A History of the Progress of the Calculus of Variations During the 19th Century (Dover Phoenix Editions)

I. Todhunter

ISBN 10: 0486442632 / ISBN 13: 9780486442631

Editore: Dover Publications, 2005

Riguardo questo articolo

2005. Hardcover. Library binding. No dj. Very little shelf-wear. Very Good.

Codice articolo SON000001259

Dati bibliografici

• Titolo: A History of the Progress of the Calculus of Variations During the 19th Century (Dover Phoenix Editions)
• Editore: Dover Publications
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 0486442632
• ISBN 13: 9780486442631
• Rilegatura: Rilegato
• Condizione: Used - Very Good
• Cataloghi dei venditori:
  • Mathematics

Descrizione articolo

Riassunto

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.

Product Description

Book by Todhunter I Mathematics