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＜電子ブック＞
Calculus of Variations I / by Mariano Giaquinta, Stefan Hildebrandt
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 310)

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, 474 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	of Calculus of Variations I -- 1. The First Variation -- 2. Variational Problems with Subsidiary Conditions -- 3. General Variational Formulas -- 4. Second Variation, Excess Function, Convexity -- 5. Weak Minimizers and Jacobi Theory -- 6. Weierstrass Field Theory for One-Dimensional Integrals and Strong Minimizers -- Supplement. Some Facts from Differential Geometry and Analysis -- 1. Euclidean Spaces -- 2. Some Function Classes -- 3. Vector and Covector Fields. Transformation Rules -- 4. Differential Forms -- 6. Mean Curvature and Gauss Curvature 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 HTTP:URL=https://doi.org/10.1007/978-3-662-03278-7

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