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Variational Calculus and Optimal Control - John L. Troutman
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ISBN: 9780387945118

ID: 736787888

Although the calculus of variations has ancient origins in questions of Ar­ istotle and Zenodoros, its mathematical principles first emerged in the post­ calculus investigations of Newton, the Bernoullis, Euler, and Lagrange. Its results now supply fundamental tools of exploration to both mathematicians and those in the applied sciences. (Indeed, the macroscopic statements ob­ tained through variational principles may provide the only valid mathemati­ cal formulations of many physical laws. ) Because of its classical origins, variational calculus retains the spirit of natural philosophy common to most mathematical investigations prior to this century. The original applications, including the Bernoulli problem of finding the brachistochrone, require opti­ mizing (maximizing or minimizing) the mass, force, time, or energy of some physical system under various constraints. The solutions to these problems satisfy related differential equations discovered by Euler and Lagrange, and the variational principles of mechanics (especially that of Hamilton from the last century) show the importance of also considering solutions that just provide stationary behavior for some measure of performance of the system. However, many recent applications do involve optimization, in particular, those concerned with problems in optimal control. Optimal control is the rapidly expanding field developed during the last half-century to analyze optimal behavior of a constrained process that evolves in time according to prescribed laws. Its applications now embrace a variety of new disciplines, including economics and production planning. Optimization with Elementary Convexity Bücher > Fremdsprachige Bücher > Englische Bücher gebundene Ausgabe 01.12.1995 Buch (fremdspr.), Springer, .199

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Optimization with Elementary Convexity Although the calculus of variations has ancient origins in questions of Ar­ istotle and Zenodoros, its mathematical principles first emerged in the post­ calculus investigations of Newton, the Bernoullis, Euler, and Lagrange. Its results now supply fundamental tools of exploration to both mathematicians and those in the applied sciences. (Indeed, the macroscopic statements ob­ tained through variational principles may provide the only valid mathemati­ cal formulations of many physical laws. ) Because of its classical origins, variational calculus retains the spirit of natural philosophy common to most mathematical investigations prior to this century. The original applications, including the Bernoulli problem of finding the brachistochrone, require opti­ mizing (maximizing or minimizing) the mass, force, time, or energy of some physical system under various constraints. The solutions to these problems satisfy related differential equations discovered by Euler and Lagrange, and the variational principles of mechanics (especially that of Hamilton from the last century) show the importance of also considering solutions that just provide stationary behavior for some measure of performance of the system. However, many recent applications do involve optimization, in particular, those concerned with problems in optimal control. Optimal control is the rapidly expanding field developed during the last half-century to analyze optimal behavior of a constrained process that evolves in time according to prescribed laws. Its applications now embrace a variety of new disciplines, including economics and production planning. Bücher / Fremdsprachige Bücher / Englische Bücher 978-0-387-94511-8, Springer

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Variational Calculus and Optimal Control - John L. Troutman
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John L. Troutman:
Variational Calculus and Optimal Control - neues Buch

ISBN: 9780387945118

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Although the calculus of variations has ancient origins in questions of Ar­ istotle and Zenodoros, its mathematical principles first emerged in the post­ calculus investigations of Newton, the Bernoullis, Euler, and Lagrange. Its results now supply fundamental tools of exploration to both mathematicians and those in the applied sciences. (Indeed, the macroscopic statements ob­ tained through variational principles may provide the only valid mathemati­ cal formulations of many physical laws. ) Because of its classical origins, variational calculus retains the spirit of natural philosophy common to most mathematical investigations prior to this century. The original applications, including the Bernoulli problem of finding the brachistochrone, require opti­ mizing (maximizing or minimizing) the mass, force, time, or energy of some physical system under various constraints. The solutions to these problems satisfy related differential equations discovered by Euler and Lagrange, and the variational principles of mechanics (especially that of Hamilton from the last century) show the importance of also considering solutions that just provide stationary behavior for some measure of performance of the system. However, many recent applications do involve optimization, in particular, those concerned with problems in optimal control. Optimal control is the rapidly expanding field developed during the last half-century to analyze optimal behavior of a constrained process that evolves in time according to prescribed laws. Its applications now embrace a variety of new disciplines, including economics and production planning. Optimization with Elementary Convexity Buch (fremdspr.) Bücher>Fremdsprachige Bücher>Englische Bücher, Springer

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Springer. Hardcover. New. Hardcover. 462 pages. Dimensions: 9.2in. x 6.2in. x 1.3in.An introduction to the variational methods used to formulate and solve mathematical and physical problems, allowing the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency, laying as it does the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, as well as computer science. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN., Springer

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Variational Calculus and Optimal Control
Autor:

Troutman, John L.

Titel:

Variational Calculus and Optimal Control

ISBN-Nummer:

0387945113

An introduction to the variational methods used to formulate and solve mathematical and physical problems, allowing the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency, laying as it does the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, as well as computer science.

Detailangaben zum Buch - Variational Calculus and Optimal Control


EAN (ISBN-13): 9780387945118
ISBN (ISBN-10): 0387945113
Gebundene Ausgabe
Erscheinungsjahr: 2007
Herausgeber: Springer-Verlag GmbH
482 Seiten
Gewicht: 0,906 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 12.06.2007 10:39:47
Buch zuletzt gefunden am 27.01.2017 12:26:50
ISBN/EAN: 0387945113

ISBN - alternative Schreibweisen:
0-387-94511-3, 978-0-387-94511-8

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