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…mehr
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.
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.
Inhaltsangabe
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
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
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