A History of the Progress of the Calculus of Variations During the 19th Century (Dover Books on Mathematics)
Language: English
Published by Dover Publications, 2005
- Hardcover
- New
Seller: Newsboy Books, Ontario, CA, U.S.A.Newsboy Books
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- Title
- A History of the Progress of the Calculus of Variations During the 19th Century (Dover Books on Mathematics)
- Author
- Todhunter, I.; Mathematics
- Publisher
- Dover Publications
- Publication year
- 2005
- Condition
- New
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 0486442632
- ISBN 13
- 9780486442631
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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