Home page for Math 509, Advanced Analysis
Instructor: Charles L. Epstein
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In this course we continue our study of the foundations of analysis.
of this course is to further develop your instincts as a mathematical
entails understanding the basic concepts and techniques of analysis, 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 3:00-5:00 on Monday. Send e-mail if you have a question or would like to come see me at some other time.
Send e-mail or call if you need to see me at some other time.
My office is DRL 4E7, my telephone number is: 8-8476.
- 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