経済動態と配分：微分方程式、最適制御と応用 Economic Dynamics and Distributions : Differential Equations, Optimal Control and Applications

著者名：Brito, Paulo B.

Springer（2026/04/08発売）

• 言語：ENG
• ISBN：9783031947162
• eISBN：9783031947179

Description

This textbook introduces readers to the economic dynamics of growth and distribution and presents dynamic mathematical tools essential to understanding various economic phenomena. From ordinary differential equations to partial differential equations and stochastic differential equations, it guides readers through the mathematical landscape. Optimization problems are also highlighted, from maximizing static functionals to optimal control problems involving systems governed by the previously mentioned types of differential equation. The applications of these formal structures cover various areas of economics, including macroeconomics, growth theory, microeconomics, spatial economics, finance, income and wealth distribution, and social mobility.

Written primarily for Master’s and Ph.D. students, the book also offers a comprehensive reference guide for economists and applied mathematicians alike.

Table of Contents

Chapter 1. Introduction and overview.- Part I. Ordinary differential equations.- Chapter 2. Scalar linear ODE.- Chapter 3. Scalar non-linear ODE: the regular case.- Chapter 4. Planar linear ODE.- Chapter 5. Planar non-linear ODE: the regular case.- Chapter 6. Piecewise smooth or continuous ODE.- Chapter 7. Singular ODE.- Part II. Functional calculus and calculus of variations.- Chapter 8. Introduction to functional calculus.- Chapter 9. Introduction to calculus of variations.- Chapter 10. Introduction to optimal control: the maximum principle approach.- Chapter 11. Introduction to the dynamic programming principle.- Chapter 12. Optimal control of ODE: extensions.- Part III. Partial differential equations.- Chapter 13. First-order PDE.- Chapter 14. Optimal control of first order PDE.- Chapter 15. Scalar parabolic partial differential equations.- Chapter 16. Optimal control of parabolic partial differential equations.- Part IV. Stochastic differential equations.- Chapter 17. Introduction to stochastic calculus and stochastic differential equations.- Chapter 18. Scalar linear stochastic differential equations.- Chapter 19. Stochastic optimal control.