Differential Equation Models: (Modules in Applied Mathematics)

The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of classroom settings, and all have undergone extensive peer review and revision. Illustrations and exercises are included in most chapters. Some units can be covered in one class, whereas others provide sufficient material for a few weeks of class time. Volume 1 contains 23 chapters and deals with differential equations and, in the last four chapters, problems leading to partial differential equations. Applications are taken from medicine, biology, traffic systems and several other fields. The 14 chapters in Volume 2 are devoted mostly to problems arising in political science, but they also address questions appearing in sociology and ecology. Topics covered include voting systems, weighted voting, proportional representation, coalitional values, and committees. The 14 chapters in Volume 3 emphasize discrete mathematical methods such as those which arise in graph theory, combinatorics, and networks.

Table of Contents:
I. Differential Equations, Models, and What To Do with Them.- 1. Setting Up First-Order Differential Equations from Word Problems.- 2. Qualitative Solution Sketching for First-Order Differential Equations.- 3. Difference and Differential Equation Population Growth Models.- II. Growth and Decay Models: First-Order Differential Equations.- 4. The Van Meegeren Art Forgeries.- 5. Single Species Population Models.- 6. The Spread of Technological Innovations.- III. Higher Order Linear Models.- 7. A Model for the Detection of Diabetes.- 8. Combat Models.- 9. Modeling Linear Systems by Frequency Response Methods.- IV. Traffic Models.- 10. How Long Should a Traffic Light Remain Amber?.- 11. Queue Length at a Traffic Light via Flow Theory.- 12. Car-Following Models.- 13. Equilibrium Speed Distributions.- 14. Traffic Flow Theory.- V. Interacting Species: Steady States of Nonlinear Systems.- 15. Why the Percentage of Sharks Caught in the Mediterranean Sea Rose Dramatically During World War I.- 16. Quadratic Population Models: Almost Never Any Cycles.- 17. The Principle of Competitive Exclusion in Population Biology.- 18. Biological Cycles and the Fivefold Way.- 19. Hilbert’s 16th Problem: How Many Cycles?.- VI. Models Leading to Partial Differential Equations.- 20. Surge Tank Analysis.- 21. Shaking a Piece of String to Rest.- 22. Heat Transfer in Frozen Soil.- 23. Network Analysis of Steam Generator Flow.