Variational Calculus Optimal Control by Troutman John (40 results)

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Paperback. Condition: new. Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Hardcover. Condition: new. Hardcover. The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.

Buch. Condition: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 482 pp. Englisch.

Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.

Paperback. Condition: new. Paperback. 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. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Hardcover. Condition: new. Hardcover. The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Originalpappband. 25cm. Condition: Wie neu. SECOND edition. XV,461 pages, Index. In EXCELLENT shape. - ( We offer a lot of books on PHYSICS and MATHEMATICS on stock in EXCELLENT shape). Contents: Basic Theory Standard Optimization Problems Linear Spaces and Gateaux Variations Minimization of Convex Functions The Lemmas of Lagrange and Du Bois-Reymond Local Extrema in Normed Linear Spaces The Euler-Lagrange Equations Advanced Topics Piecewise C-hoch1 - Extremal Functions Variational Principles in Mechanics Sufficient Conditions for a Minimum Sprache: Englisch Gewicht in Gramm: 1100.

Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 484 pp. Englisch.