Calculus of Variations II
By: by Mariano Giaquinta, Stefan Hildebrandt
Contributors: Hildebrandt, Stefan
Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics -- 311; Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics -- 311
Publisher: Springer Berlin Heidelberg
Published: 2004
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 652
ISBN-13: 9783642081927; 9783662062012
Subjects: Global differential geometry; Mathematics; Mathematical optimization
Description: 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.
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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.