MATHEMATICS 423
Complex Analysis


Professor: Dr. Mel Friske
Office:  S147 (Science Building)
Office Phone: (414)443-8836
E-mail: mfriske@wlc.edu
Office Hours: 12:30 - 11:30 MWF; 1:30 - 2:30 TR; other times by appointment
Course webpage: http://faculty.wlc.edu/friske/

Text:  Marsden & Hoffman. Basic Complex Analysis. 3rd ed. New York: Freeman, 1999.


Catalog Description. Complex numbers and analytic functions, Cauchy integral theorems and formulas, Taylor series and entire functions, singularities and the Laurent expansion, residues. Prereq: MAT 421.

Objectives. (1) To develop understanding of the definition and topology of the complex number system and the principal concepts involved with the analysis of complex-valued functions of one complex variable, and (2) To improve your appreciation for and ability to deal with mathematical rigor.

Course Content. The course will consist of topics chosen from chapters 1 - 4 of the text plus supplementary material to be provided. On exams you are responsible for all material presented in class including that which is not in the text.

Methodology. Reading material and homework exercises will be assigned almost every time the class meets. Homework exercises will not be collected. It is your responsibility to ask questions about any difficulties encountered in these assignments. Not all material for which you are responsible will be presented in class. Since this is a 400-level course, the responsibility for learning is yours. The role of the professor is much more to facilitate your learning than to present material. You should come prepared to participate in class discussion and may anticipate being "called on" every time the class meets. Please note that class participation is a major component of the final grade.

Problem Assignments. There will be approximately 5 - 8 problem assignments, each consisting of several problems (usually proofs). These will be submitted and receive a percentage grade. Due Dates: each assignment will have a specified due date. Problem assignments will not be accepted late except for circumstances beyond your control.

Exams. There will be three exams. Exam 1 will cover the first third of the course, Exam 2 will cover the second third of the course, and the Final Exam will cover the entire course.

Final Grades. The final average (AVE) will be computed as follows:

C = class participation (20%)

P = problem assignment average (20%)

E1 = score on Exam 1 (20%)

E2 = score on Exam 2 (20%)

F = score on Final exam (20%)

AVE = (C + P + E1 + E2 + F)/5

The grade for the course is determined by the value of AVE: A: 100-93, AB: 92-88, B: 87-83, BC: 82-78, C: 77-73, CD: 72-68, D: 67-60, F: below 60. The instructor reserves the right to lower the grade ranges (e.g. the bottom of the B range might be lowered from 83 to 82). The grade ranges will not be raised. The instructor also reserves the right to exercise discretion in raising your grade if he feels that the value of AVE does not properly reflect the quality of your work (e.g. because of one low exam score). This does not imply in any way that the lowest test score necessarily will be dropped. The instructor will not use discretionary judgments to lower your final grade.

Attendance Policy. Attendance at each class is expected. If your judgment is so misguided that you choose to cut this class, you will bear the consequences of a reduced class participation grade and poor performance on exams.



SELECTED BIBLIOGRAPHY

Introductory level

Knopp, Konrad. Elements of the Theory of Functions. (translated from German by Frederick Bagemihl) New York: Dover, 1952.

---. Theory of Functions. (2 Volumes) (translated from German by Frederick Bagemihl) New York: Dover, 1945 & 1947.

---. Problem Book in the Theory of Functions. (2 Volumes) (translated from German by Frederick Bagemihl) New York: Dover, 1948 & 1952.

Advanced level

Ahlfors, Lars V. Complex Analysis. 2nd ed. New York: McGraw-Hill, 1966.

Markushevich, A. I. Theory of Functions of a Complex Variable. (Vol. 1) (translated from Russian by Richard A. Silverman) Englewood Cliffs: Prentice-Hall, 1965.

Rudin, Walter. Real and Complex Analysis. New York: McGraw-Hill, 1966.

Titchmarsh, E. C. The Theory of Functions. 2nd ed. London: Oxford, 1939.


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