Course Website:

• http://www.math.washington.edu/~robin/courses/554.A11/index.html

Texts:

• Horn and Johnson, Matrix Analysis , second edition (required)

• Coddington and Levinson, Theory of Ordinary Differential Equations (required)

• Birkhoff and Rota, Ordinary Differential Equations (optional)

• Course notes will also be made available.

Books on reserve: (Math Research Library, C-306 Padelford)

• Horn and Johnson, Matrix Analysis , second edition

• Halmos, Finite Dimensional Vector Spaces

• Nering, Linear Algebra and Matrix Theory

• Lipschutz, Schaum's Outline of Theory and Problems of Linear Algebra

• Kato, A Short Introduction to Perturbation Theory for Linear Operators

• Ortega, Numerical Analysis: A Second Course

• Golub and Van Loan, Matrix Computations

• Cheney, Analysis for Applied Mathematics

Horn and Johnson will be our main text for the linear algebra portion of this quarter. Halmos, Nering, and Lipschutz are advanced undergraduate texts; they are good for reviewing material on linear algebra you have studied previously. Kato is an excellent reference for some of the more advanced topics we will cover, especially for the resolvent. Ortega is a gem of a book with a straightforward exposition of many hard-to-find results useful in numerical linear algebra. Golub and Van Loan is a modern classic on numerical linear algebra. Cheney covers a similar selection of topics as our whole three quarters-his first chapter has a good treatment of some of the analytic topics we will discuss this quarter.

• Coddington and Levinson, Theory of Ordinary Differential Equations

• Birkhoff and Rota, Ordinary Differential Equations

Coddington and Levinson will be our main reference for the ODE portion of the course. Birkhoff and Rota is a good book to review ODE material you may have studied previously.

Course Content:

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 (8-9 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, continuing into Winter Quarter): existence and uniqueness theory, linear systems, numerical approximations.

Background and Prerequisites:

MATH 424, 425, 426 and familiarity with complex analysis at the level of 427 (the latter may be obtained concurrently).

Grading:

Homework: 60% -- Final Exam: 40%

Homework:

There will be one written problem set per week. Students are encouraged to work together on the homework, but each student must prepare his/her own homework paper for grading.

Final Exam:

There will be an "in class", closed book, closed notes, final exam on Thursday, Dec. 12, 8:30 am.

Office Hours

Robin Graham: Monday and Wednesday 2:30-3:30

Tvrtko Tadić: Tuesday 2:30-3:30 and Thursday 4:30-5:30

You may also make an appointment to see either of us at another time.

Important Dates:

Holidays:

Monday, November 11, Veterans Day.

Thursday and Friday, November 28-29, Thanksgiving.

Final Exam: Thursday, December 12, 8:30 am