ESAPPM 311-1
Methods of Applied Mathematics
Fall 2007

Administrative information:

Hermann Riecke, Tech M458,
Section 20:
MWF 12:00 - 12:50 p.m., Tech Room LG52
Section 21:
MWF 11:00 - 11:50 a.m., Tech Auditorium
Office hours:
Daniel Grady: Monday 1-2 (in M453)
Hermann Riecke: Tuesday 4-5 Thursday 1-2 Friday 4-5 (in M458) Please indicate which times do not work for you on this form <---!>
Additional Source for Help
Tech Tutoring is available every weekday 2-5 and 7-10 in LG52.
There are three applied math. graduate students on the team who definitely will be able to answer your differential equations questions.
Lecture Notes by Profs. Volpert and Olmstead. Photo copies are available for purchase in ESAM department office M426 ($15; please have correct change).
Elementary ordinary differential equations
will be collected and graded. There will be six homeworks. Solutions will be posted on the website.
midterm (Wednesday, Nov. 7, during regular class hours) and Final (Wednesday, Dec. 12, 12-2 p.m. in LR 2)
homework - 30%, midterm - 30%, final - 40%


Review of Elementary ODE's:
linear and nonlinear ODE's; solution of 1st order linear differential equations; 2nd order linear ODE's; linear differential equations with constant coefficients; particular solutions by variation of parameters; reduction of order; reduction to standard forms; linear dependence; Wronskian

Some applications of ODE's:
mass-spring systems, electrical circuits
Links for resonances in bridges and collapse:
NOVA program on bridges
Bridge collapse page
Millenium Bridge.

Initial Value Problems and Boundary Value Problems:
existence and uniqueness of solutions; examples of boundary value problems, Fredholm alternative theorem

Power Series Solutions of 2nd order linear ODE's:
illustrative examples; method of Frobenius; treatment of exceptional cases

Special Functions:
Bessel functions; modified Bessel functions; ODE's related to Bessel's equation; Legendre's equation; Hermite's equation; hypergeometric equation
Abramowitz & Stegun

Fourier Analysis:
Fourier sine, cosine and complete series; convergence of Fourier series; complex form of Fourier series; Fourier integrals; Fourier transforms

Eigenvalue Problems:
solution of PDE's by separation of variables - examples; Sturm-Liouville eigenvalue problem; properties of eigenvalues and eigenfunctions; eigenfunction expansions

Homework 1 Solutions
Homework 2 Solutions
Homework 3 Solutions
Midterm Review Sheet
Sketch of Solutions for Midterm
Homework 4 Solutions
Animations of various drum modes
Homework 5 Solutions
Homework 6 Solutions
Review Sheet for Final Solutions

CTEC Course Evaluations:

Section 20
Section 21

Hermann Riecke 2007-09-24