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A Primer on the Calculus of Variations and Optimal Control Theory
Mike Mesterton-Gibbons, Florida State University, Tallahassee, FL
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Student Mathematical Library
2009; 252 pp; softcover
Volume: 50
ISBN-10: 0-8218-4772-4
ISBN-13: 978-0-8218-4772-5
List Price: US$45 Institutional Members: US$36
All Individuals: US\$36
Order Code: STML/50

An Introduction to Game-Theoretic Modelling: Second Edition - Mike Mesterton-Gibbons

Six Themes on Variation - Steven J Cox, Robin Forman, Frank Jones, Barbara Lee Keyfitz, Frank Morgan, Michael Wolf and Robert Hardt

Real Analysis and Applications: Including Fourier Series and the Calculus of Variations - Frank Morgan

Optimal Control of Partial Differential Equations: Theory, Methods and Applications - Fredi Troltzsch

The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations.

This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting.

The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical software. It is suitable for an undergraduate or beginning graduate course, or for self study. It provides excellent preparation for more advanced books and courses on the calculus of variations and optimal control theory.