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AuthorGiaquinta, Mariano. author
TitleCalculus of Variations I [electronic resource] / by Mariano Giaquinta, Stefan Hildebrandt
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004
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Descript XXIX, 474 p. online resource


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


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

Mathematics Differential geometry Calculus of variations Physics Mathematics Calculus of Variations and Optimal Control; Optimization Differential Geometry Theoretical Mathematical and Computational Physics


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