A History of the Progress of the Calculus of Variations During the Nineteenth Century (Dover Phoenix Editions) - Hardcover

Todhunter, Isaac

Hardcover

ISBN 10: 0486442632 ISBN 13: 9780486442631

Verlag: Dover Publications Inc., 2005

Inhaltsangabe

Accurate and complete, this classic volume surveys a century of progress in the calculus of variations. In addition to introductions to a variety of treatises and memoirs, the author provides numerous remarks, criticisms, and corrections that clarify important developments in mathematical history.
Beginning with a brief account of works by Lagrange and Lacroix, the text proceeds to examinations of treatises by Dirksen and Ohm, a remarkable memoir by Gauss featuring the earliest discussion of a problem involving the variation of a double integral with variable limits of integration, and a memoir by Poisson on the calculus of variations that exhibits the variation of a double integral within variable limits of integration. Poisson's memoir inspired a work by Ostrogradsky, discussed here, which exhibits the variation of a multiple integral within variable limits of integration. This section on the variation of multiple integrals concludes with memoirs by Delaunay, Sarrus, and Cauchy.
The following chapters examine the criteria distinguishing a maximum from a minimum, including a remarkable memoir by Jacobi. Subsequent memoirs relate principally to geometry, differential equations, and mechanics, but all incorporate elements of the calculus of variations. The final chapter relates the history of the theory of the conditions of integrability.

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Reseña del editor

Accurate and complete, this classic volume surveys a century of progress in the calculus of variations. In addition to introductions to a variety of treatises and memoirs, the author provides numerous remarks, criticisms, and corrections that clarify important developments in mathematical history.
Beginning with a brief account of works by Lagrange and Lacroix, the text proceeds to examinations of treatises by Dirksen and Ohm, a remarkable memoir by Gauss featuring the earliest discussion of a problem involving the variation of a double integral with variable limits of integration, and a memoir by Poisson on the calculus of variations that exhibits the variation of a double integral within variable limits of integration. Poisson's memoir inspired a work by Ostrogradsky, discussed here, which exhibits the variation of a multiple integral within variable limits of integration. This section on the variation of multiple integrals concludes with memoirs by Delaunay, Sarrus, and Cauchy.
The following chapters examine the criteria distinguishing a maximum from a minimum, including a remarkable memoir by Jacobi. Subsequent memoirs relate principally to geometry, differential equations, and mechanics, but all incorporate elements of the calculus of variations. The final chapter relates the history of the theory of the conditions of integrability.

Reseña del editor

In 1810 a work was published inC ambridge under the following title AT reatise on I soperimetncal Problems and the Calculus of Variations. By Robert Woodhouse, A.M., F.R.S., Fellow of Caius College, Cambridge. This work details the history of the Calculus of Variations from its origin until the close of the eighteenth century, and has obtained a high reputation for accuracy and clearness. During the present century some of the most eminent mathematicians have endeavoured to enlarge the boundaries of the subject, and it seemed probable that a survey of what had been accomplished would not be destitute of interest and value. Accordingly the present work has been undertaken, and a short account will now be given of its plan.
(Typographical errors above are due to OCR software and don't occur in the book.)

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Details zur Ausgabe

• Verlag: Dover Publications Inc.
• Erscheinungsdatum: 2005
• Sprache: Englisch
• ISBN 10: 0486442632
• ISBN 13: 9780486442631
• Einband: Tapa dura
• Anzahl der Seiten: 534
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italien