Math 556 Fall 2006

Methods of Mathematical Physics I

Room: 441 Altgeld

Time: TTh 9:00 - 10:20 am

Office: Illini Hall 335
E-mail: ekirr@math.uiuc.edu
Phone: 265-5418
Office hours:
- Tuesdays 4:00 - 5:30 pm
- Wednesdays 3:00 - 4:30 pm
- By appointment

Midterm : October 12, in class. Counts for 30% of your grade.

Final Exam: 1:30-4:30 PM, Tuesday, December 12, in room TBA. Counts for 40% of your grade.

Test Policies: No books, notes, calculators or computers allowed. Make up tests will be given only if you present written evidence, as soon as possible, that you did (or will have to) miss an exam for a legitimate reason, e.g. illness or family emergency. Travel and leisure plans are never a legitimate reason.

Syllabus: We will cover Ch 1-5 and 7 from the textbook below. We will start by reviewing finite dimensional linear algebra. We will extend its principles to infinite dimensional vector spaces, like Banach and Hilbert spaces, and use this framework to study:

integral equations via compact operators and their spectral theory,
differential equations via unbounded operators, Green functions and eigenfunctions,
calculus of variations and its application in eigenvalue and nonlinear problems,
integral transforms (Fourier, Laplace, Z transforms) and their applications in spectral theory of unbounded (differential) operators.

Prerequisites: Advanced Calculus and Ordinary Differential Equations (undergraduate)

Text: James P. Keener, Principles of Applied Mathematics: Transformation and Approximation, Revised Edition

Homework: Assignments will be given every two weeks. Count for 30% of your grade. I encourage you to work together on the homework but solutions should be written up independently and turned in by the deadline for each assignment. Check back this page for actual assignments and deadlines. Solutions will be posted on this page, if necessary, after the due date. Late homework accepted only if you get an extension from me.