University of Delaware

Department of Mathematical Sciences  

Spring 2009 MATH 602 

Fundamentals of Real and Complex Analysis II

Instructor:     Dr. Fioralba Cakoni

Office:          402 Ewing Hall

Phone:          831-0592

E-mail: cakoni@math.udel.edu

Website: http://www.math.udel.edu/~cakoni/math602.html

Office Hours: Monday, Wednesday 9:00-10:00 am and 11:10-12:00 am or by appointments.

Basic Text:  Mathematical Analysis, 2^nd ed., T. Apostol

Recommended reading:  Principles of Mathematical Analysis, W. Rudin

Course Content

1. The Lebesgue Integral: Chapter 10

Lebesgue’s criterion for existence of Riemann integrals, the class of Lebesgue-integrable functions on general interval, basic properties of Lebesgue integral, the Lebesgue dominated convergence theorem, measurable functions, differentiation under the integral sign, interchanging the order of integration, the space L²(I).

     2.  Analytic Function Theory: Chapter 16

Analytic functions, Cauchy’s theorem, Cauchy’s integral theorem,

the maximum principle, the identity theorem, Taylor and Laurent series, the residue theorem, elementary conformal mappings.

Grading

Two hourly exams (each 100 points), the final (200 points) and several sets of homework assignment (100 points).

Academic Honesty

The University has explicit rules on academic honesty

http://www.udel.edu/stuguide/08-09/code.html#honesty