Differential Equation Models

by Martin Braun (Editor), Courtney S. Coleman (Editor), Donald A. Drew (Editor)

I. Differential Equations, Models, and What To Do with Them.- 1. Setting Up First-Order Differential Equations from Word Problems.- 1. Introduction.- 2. Guidelines.- 3. Examples.- Exercises.- Solutions.- Notes for the Instructor.- 2. Qualitative Solution Sketching for First-Order Differential Equations.- 1. Introduction.- 2. Direction Field.- 3. Relevance of Uniqueness Theorems.- 4. Sketching of Solutions.- 5. Discussion of Equilibria and Stability.- 6. A More Difficult Example.- Exercises.- Solutions to Exercises.- Notes for the Instructor.- 3. Difference and Differential Equation Population Growth Models.- 1. Introduction.- 2. Solution of the Difference Equation.- 3. Solution of the Differential Equation.- 4. Linearized Stability Analysis.- 5. Interpretation of Results.- 6. Concluding Remarks.- 7. The Basic Model.- Exercises.- Solutions.- References.- Notes for the Instructor.- II. Growth and Decay First-Order Differential Equations.- 4. The Van Meegeren Art Forgeries.- Exercises.- References.- Notes for the Instructor.- 5. Single Species Population Models.- Exercises.- References.- Notes for the Instructor.- 6. The Spread of Technological Innovations.- Martin Braun.- Exercises.- References.- Notes for the Instructor.- III. Higher Order Linear Models.- 7. A Model for the Detection of Diabetes.- Exercises.- References.- Notes for the Instructor.- 8. Combat Models.- 1. Introduction.- 2. Three Lanchester Combat Models.- 3. Conventional The Square Law.- 4. Guerrilla The Linear Law.- 5. The Parabolic Law.- 6. The Battle of Iwo Jima.- 7. Mathematical Models of The Dark Side of Modeling.- Exercises.- Project.- References.- Notes for the Instructor.- 9. Modeling Linear Systems by Frequency Response Methods.- 1. Introduction.- 2. Modeling the Human Operator.- 3. Properties and Techniques of Frequency Response Modeling.- 4. Project Human Operator Experimental Data.- 5. Further Topics.- References.- Notes for the Instructor.- IV. Traffic Models.- 10. How Long Should a Traffic Light Remain Amber?.- 1. The Problem and the Model.- 2. The Solution.- Exercises.- References.- Notes for the Instructor.- 11. Queue Length at a Traffic Light via Flow Theory.- 1. The A Simple Model.- 2. A Better Model.- Exercises.- References.- Notes for the Instructor.- 12. Car-Following Models.- 1. Introduction.- 2. Complexity of Actual Simplicity of Car-Following Models.- 3. Pipes' Model.- 4. Linear Car-Following with Delays.- 5. Incorporation of Pipes' Model into Linear Car-Following.- 6. Stability of Linear Car-Following Theory.- 7. Nonlinear Car-Following Laws.- 8. Steady-State Flow.- 9. Conclusion.- 10. Appendices.- Exercises.- References.- Notes for the Instructor.- 13. Equilibrium Speed Distributions.- 1. Speed Distributions.- 2. Overtaking.- 3. Passing.- 4. Equilibrium Distributions.- Exercises.- References.- Notes for the Instructor.- 14. Traffic Flow Theory.- 1. Basic Equations.- 2. Propagation of a Disturbance.- 3. Shocks.- Exercises.- References.- Notes for the Instructor.- V. Interacting Steady States of Nonlinear Systems.- 15. Why the Percentage of Sharks Caught in the Mediterranean Sea Rose Dramatically During World War I.- Exercises.- References.- Notes for the Instructor.- 16. Quadratic Population Almost Never Any Cycles.- 1. Quadratic Population Models.- 2. Equilibrium No Cycles.- 3. The D'Ancona-Volterra All Cycles.- 4. Stability.- 5. Which Model?.- Exercises.- References.- Notes for the Instructor.- 17. The Principle of Competitive Exclusion in Population Biology.- Exercises.- References.- Notes for the Instructor.- 18. Biological Cycles and the Fivefold Way.- 1. Prologue.- 2. The Canadian Lynx Cycle.- 3. The Canadian Lynx-Snowshoe Hare Cycle.- 4. A Two-Species Population Model.- 5. Differential Systems-Solutions, Orbits, Equilibria.- 6. The Fivefold Way.- 7. Predator-Prey Kolmogorov's Theorem.- 8. Do Hares Ea

404 pages, Paperback

First published January 11, 1983