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 will complete several topics from the Fall. After a quick discussion of differential calculus in several variables, we turn to Riemann integration in the plane and prove Green's theorem. We will then introduce basic concepts of functions of a complex variable, and finish up with a  study of Fourier series in 1-variables and applications.     For the first  part of the course we will continue to use Strichartz (the textbook from the fall).  Marsden's book Elementary Classical Analysis is also a good reference for the material on differential and integral calculus of several variable. We will use other sources for the complex analysis unit. Fourier Series and Complex Analysis by E.M. Stein and R. Shakarchi are excellent  references, but more advanced and detailed than our treatment of these subjects will be.  Strichartz also has a good treatment of Fourier series.

A problem set will be assigned every week, on Tuesdays. We may have a midterm and final exam. 

Syllabus for the course

Lecture Notes


Problem Sets