Home page for AMCS 610: Analytic Techniques II/Functional Analysis 

Spring 2014
Instructor: Charles L. Epstein

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The Course

The main goal of analysis is the solution of equations.   In the first semester we covered  1-variable complex analysis; for most of this semester we turn to the analysis of linear equations in infinite dimensional.  Unlike the finite dimensional case, this requires the introduction of a topology, and so becomes a topic in analysis. Amongst other things, we will develop the framework needed to find solutions of ordinary and partial differential equations.

We use Peter D. Lax, Functional Analysis as our principal text book. Good additional references for functional analysis are: Walter Rudin: Real and Complex Analysis and Functional Analysis; E. Stein and R. Shakarchi, Functional Analysis; Ward Cheney, Analysis for Applied Mathematics; Michael Reed and Barry Simon,  Methods of Modern Mathematical Physics, Vol. 1; Tosio Kato,  Perturbation Theory of Linear Operators. Good references for finite dimensional linear analysis are: Peter Lax, Linear Algebra.

A problem set will be assigned every week on Tuesday, due the following week on Tuesday. I very much prefer that students do the problem sets alone. We may have a take-home midterm and/or final exams.


The numbers in parentheses are chapters numbers in Lax, Functional Analysis


Problem sets

  1. Problem set 1, due February 4, 2014.
  2. Problem set 2, due February 11, 2014.
  3. Problem set 3, due February 25, 2014.
  4. Problem set 4, due March 4, 2014.
  5. Problem set 5, due March 18, 2014.
  6. Problem set 6, due April 1, 2014.
  7. Problem set 7, due April 8, 2014.
  8. Problem set 8, due April 22, 2014.
  9. Problem set 9, due April 29, 2014 (you can actually turn it in before May 2).

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