MAT 528 -- Complex Variables II 
Course Information

 
Professor: D. Bradley

Office: 322 Neville Hall  Hours: 2:00-2:50 p.m. MWF*  Phone: (207) 581-3920

Announcements  Homework  Additional Reading

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

This course is a continuation of MAT 527. As such, we will be reinforcing many of the concepts and topics of MAT 527 as well as forging ahead with new material in the study of complex analysis. Grades will be assigned on the basis of in-class participation and successful completion of written homework assignments. Homework problems based on the lecture material will be assigned throughout the semester. A substantial majority of correct solutions will be required to acheive a grade of "A".

Students who will profit:

Anyone contemplating the pursuit of an advanced degree in a subject with technical requirements in higher mathematics.

Text:

Serge Lang, Complex Analysis, (4th ed.) Springer-Verlag Graduate Texts in Mathematics #103, New York, 1999.

Syllabus: I plan to cover most of chapters VIII through XVI of Lang. In more detail:

• Harmonic functions
• Mean value theorem
• Poisson formula
• Schwarz reflection
• Riemann mapping theorem
• Analytic continuation
• Entire functions
• Weierstrass products
• Functions of finite order
• Hadamard's factorization theorem
• The Euler gamma function
• Weierstrass product representation
• functional equation
• reflection formula
• Gauss multiplication formula
• Euler's integral representation
• Stirling's formula
• The Hurwitz and Riemann zeta functions
• Lerch's formula
• functional equation
• Newman's proof of the prime number theorem
• Mittag-Leffler's theorem, partial fraction expansions
• Elliptic Functions
• Liouville's theorems
• The Weierstrass p-function
• The addition theorem
• The sigma and zeta functions
• Additional topics as time permits