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Mathematical Concepts and Methods in Science and Engineering

The Calculus of Variations and Optimal Control

An Introduction

Authors: Leitmann, George

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About this book

When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching the rope into the shape of a circular arc and thereby maximized the area of the land upon which she was to found Carthage. This story of the founding of Carthage is apocryphal. Nonetheless it is probably the first account of a problem of the kind that inspired an entire mathematical discipline, the calculus of variations and its extensions such as the theory of optimal control. This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. The discussion in Part I is restricted to the simplest problem of the calculus of variations. The topic is entirely classical; all of the basic theory had been developed before the turn of the century. Consequently the material comes from many sources; however, those most useful to me have been the books of Oskar Bolza and of George M. Ewing. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

Table of contents (17 chapters)

Table of contents (17 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-4899-0333-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-0-306-40707-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.99
price for USA in USD
  • ISBN 978-1-4899-0335-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Calculus of Variations and Optimal Control
Book Subtitle
An Introduction
Authors
Series Title
Mathematical Concepts and Methods in Science and Engineering
Series Volume
24
Copyright
1981
Publisher
Springer US
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4899-0333-4
DOI
10.1007/978-1-4899-0333-4
Hardcover ISBN
978-0-306-40707-9
Softcover ISBN
978-1-4899-0335-8
Edition Number
1
Number of Pages
XVI, 312
Topics