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Differential Equations: A Modeling Approach de Courtney M. Brown

Differential Equations: A Modeling Approach: Quantitative Applications in the Social Sciences, cartea 150

Autor Courtney M. Brown
en Limba Engleză Paperback – 9 iul 2007
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.
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Specificații

ISBN-13: 9781412941082
ISBN-10: 1412941083
Pagini: 120
Dimensiuni: 140 x 216 x 7 mm
Greutate: 0.14 kg
Ediția:1
Editura: SAGE Publications
Colecția Sage Publications, Inc
Seria Quantitative Applications in the Social Sciences

Locul publicării:Thousand Oaks, United States

Recenzii

"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

Cuprins

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

Notă biografică

Courtney Brown is an Associate Professor in the Department of Political Science at Emory University. Dr. Brown has taught differential equation modeling to graduate and undergraduate students for over 20 years. His teaching and research interests also include other quantitative methods, political musicology, science fiction and politics, electoral behavior, political parties, democratic development, and politics and the environment. He has authored five books that deal with differential equation models in the social sciences, including three titles for the Quantitative Applications in the Social Sciences series.