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.
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.
Paulo B. Brito is a senior associate professor in Economics at the University of Lisbon (Portugal), Lisbon School of Economics and Management (ISEG). He was the inaugural editor-in-chief of the Portuguese Economic Journal from 2002 to 2015 and continues to contribute as a member of the Advisory Board since 2015. His current research focuses on the dynamics of income and wealth distribution in economics, growth economics and economic history.
