ACM 105
Applied Real and Functional Analysis

Instructor
Eric Chung
Office: Firestone 315
Phone: 626.395.4550
Office Hours: M 2:00-3:00 pm, W 3:00-4:00 pm, or by appointment
Website: www.acm.caltech.edu/~tschung
Email: tschung@acm.caltech.edu

TA
Stephen Becker
Office: Firestone 214
Office Hours: Thursday 4:00-5:00 pm
Email: srbecker@acm.caltech.edu

Textbook
Introductory Functional Analysis with Applications, Kreyszig
(Chapter 1,2,4,7 and possibly 8)
Measure and Integral, Wheeden and Zygmund
(Chapter 3,4,5,6,8,9,10, we assume the material in Chap 1)

Topics
The Lebesgue integral on the line, general measure and integration theory, convergence theorems, Fubini, Tonelli, the Lebesgue integral in n dimensions and the transformation theorem, L_p spaces, convolution, Fourier transform and Sobolev spaces with application to PDEs, the convolution theorem, Friedrich's mollifiers, dense subspaces and approximation, normed vector spaces, completeness, Banach spaces, linear operators, the Baire, Banach-Steinhaus, open mapping and closed graph theorems with applications to differential and integral equations, dual spaces, weak convergence and weak solvability theory of boundary value problems, spectral theory of compact operators.

Grading
There will be homework assignments throughout the semester as well as a take-home midterm and final. Grades will be assigned according to the following allocation.
HW: 20%
Midterm: 30%
Final: 50%