Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics.

Contents:

• Dimension One:
• Scalar Linear Differential Equations
• Scalar Nonlinear Differential Equations
• Economic Dynamics with Scalar Differential Equations
• Dimension Two:
• Planar Linear Differential Equations
• Planar Nonlinear Differential Equations
• Planar Dynamical Economical Systems
• Higher Dimensions:
• Higher-Dimensional Differential Equations
• Higher-Dimensional Nonlinear Differential Equations
• Higher-Dimensional Economic Evolution
• Epilogue: Economic Evolution with Changeable Speeds and Structures

“This book is clearly designed on the basis of an interesting intellectual project: to teach differential equations, bifurcations and chaos with special attention to their applications in economics.”

“This book provides a comprehensive introduction to most important concepts and theorems in differential equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra.”