Analysis for Applications I
Math 641-600 Fall 2013
Catalog Description: MATH 641. Analysis for
Applications I. Review of preliminary concepts; sequence and
function spaces; normed linear spaces, inner product spaces; spectral
theory for compact operators; fixed point theorems; applications to
integral equations and the calculus of variations. Prerequisites:
MATH 447, 640, or approval of instructor.
- Instructor: Dr. Francis J.
- Office: 302 Milner Hall
- E-mail: firstname.lastname@example.org
- Phone: 979-845-7554 (Message only.)
- Office Hours: MWF 11-1, and by
Lecture Notes: Online notes will be provided.
Optional Text: James P. Keener, Principles of Applied
Mathematics: Transformation and Approximation, second (revised)
Westview Press, Boulder, Colorado, 2000.
Time and Place: TR 12:45-2:00 p.m. in ZACH 333A
- Review of Linear algebra and various topics, including inner
products, norms, and self-adjoint matrices, and the Courant-Fischer
- Function spaces Hilbert spaces, Banach spaces, the
Lebesgue integral, Lp, elementary Sobolev spaces,
Ck, ℓ p.
- Polynomials orthogonal polynomials, Weierstrass
approximation theorem, density and completeness theorems.
- Fourier series L2 theory, convergence
theorems, discrete Fourier transform.
- Other approximation tools splines and finite elements.
- Operators and integral equations bounded operators,
compact operators, spectral theory, applications
- Distributions and differential operators definition and
properties of distributions, Green's functions, differential
operators, eigenfunctions of differential operators
- Calculus of variations basic material
Grading System & Tests: Your grade will be based
a mid-term (time TBA), a final exam (Wednesday, 11 December, 8-10 am),
and homework. The mid-term will count for 40% of your grade, the
homework for 20%, and the final examination will count for the
remaining 40%. Your letter grade will be assigned this way: 90-100%,
A; 80-89%, B; 70-79%, C; 60-69%, D; 59% or less, F.
Make-up Policy: I will give make-ups (or satisfactory
equivalents) only in cases authorized under TAMU Regulations. In
borderline cases, I will decide whether or not the excuse is
authorized. Also, if you miss a test, contact me as soon as possible.
Copying Course Materials: "All printed
hand-outs and web-materials are protected by US Copyright Laws. No
multiple copies can be made without written permission by the
- Aggie Honor
Code: "An Aggie does not lie, cheat, or steal or
tolerate those who do."
Americans with Disabilities Act Policy Statement:
"The Americans with Disabilities Act (ADA) is a federal
anti-discrimination statute that provides comprehensive civil rights
protection for persons with disabilities. Among other things, this
legislation requires that all students with disabilities be guaranteed
a learning environment that provides for reasonable accommodation of
their disabilities. If you believe that you have a disability
requiring an accommodation, please contact the Disability Services, in
Room 126 of Cain Hall, or call 845-1637. For additional information,
Updated 8/22/13 (fjn).