**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)**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%

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.

**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 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