Calculus of Variations I
By: by Mariano Giaquinta, Stefan Hildebrandt
Contributors: Hildebrandt, Stefan
Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics -- 310; Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics -- 310
Publisher: Springer Berlin Heidelberg
Published: 2004
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 474
ISBN-13: 9783642080746; 9783662032787
Subjects: Global differential geometry; Mathematics; Mathematical optimization
Description: 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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Table of contents: title: 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; title: 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; title: Part IV: Hamilton-Jacobi Theory and Canonical Transformations: Hamilton-Jacobi Theory and Canonical Transformations; Partial Differential Equations of First Order and Contact Transformations.