Lectures: MWF 2:00PM-2:50PM at Thack 704
Office hours: M 11:00-12:00 and Th 3:30-4:30 or by appointment, held at Thackeray Hall 610.
Content and Prerequisites:
This is a continuation of Analysis I graduate course offered in Fall 2011. We will first cover
some complementary topics in Real Analysis, such as functional analysis,
Sobolev spaces, signed measures, BV functions and sets of finite
perimeters, before proceeding to Complex Analysis and Fourier/Harmonic
Analysis. In Complex Analysis, topics include: holomorphic functions, Conformal and M\"obius
transformations, the Cauchy Integral Formula, Power Series, and the Maximum Modulus Principle.
In Fourier/Harmonic Analysis, topics include: Fourier Series and the
Textbook: There is no required textbook. The following resources are recommended.
Functional Analysis, Sobolev Spaces and Partial Differential Equations (Universitext) by H. Brezis
Measure Theory and Fine Properties of Functions by C.L. Evans and R.F. Gariepy
Real and Complex Analysis (International Series in Pure and Applied Mathematics) by W. Rudin
Complex Analysis by Lars Ahlfors
Homework (40%), , Class midterm (30%), Final (30%).
Midterm exam: It will be held in class on Wed. Mar. 14 . The cut-off will be all the covered material before the beginning of the topics in complex analysis.
Final Exam: The time, date and place of the final exam will be announced