Calculus of variations and partial differential equations of the first order

著者

書誌事項

Calculus of variations and partial differential equations of the first order

C. Carathéodory ; translated by Robert B. Dean ; Julius J. Brandstatter, translating editor

AMS Chelsea Pub., c1989

3rd ed

タイトル別名

Variationsrechnung und partielle Differentialgleichungen erster Ordnung

Calculus of variations

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注記

"Originally published as Variationsrechnung und partielle Differentialgleichungen erster Ordnung, by B.G.Teubner, Berlin, 1935"--t.p.verso

Bibliography: p. 381-395

Includes index

内容説明・目次

内容説明

In this second English edition of Caratheodory's famous work (originally published in German), the two volumes of the first edition have been combined into one (with a combination of the two indexes into a single index). There is a deep and fundamental relationship between the differential equations that occur in the Calculus of Variations and partial differential equations of the first order: in particular, to each such partial differential equation there correspond variational problems. This basic fact forms the rationale for Caratheodory's masterpiece. Includes a Guide to the Literature and an Index.

目次

Continuous convergence, implicit functions, ordinary differential equations Fields of curves and multidimensional surfaces, complete systems Partial differential equations of the first order, theory of characteristics Poisson brackets, systems of partial differential equations of the first order Elements of tensor calculus Canonical transformations Contact transformations The Pfaff problem Function groups The integration theories of Lagrange, Jacobi, Adolph Mayer and Lie Ordinary maxima and minima. Quadratic forms Simple variational problems in the small Variational problems in parametric representation Positive-definite variational problems Quadratic variational problems. Theory of the second variation The boundary-value problem and the question of the absolute minimum Closed extremals. Periodic variational problems The problem of Lagrange Guide to the literature Index.

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