Spring 2012

** 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
Fourier Transform.

** 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

** Grading: **
Homework (40%), , Class midterm (30%), Final (30%).

** Homework:**

Homework 1.

Homework 2.

Homework 3.

Homework 4.

Homework 5.

Homework 6.

** 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
later on.