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Differential Equations

Differential Equations
A Modeling Approach

July 2007 | 120 pages | SAGE Publications, Inc
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
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


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


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


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

Nonautonomous Differential Equations


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


8. Frontiers of Exploration
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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