Home page for Math 509, Advanced Analysis
Spring 2018
Instructor: Charles L. Epstein
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The Course
In this course we continue our study of the foundations of analysis.
The goal
of this course is to further develop your instincts as a mathematical
analyst.
This
entails understanding the basic concepts and techniques of analysis, as
well as
developing intuition and proficiency in the construction of rigorous
proofs. We continue the study of the Fourier transform and its
applications, which we began in the Fall. We then turn to Advanced
Calculus in several variables, culminating with Green's theorem. Using
Green's theorem we will then introduce the basic concepts of functions
of a complex variable. I have not yet selected the
textbook. For part of the course we will use Strichartz (the
textbook from the fall), as well as other sources for the complex
analysis unit. Fourier Series and Complex Analysis by E.M. Stein and R. Shakarchi are excellent (though somewhat advanced) references.
A problem set will be assigned every week, on Thursdays. We may have a take home final exam.
 The class will meet from 3:00 to 4:30 on Tuesdays and Thursday.
 Each student is required to register for and attend an evening lab session.

My office hour is 3:005:00 on Monday. Send email if you have a question or would like to come see me at some other time.

email: cle@math.upenn.edu.
Send email or call if you need to see me at some other time.

My office is DRL 4E7, my telephone number is: 88476.
 The TA is ???. His email is ???? and his office is ???? in DRL.
Syllabus for the course
 Basic properties of Fourier Series
 Convergence of Fourier Series
 Applications of Fourier Series

The Fourier transform on the real line
 Differential Calculus is Several Variables
 The Inverse and Implicit function theorems
 Riemann Integration in several variables
 Integration by parts and Green's Theorem in the plane
 Introduction to Complex Analysis
Lecture Notes
Announcements
Problem Sets