Analysis for Applications I

Instructor: Dr. Francis J. Narcowich

Office: 302 Milner Hall

E-mail: fnarc@math.tamu.edu

Phone: 979-845-7554 (Message only.)

URL: /~francis.narcowich/

Office Hours: MWF 11-1, and by appointment

Lecture Notes: Online notes will be provided.

Optional Text: James P. Keener, Principles of Applied Mathematics: Transformation and Approximation, second (revised) edition, Westview Press, Boulder, Colorado, 2000.

Time and Place: TR 12:45-2:00 p.m. in ZACH 333A

Topics:

• Review of Linear algebra and various topics, including inner products, norms, and self-adjoint matrices, and the Courant-Fischer theorem.
• Function spaces — Hilbert spaces, Banach spaces, the Lebesgue integral, L^p, elementary Sobolev spaces, C^k, 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.

Academic Integrity

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 instructor."

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, visit http://disability.tamu.edu."

Updated 8/22/13 (fjn).