MAT 528 -- Complex Variables II 
Spring 2000 Course Description

E-mail: bradley@gauss.umemat.maine.edu
Website: http://www.umemat.maine.edu/faculty/bradley/index.html

Text: John B. Conway, "Functions of One Complex Variable I," (2nd ed.) Springer-Verlag Graduate Texts in Mathematics #11, New York, 1978.

References:

• Serge Lang, "Complex Analysis," (2nd ed.) Springer-Verlag Graduate Texts in Mathematics #103, New York, 1985.
• Joseph Bak and Donald J. Newman, "Complex Analysis," (2nd ed.) Springer-Verlag, New York, 1997.
• E. T. Whittaker and G. N. Watson, "A Course of Modern Analysis," Cambridge University Press, London, 1969.
• Konrad Knopp, "Theory of Functions," (5 Volumes), Dover, New York, 1975.
• Stanislaw Saks and Antoni Zygmund, "Analytic Functions," (2nd ed.) Polska Akademia Nauk, Warsaw, 1965.
• Einar Hille, "Analytic Function Theory," (2 Volumes), Blaisdell Publishing Company, New York, 1963.

Syllabus: This course is a continuation of MAT 527, Complex Variables I. Topics covered included:

• Analytic Continuation and the Schwarz Reflection Principle
• Laplace and Mellin Transforms
• Liouville's Theorem for Re(f)
• Newman's Proof of the Prime Number Theorem
• Phragmén-Lindelöf Theorem, Borel-Caratheodory Theorem
• Weierstrass Factorization Theorem, Mittag-Leffler's Theorem
• The Gamma and Riemann zeta functions, Applications to Number Theory
• Entire Functions, An entire function bounded in every direction
• Elliptic Functions
• Jensen's Formula, The Little and Great Picard Theorems