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＜電子ブック＞
Calculus of Variations II / by Mariano Giaquinta, Stefan Hildebrandt
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 311)

版	1st ed. 2004.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2004
本文言語	英語
大きさ	XXIX, 655 p : online resource
著者標目	*Giaquinta, Mariano author Hildebrandt, Stefan author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Geometry, Differential LCSH:Mathematical physics FREE:Calculus of Variations and Optimization FREE:Differential Geometry FREE:Theoretical, Mathematical and Computational Physics
一般注記	CALCULUS OF VARIATIONS I - The Lagrangian Formalism: Part I: The First Variation and Necessary Conditions: The First Variation; Variational Problems with Subsidiary Conditions; General Variational Formulas -- Part II: The Second Variation and Sufficient Conditions; Second Variation, Excess Function, Convexity; Weak Minimizers and Jacobi Theory; Weierstrass Field Theory for One-dimensional Integrals and Strong Minimizers. CALCULUS OF VARIATIONS II - The Hamiltonian Formalism: Part III: Canonical Formalism and Hamilton-Jacobi Theory; Legendre Transformation, Hamiltonian Systems, Convexity, Field Theories; Parametric Variational Integrals -- Part IV: Hamilton-Jacobi Theory and Canonical Transformations: Hamilton-Jacobi Theory and Canonical Transformations; Partial Differential Equations of First Order and Contact Transformations This long-awaited book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins, partly in applications, e.g. from geometrical optics, of parts of the theory. A variety of aids to the reader are provided: besides the very detailed table of contents, an introduction to each chapter, section and subsection, an overview of the relevant literature (in Vol. 2) plus the references in the Scholia to each chapter, in the (historical) footnotes, and in the bibliography, and finally an index of the examples used throughout the book. Both individually and collectively these volumes have already become standard references HTTP:URL=https://doi.org/10.1007/978-3-662-06201-2

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