Advanced Engineering Mathematics

Math 401-501/502— Spring 2013

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: Monday and Wednesday, 11-1, and by appointment.

Catalogue Description: MATH 401. Advanced Engineering Mathematics. Engineering mathematics including perturbation theory, Fourier series and partial differential equations. Designed primarily for engineering majors. Others must have consent of instructor. Prerequisite: MATH 308 (Differential Equations).

Required Texts:

Time & Place: Section 501, TR 9:35 am - 10:50 am, RICH 114; Section 502, TR 12:45 pm - 2:00 pm, RICH ARCC 207.

Grading System & Tests: Your grade will be based on homework and two in-class tests ( March 7 & April 23). In addition, there will be an optional final exam that can replace the lower of the scores on the two tests. The homework will count for 14% of your grade and each in-class test for 43%. 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.

Homework: You may consult with each other on homework problem sets, BUT only submit work which is in your own words. Late homework will not be accepted. If, for a legitimate reason, an assignment is missed, it will be dropped from the homework grade. No make-ups will be given.

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."

Tentative Schedule

C=Costanda, F=Fulling's notes, S=Simmonds and Mann
Date Section Topic
1/15/13 F3-10 Perturbation theory — basic ideas
1/17/13 F11-17, S29-31 Perturbation of algebraic equations
1/22/13 F18-23 Regular perturbations of ODEs
1/24/13 F23-25, S6-8, 11 Big "O", little "o", and asymptotic approximation
1/29/13 F25-31, S39-44 Asymptotics and uniformity
1/31/13 Class notes Stirling's formula for n!, n large
2/5/13 F32-36, S61-65 Uniform asymptotic approximations & ODEs
2/7/13 F36-40, S66-67 Two time scales
2/12/13 F41-44, S71-74 WKB approximation
2/14/13 F45-50 WKB approximation, cont.
2/19/13 F51-56 Boundary-layer problems
2/21/13 S101-105 Matched asymptotic expansions
2/26/13 C11-16 Fourier series
2/28/13 Class notes, C17-23 Complex Fourier series, sine series, cosine series
3/5/13 Catch up, review
3/7/13 Test 1
3/11/13 - 3/15/13 Spring Break
3/19/13 C23-24, class notes Operations on FS, convergence of FS
3/21/13 C83-88 Heat equation & separation of variables
3/26/13 C91, 95-99 Heat equation & wave equation
3/28/13 C105-109, C165-167 Laplace's equation & the Fourier transform
3/29/13 Good Friday/Reading day
4/2/13 C167-172 Heat & wave equations on −∞ < x < ∞
4/4/13 C27-33 Sturm-Liouville problems
4/16/13 C41-C46 Bessel functions
4/18/13 Catch up, review
4/23/13 Test 2
4/25/13 Finish up

Updated 1/14/2013.
© F. J. Narcowich, 2013.