| Math 554 | FALL 2014 |
|---|---|
| LINEAR ANALYSIS | |
| Instructor: | Jim Burke | TA: | Tvrtko Tadic | E-Mail: | burke(at)math(d0t)washington(dot)edu | E-Mail: | tadic(at)math(dot)washingtonton(d0t)edu |
|---|---|---|---|---|---|---|---|
| Office: | C-443 Padelford | Office: | C-404 Padelford | Office Hours: | M 1:30-2:20, Tu 12-1. | Office Hours: | Th. 4-6pm |
| Phone: | 543-6183 |
Course notes will also be made available.
Math 554 is the first quarter of a three-quarter sequence covering advanced linear algebra and matrix analysis, ordinary differential equations (existence and uniqueness theory, linear systems, numerical approximations), Fourier analysis, introductions to functional analysis and partial differential equations, distribution theory. The topics covered in the first quarter break down approximately as follows: Linear algebra (6--7 weeks): review undergraduate material from an abstract perspective, infinite dimensional vector spaces, norms, completeness, linear transformations and matrices, bilinear forms, finite dimensional spectral theory, normal forms, factorization theorems, resolvents, applications to optimization, least squares problems, numerical issues. ODE (4--5 weeks): existence and uniqueness results, linear systems, numerical approximations.
MATH 426 and familiarity with complex analysis at the level of 427 (the latter may be obtained concurrently).
Homework: 75% -- Final Exam: 25%
Homework:
The are 9 weekly homework assignments. The first assignment is due Friday, October 7. Typically assigments will be due each Friday thereafter except November 11 and 25 which are holidays. The homework set for the week of November 11 will be due on Thursday, November 10, and there will be no homework due the week of November 25.
Students may collaborate on the homework, but each student must prepare their own homework papers for grading. Homework is due at the beginning of class on the day it is due except for Thursday, November 10, when it must be hand delivered or placed in my mailbox by 1pm. Late homework submitted after the time it is due, but before 4:00pm on the day it is due will be docked 10% in value. Late homework will be accepted before the beginning of class on the Monday following the due date, but it will be docked 30% in value. Late homework will not be accepted after that time.
Final Exam:
There is an in class final exam on Thursday, December 11, from 8:30am to 10:20am. The final exam will be closed book and notes and will consist of questions similar to those that are to be found on the preliminary exam for this course content.
Incomplete:
A grade of Incomplete will be given only if a student is doing satisfactory work up until the end of the quarter, and then misses the final exam due to a documented medical or family emergency.
Office hours will be held immediately following class on Mondays and between noon and 1pm on Tuesdays. You may also make an appointment to see me at another time. In addition, if I am in my office and not otherwise occupied, you can stop by my office to ask questions. I prefer that you not drop by MWF mornings as I am usually preparing lectures or teaching my other class.
Holidays: November 11, Veterans Day: November 27-28, Thanksgiving Holiday.
Final Exam: Thursday, December 11, from 8:30am to 10:20am.