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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

Chapter:
(p.16) (p.17) 2 Ordinary Differential Equations
Source:
Optimal Control Theory with Applications in Economics
Author(s):

Thomas A. Weber

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262015738.003.0002

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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