will be posted on the class homepage http://www.mth.msu.edu/Help_Room/Info/Pages/425-001.html and NOT handed out in class.

OFFICE HOURS: Tue 3-4 p.m., Wed  2:45-3:45 p.m., Thu 2-3 p.m., and by appointment. See also our TA's office hours in Getting Help below.

TEXT:  Complex Variables and Applications by J. W. Brown and R. V. Churchill (6th Edition).

GOALS: This is an introductory course in complex analysis, giving the basics of the theory along with applications, with an emphasis on applications of conformal mappings. Students should have a background in real analysis (as in the course MTH 320), including the ability to write a simple proof in an analysis context. This course (together with MTH 419H) should prepare the student for graduate-level work in complex analysis and areas of mathematics, science, and engineering which use substantial amounts of complex analysis.

CONTENT: Chapters 1-4 and 8-10 of the textbook. Topics include: the geometry of complex numbers, Cauchy-Riemann equations, harmonic functions, mapping properties of logarithm, exponential, and other functions, contour integrals, the Cauchy-Goursat Theorem, Cauchy integral formulas, Morera's Theorem, maximum modulus principle, Liouville's theorem, linear fractional transformations as mappings, preservation of angles, harmonic conjugates, applications of conformal mapping to physical problems.

GETTING HELP:

HOUR TESTS: There will be two hour tests: Friday, October 6, and Friday, November 10. If you miss an hour test, your grade on it will be determined by the final exam, prorated to 100 points.

FINAL EXAM: The final exam will be given on Thursday, December 14, 12:45-2:45 p.m. in C105 Wells Hall. This is NOT the classroom used for class meetings during the semester.

HOMEWORK:  There will be weekly problem sets assigned to be turned in. A few problems from each set will be selected at random and graded. You are expected to do your homework regularly during the week (I recommend three times a week) and hand it in at the beginning of each Wednesday class, except the first week of classes and the test weeks. The test weeks' homework will be assigned, but not collected. You are encouraged to cooperate in doing homework, forming study groups. (For example, the whole class may become one study group.) However, everyone should work on every problem; a solution you get together with other students should be written down in your own words. Copying someone else's solution will be penalized. Assignments handed in late will get a 10% penalty per any fraction of a day after 1:55 p.m. on the due day. The maximum penalty is limited to 50%.

It is suggested that after each class you review your lecture notes, read the corresponding sections of the text, and do the homework problems from these sections.

GRADING: Based on two hour tests (100 points each), problem sets (200 points total), and final exam (200 points). Grading will be done on curve. I expect the students to be good enough to earn grades not lower than 3.0. In principle, depending on your particular performance, you may get any grade between 1.0 and 4.0.

IMPORTANT DATES:

Friday, September 1 - close of computer/telephone enrollment.

Monday, September 4 - Labor Day. Classes cancelled.

Friday, September 8 - last day to late add or change sections [Note: from September 4 to 8, students MUST go to A-212 to make these changes.]

Thursday, September 21 - last day to drop a course and receive a 100% refund.

Tuesday, October 17  - last day to drop a course with no grade reported.

Thursday-Friday, November 23-24 - Thanksgiving. Classes Cancelled.