Ebook: Differential Equation Models

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.

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Content:
Front Matter....Pages i-xix
Front Matter....Pages 1-1
Setting Up First-Order Differential Equations from Word Problems....Pages 3-27
Qualitative Solution Sketching for First-Order Differential Equations....Pages 28-52
Difference and Differential Equation Population Growth Models....Pages 53-68
Front Matter....Pages 69-69
The Van Meegeren Art Forgeries....Pages 71-80
Single Species Population Models....Pages 81-90
The Spread of Technological Innovations....Pages 91-97
Front Matter....Pages 99-99
A Model for the Detection of Diabetes....Pages 101-108
Combat Models....Pages 109-131
Modeling Linear Systems by Frequency Response Methods....Pages 132-154
Front Matter....Pages 155-155
How Long Should a Traffic Light Remain Amber?....Pages 157-161
Queue Length at a Traffic Light via Flow Theory....Pages 162-167
Car-Following Models....Pages 168-197
Equilibrium Speed Distributions....Pages 198-206
Traffic Flow Theory....Pages 207-217
Front Matter....Pages 219-219
Why the Percentage of Sharks Caught in the Mediterranean Sea Rose Dramatically during World War I....Pages 221-228
Quadratic Population Models: Almost Never Any Cycles....Pages 229-242
The Principle of Competitive Exclusion in Population Biology....Pages 243-250
Biological Cycles and the Fivefold Way....Pages 251-278
Hilbert’s 16th Problem: How Many Cycles?....Pages 279-297
Front Matter....Pages 299-299
Surge Tank Analysis....Pages 301-309
Front Matter....Pages 299-299
Shaking a Piece of String to Rest....Pages 310-329
Heat Transfer in Frozen Soil....Pages 330-351
Network Analysis of Steam Generator Flow....Pages 352-380

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Content:
Front Matter....Pages i-xix
Front Matter....Pages 1-1
Setting Up First-Order Differential Equations from Word Problems....Pages 3-27
Qualitative Solution Sketching for First-Order Differential Equations....Pages 28-52
Difference and Differential Equation Population Growth Models....Pages 53-68
Front Matter....Pages 69-69
The Van Meegeren Art Forgeries....Pages 71-80
Single Species Population Models....Pages 81-90
The Spread of Technological Innovations....Pages 91-97
Front Matter....Pages 99-99
A Model for the Detection of Diabetes....Pages 101-108
Combat Models....Pages 109-131
Modeling Linear Systems by Frequency Response Methods....Pages 132-154
Front Matter....Pages 155-155
How Long Should a Traffic Light Remain Amber?....Pages 157-161
Queue Length at a Traffic Light via Flow Theory....Pages 162-167
Car-Following Models....Pages 168-197
Equilibrium Speed Distributions....Pages 198-206
Traffic Flow Theory....Pages 207-217
Front Matter....Pages 219-219
Why the Percentage of Sharks Caught in the Mediterranean Sea Rose Dramatically during World War I....Pages 221-228
Quadratic Population Models: Almost Never Any Cycles....Pages 229-242
The Principle of Competitive Exclusion in Population Biology....Pages 243-250
Biological Cycles and the Fivefold Way....Pages 251-278
Hilbert’s 16th Problem: How Many Cycles?....Pages 279-297
Front Matter....Pages 299-299
Surge Tank Analysis....Pages 301-309
Front Matter....Pages 299-299
Shaking a Piece of String to Rest....Pages 310-329
Heat Transfer in Frozen Soil....Pages 330-351
Network Analysis of Steam Generator Flow....Pages 352-380
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