ESAPPM 311-1
Methods of Applied Mathematics
Fall 2007

Instructor:
Hermann Riecke, Tech M458, h-riecke@northwestern.edu
Classes:
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 <---!>
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.
Text:
Lecture Notes by Profs. Volpert and Olmstead. Photo copies are available for purchase in ESAM department office M426 (\$15; please have correct change).
Prerequisites:
Elementary ordinary differential equations
Homework:
will be collected and graded. There will be six homeworks. Solutions will be posted on the website.
Exams:
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%

Topics:

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 ASSIGNMENTS
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:

Hermann Riecke 2007-09-24