Spotlights on ODE Topics

Resource originally made available by CODEE on February 9, 2012

In the second edition of the Borrelli/Coleman ODE Textbook [1] an effort was made to focus every section by removing material that was optional. This material was then gathered up into special sections called Spotlights and some of these sections were put at the end of chapters in the text. The remaining 27 Spotlight sections were put on a CD-ROM (along with ODE Architect) which was distributed along with the text. Wiley has given us permission to take the 27 web Spotlights and make them available here as additional resources to enrich a differential equations course.

Differential equations form a very broad subject area with applications to almost anything that moves or changes. This fact is amply demonstrated by Spotlight sections that appear below (and in the text). For example check out the Spotlights below on The Motion of a Satellite, The Chaotic Behavior of Current and Voltage in a Nonlinear Circuit, A Possum Plague in New Zealand, Temperature Change in a Body, Filtering out Noise, and Sending a Message Over a Coaxial Cable.

In addition to providing a variety of interesting models, Spotlight sections also elaborate on techniques and concepts that play a role in the modeling process; for example, see the Spotlight section Scaling and Units. Every Spotlight section has a problem set at the end and hence it is suitable for self-study, student project work, or even class lectures. The reference line under the Spotlight title indicates its connection with the text and other Spotlight sections.

Reference

[1] Borrelli, Robert, and Coleman, Courtney, (2004) Differential Equations:A Modeling Perspective, 2nd edition, John Wiley & Sons (http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471433322.html)

Table of Contents

- Spotlight on Slope Fields I
- Spotlight on Slope Fields II
- Spotlight on Sending a Message via a Coaxial Cable
- Spotlight on Exact ODEs
- Spotlight on Sensitivity of Solutions to the Data
- Spotlight on Complex-Valued Functions
- Spotlight on Minimal Time of Descent
- Spotlight on Time-state Curves and Projections
- Spotlight on Optical Illusions
- Spotlight on Orbits of Satellites
- Spotlight on Modeling: Noise Filter
- Spotlight on Locating Eigenvalues
- Spotlight on Modeling: The shape of a Paper Cutter
- Spotlight on Deficient Eigenspaces
- Spotlight on Modeling: Coupled Springs
- Spotlight on Coupled Springs: Normal Modes
- Spotlight on Pendulum Motion: Sensitivity
- Spotlight on Modeling: The Possum Plague
- Spotlight on Scaling and Units
- Spotlight on Quadratic Rates and Limit Cycles
- Spotlight on Chaos in a Nonlinear Circuit
- Spotlight on Chaos in Numerics
- Spotlight on Properties of the Wave Equation
- Spotlight on Initial Value Problems
- Spotlight on Laplace’s Equation
- Spotlight on the Extended Method of Frobenius
- Spotlight on Steady Temperatures

You may also download all of the Spotlights in a single PDF file or as separate PDF files in a zip archive.