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Optimal Control Theory with Applications in Economics$
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Thomas A. Weber

Print publication date: 2011

Print ISBN-13: 9780262015738

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262015738.001.0001

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Ordinary Differential Equations

Ordinary Differential Equations

(p.16) (p.17) 2 Ordinary Differential Equations
Optimal Control Theory with Applications in Economics

Thomas A. Weber

The MIT Press

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.

Keywords:   first-order ordinary differential equations, higher-order ODEs, time derivatives, Laplace transform

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