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.

"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

• Series Editor′s IntroductionAcknowledgments1. Dynamic Models and Social ChangeTheoretical Reasons for Using Differential Equations in the Social SciencesAn ExampleThe Use of Differential Equations in the Natural and Physical SciencesDeterministic Versus Probabilistic Differential Equation ModelsWhat Is a Differential Equation?What This Book Is and Is Not2. First-Order Differential EquationsAnalytical Solutions to Linear First-Order Differential EquationsSolving First-Order Differential Equations Using Separation of VariablesAn Example From SociologyNumerical Methods Used to Solve Differential EquationsSummaryChapter 2 Appendix3. Systems of First-Order Differential EquationsThe Predator-Prey ModelThe Phase DiagramVector Field and Direction Field DiagramsThe Equilibrium Marsh and Flow DiagramsSummaryChapter 3 Appendix4. Some Classic Social Science Examples of First-Order SystemsRichardson′s Arms Race ModelLanchester′s Combat ModelRapoport′s Production and Exchange ModelSummary5. Transforming Second-Order and Nonautonomous Differential Equations Into Systems of First-Order Differential EquationsSecond- and Higher-Order Differential EquationsNonautonomous Differential EquationsSummary6. Stability Analyses of Linear Differential Equation SystemsA Motivating Example of How Stability Can Dramatically Change in One SystemScalar MethodsMatrix MethodsEquilibrium CategoriesSummarizing the Stability Criteria7. Stability Analyses of Nonlinear Differential Equation SystemsThe JacobianSummary8. Frontiers of ExplorationReferencesIndexAbout the Author

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.

"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

• Series Editor′s IntroductionAcknowledgments1. Dynamic Models and Social ChangeTheoretical Reasons for Using Differential Equations in the Social SciencesAn ExampleThe Use of Differential Equations in the Natural and Physical SciencesDeterministic Versus Probabilistic Differential Equation ModelsWhat Is a Differential Equation?What This Book Is and Is Not2. First-Order Differential EquationsAnalytical Solutions to Linear First-Order Differential EquationsSolving First-Order Differential Equations Using Separation of VariablesAn Example From SociologyNumerical Methods Used to Solve Differential EquationsSummaryChapter 2 Appendix3. Systems of First-Order Differential EquationsThe Predator-Prey ModelThe Phase DiagramVector Field and Direction Field DiagramsThe Equilibrium Marsh and Flow DiagramsSummaryChapter 3 Appendix4. Some Classic Social Science Examples of First-Order SystemsRichardson′s Arms Race ModelLanchester′s Combat ModelRapoport′s Production and Exchange ModelSummary5. Transforming Second-Order and Nonautonomous Differential Equations Into Systems of First-Order Differential EquationsSecond- and Higher-Order Differential EquationsNonautonomous Differential EquationsSummary6. Stability Analyses of Linear Differential Equation SystemsA Motivating Example of How Stability Can Dramatically Change in One SystemScalar MethodsMatrix MethodsEquilibrium CategoriesSummarizing the Stability Criteria7. Stability Analyses of Nonlinear Differential Equation SystemsThe JacobianSummary8. Frontiers of ExplorationReferencesIndexAbout the Author

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.

"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

• Series Editor′s IntroductionAcknowledgments1. Dynamic Models and Social ChangeTheoretical Reasons for Using Differential Equations in the Social SciencesAn ExampleThe Use of Differential Equations in the Natural and Physical SciencesDeterministic Versus Probabilistic Differential Equation ModelsWhat Is a Differential Equation?What This Book Is and Is Not2. First-Order Differential EquationsAnalytical Solutions to Linear First-Order Differential EquationsSolving First-Order Differential Equations Using Separation of VariablesAn Example From SociologyNumerical Methods Used to Solve Differential EquationsSummaryChapter 2 Appendix3. Systems of First-Order Differential EquationsThe Predator-Prey ModelThe Phase DiagramVector Field and Direction Field DiagramsThe Equilibrium Marsh and Flow DiagramsSummaryChapter 3 Appendix4. Some Classic Social Science Examples of First-Order SystemsRichardson′s Arms Race ModelLanchester′s Combat ModelRapoport′s Production and Exchange ModelSummary5. Transforming Second-Order and Nonautonomous Differential Equations Into Systems of First-Order Differential EquationsSecond- and Higher-Order Differential EquationsNonautonomous Differential EquationsSummary6. Stability Analyses of Linear Differential Equation SystemsA Motivating Example of How Stability Can Dramatically Change in One SystemScalar MethodsMatrix MethodsEquilibrium CategoriesSummarizing the Stability Criteria7. Stability Analyses of Nonlinear Differential Equation SystemsThe JacobianSummary8. Frontiers of ExplorationReferencesIndexAbout the Author