COURSE: MATH 5510 Call # 33228

TIME AND PLACE: 9:45--11:05 TR in Room 313 of Gilbreath Hall

INSTRUCTOR: Dr. Robert Gardner OFFICE HOURS: 10:15-11:10 MWF

OFFICE: Room 308G of Gilbreath Hall

PHONE: 439-6977 (308G Gilbreath), Math Department Office 439-4349

E-MAIL: gardnerr@etsu.edu
HOMEPAGE: www.etsu.edu/math/gardner/gardner.htm (see my homepage for a copy of this course syllabus and updates for the course).

TEXT: Complex Analysis, 2nd Edition, by John Conway.

PREREQUISITE: An undergraduate real analysis class or advanced calculus class.

ABOUT THE COURSE: It will be assumed that the student has been exposed to (and has a reasonable recollection of) the topology of R (open and closed sets, limit points, connectedness, compactness, completeness, lub and sup, glb and inf, sequences and series of real numbers (convergence, uniform convergence, comparison tests, Cauchy sequences), and properties of fuctions of a real variable (continutiy, differentiaility, power series representation). It is also assumed that the student has been exposed to some elementary properties of the complex numbers (algebra, geometry, roots of unity, modulus).

BACKGROUND: The background material in real variables can be found in:

1. An Introduction to Analysis, by J. R. Kirkwood.
2. Elements of Real Analysis, by Robert Gardner Bartle.
3. A Primer of Real Functions, by R. P. Boas.

Grading: Homework (H) will be assigned and collected regularly. We will have two tests (T₁ and T₂) and your average will be computed as follows:

SCHEDULE: Our tentative outline is:
Chapter 1. The Complex Number System: introduction to the complex plane, real and imaginary parts, modulus, polar representation, extended comples plane, Riemann sphere.
Chapter 2. Metric Spaces and Toplogy of C: extensions of several ideas from R to C and other metric spaces, open and closed sets, connectedness, sequences, completeness, compact sets, continuity, convergence, uniform convergence.
Chapter 3. Elementary Properties and Examples of Analytic Functions: series, convergence of series, differentiability, analytic functions, mappings.
Chapter 4. Complex Integration: Riemann-Stieltjes integrals, power series, zeros of analytic functions, Fundamental Theorem of Algebra, Maximum Modulus Theorem, winding number, Cauchy's Integral Formula, properties of path integrals, Open Mapping Theorem.
Chapters 5 and 6. Singularities and the Maximum Modulus Theorem}: residues, argument principle, Schwarz's Lemma, Pragmen-Lindelof Theorem.

IMPORTANT DATES:
Friday, September 7 = Last day for 75% refund.
Monday, September 24 = Last day to drop without a grade of "W."
Monday, October 22 = Last day to drop without dean's permission.
Thursday and Friday, November 22 and 23 = Thanksgiving Holiday - University closed.
Wednesday, December 5 = Last day to withdraw from the university.
Thursday, December 6 = Last day of class.
Tuesday, December 11 = Final, 8:00 a.m. to 10:00 a.m.

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