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This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems-such as those of geometric optics-of parts of the theory. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.
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This 2-volume treatise by two of the leading researchers and writers in the field, quickly established itself as a standard reference. It pays special attention to the historical aspects and the origins partly in applied problems - such as those of geometric optics - of parts of the theory. A variety of aids to the reader are provided, beginning with the detailed table of contents, and including an introduction to each chapter and each section and subsection, an overview of the relevant literature (in Volume II) besides the references in the Scholia to each chapter in the (historical) footnotes, and in the bibliography, and finally an index of the examples used through out the book.
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This is the first part of a treatise covering calculus of variations in breadth and depth, paying special attention to the historical origins, partly in applications, for example from geometrical optics, of parts of the theory. A variety of aids to the reader are provided, including an introduction to each chapter, section and subsection and historical footnotes. Later volumes deal with direct methods and regularity theory.
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- PublisherSpringer
- Publication date1995
- ISBN 10 354050625X
- ISBN 13 9783540506256
- BindingHardcover
- Edition number1
- Number of pages503
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Calculus of Variations I
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Calculus of Variations I. The Langrangian Formalism
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Calculus of Variations I
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Book Description Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as well as Hamilton Jacobi theory and the classical theory of partial differential equations of first ordel; In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus we have particularly emphasized the often neglected theory of inner variations, i. e. of variations of the independent variables, which is a source of useful information such as mono tonicity for mulas, conformality relations and conservation laws. The combined variation of dependent and independent variables leads to the general conservation laws of Emmy Noether, an important tool in exploiting symmetries. Other parts of this volume deal with Legendre-Jacobi theory and with field theories. In particular we give a detailed presentation of one-dimensional field theory for nonpara metric and parametric integrals and its relations to Hamilton-Jacobi theory, geometrical optics and point mechanics. Moreover we discuss various ways of exploiting the notion of convexity in the calculus of variations, and field theory is certainly the most subtle method to make use of convexity. We also stress the usefulness of the concept of a null Lagrangian which plays an important role in we give an exposition of Hamilton-Jacobi several instances. 508 pp. Englisch. Seller Inventory # 9783540506256
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Calculus of Variations I
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Book Description Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as well as Hamilton Jacobi theory and the classical theory of partial differential equations of first ordel; In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus we have particularly emphasized the often neglected theory of inner variations, i. e. of variations of the independent variables, which is a source of useful information such as mono tonicity for mulas, conformality relations and conservation laws. The combined variation of dependent and independent variables leads to the general conservation laws of Emmy Noether, an important tool in exploiting symmetries. Other parts of this volume deal with Legendre-Jacobi theory and with field theories. In particular we give a detailed presentation of one-dimensional field theory for nonpara metric and parametric integrals and its relations to Hamilton-Jacobi theory, geometrical optics and point mechanics. Moreover we discuss various ways of exploiting the notion of convexity in the calculus of variations, and field theory is certainly the most subtle method to make use of convexity. We also stress the usefulness of the concept of a null Lagrangian which plays an important role in we give an exposition of Hamilton-Jacobi several instances. Seller Inventory # 9783540506256
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Calculus of Variations I (Grundlehren der mathematischen Wissenschaften, 310)
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