ESAPPM 311-1
Methods of Applied Mathematics
Fall 2007
Administrative information:
- 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
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-
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.
- 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
- Grading:
- 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:
Section 20
Section 21
Hermann Riecke
2007-09-24