*Thomas A. Weber*

- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015738
- eISBN:
- 9780262298483
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015738.003.0002
- Subject:
- Mathematics, Probability / Statistics

This chapter reviews basic concepts in the theory of ordinary differential equation (ODEs). It first discusses how to analyze first-order ODEs. It then extends the framework for the analysis of ...
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This chapter reviews basic concepts in the theory of ordinary differential equation (ODEs). It first discusses how to analyze first-order ODEs. It then extends the framework for the analysis of first-order ODEs to differential equations with higher-order time-derivatives by reducing the latter to systems of the former. It also discusses a few more sophisticated solution techniques for systems of ODEs, such as the Laplace transform.Less

This chapter reviews basic concepts in the theory of ordinary differential equation (ODEs). It first discusses how to analyze first-order ODEs. It then extends the framework for the analysis of first-order ODEs to differential equations with higher-order time-derivatives by reducing the latter to systems of the former. It also discusses a few more sophisticated solution techniques for systems of ODEs, such as the Laplace transform.

*Thomas A. Weber*

- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015738
- eISBN:
- 9780262298483
- Item type:
- book

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015738.001.0001
- Subject:
- Mathematics, Probability / Statistics

This book bridges optimal control theory and economics, discussing ordinary differential equations (ODEs), optimal control, game theory, and mechanism design in one volume. Technically rigorous and ...
More

This book bridges optimal control theory and economics, discussing ordinary differential equations (ODEs), optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations is the backbone of the theory developed in the book, and Chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendices provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer’s creation of an environment in which players interact to maximize the designer’s objective. The book focuses on applications; the problems are an integral part of the text.Less

This book bridges optimal control theory and economics, discussing ordinary differential equations (ODEs), optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations is the backbone of the theory developed in the book, and Chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendices provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer’s creation of an environment in which players interact to maximize the designer’s objective. The book focuses on applications; the problems are an integral part of the text.