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Differential Equations
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Differential Equations
A Modeling Approach

Volume: 150
July 2007 | 120 pages | SAGE Publications, Inc
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Differential Equations: A Modeling Approach introduces differential equations and differential equation modeling to students and researchers in the social sciences.

Key Features:

- The text is accessibly written, so that students with minimal mathematical training can understand all of the basic concepts and techniques presented.

- The author uses social sciences examples to illustrate the relevance of differential equation modeling to readers.

- Readers can use graphical methods to produce penetrating analysis of differential equation systems.

- Linear and nonlinear model specifications are explained from a social science perspective. Most interesting differential equation models are nonlinear, and readers need to know how to specify and work with such models in the social sciences.

 
Series Editor's Introduction
 
Acknowledgments
 
1. Dynamic Models and Social Change
Theoretical Reasons for Using Differential Equations in the Social Sciences

 
An Example

 
The Use of Differential Equations in the Natural and Physical Sciences

 
Deterministic Versus Probabilistic Differential Equation Models

 
What Is a Differential Equation?

 
What This Book Is and Is Not

 
 
2. First-Order Differential Equations
Analytical Solutions to Linear First-Order Differential Equations

 
Solving First-Order Differential Equations Using Separation of Variables

 
An Example From Sociology

 
Numerical Methods Used to Solve Differential Equations

 
Summary

 
Chapter 2 Appendix

 
 
3. Systems of First-Order Differential Equations
The Predator-Prey Model

 
The Phase Diagram

 
Vector Field and Direction Field Diagrams

 
The Equilibrium Marsh and Flow Diagrams

 
Summary

 
Chapter 3 Appendix

 
 
4. Some Classic Social Science Examples of First-Order Systems
Richardson's Arms Race Model

 
Lanchester's Combat Model

 
Rapoport's Production and Exchange Model

 
Summary

 
 
5. Transforming Second-Order and Nonautonomous Differential Equations Into Systems of First-Order Differential Equations
Second- and Higher-Order Differential Equations

 
Nonautonomous Differential Equations

 
Summary

 
 
6. Stability Analyses of Linear Differential Equation Systems
A Motivating Example of How Stability Can Dramatically Change in One System

 
Scalar Methods

 
Matrix Methods

 
Equilibrium Categories

 
Summarizing the Stability Criteria

 
 
7. Stability Analyses of Nonlinear Differential Equation Systems
The Jacobian

 
Summary

 
 
8. Frontiers of Exploration
 
References
 
Index
 
About the Author

"A reader with a strong background in mathematics, at least two semesters of calculus, and interest in the social sciences will find the book helpful in learning how this area of mathematics can be used in different applications."

—S.L. Sullivan, Catawba College

S.L. Sullivan
Catawba College
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