Lectures: MWF 2:00PM-2:50PM at Thack 704
Office hours (subject to change): By appointment, held at Thackeray Hall 610.
Content and Prerequisites:
This course is an introduction to Functional Analysis.
Textbook: Functional Analysis, Sobolev Spaces and Partial Differential Equations (Universitext) by H. Brezis
It is available online though the University Library System.
Other reading resources:
Differential Calculus by A. Avez.
Functional Analysis by Rudin.
A tentative syllabus:
I. Functional Analysis: Banach spaces and linear operators, Differentiation and inverse function theorem, Implicit function theorem, The Hahn-Banach Theorem, Banach-Steinhaus theorems, Open mapping and closed graph theorems, Baire category theorem, Weak topologies and weak (*) convergence, Mazur's theorem, The separation theorems (geometrical form of Hahn-Banach). Compactness and sequential compactness, Reflexivity, separability and uniform convexity of Banach spaces. Hilbert Spaces. II. Main Function Spaces: Lebesgue and Sobolev Spaces, Jenssen's inequality, Compactness criteria, Convolution and mollification, Density theorems, Embedding theorems, Rademacher's theorem, Change of variable formula and if time permits area and co-area formulas. BV spaces.
Grading: Homework (10%), 1 Midterm (40%), Final Exam (50%).
Homework: They will appear weakly on this website and will be collected on Mondays in class. They will NOT be returned to you so make a copy for yourself before handing in your homework.
Midterm Policy: There will be no make up midterm exams. If you miss the midterm exam for a *documented* serious medical reason or similar tragedy, your grade on it will be prorated on your other exam and homework grade. No Incompletes will be accorded except in extreme circumstances. As for auditing the course, you need to talk with me about it at the latest by the end of September.
Midterm exam: It will be held in class on Friday Nov. 14 . It will mostly consist of theorems of class and problems of the homework. The cut-off will be announced.
Final exam: Will be held on the last day of classes during the
undergraduate exam week. The exact date will be announced.