Calculus of Variations I

  • Mariano Giaquinta
  • Stefan Hildebrandt

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 310)

Table of contents

  1. Front Matter
    Pages I-XXIX
  2. The First Variation and Necessary Conditions

    1. Front Matter
      Pages 1-1
    2. Mariano Giaquinta, Stefan Hildebrandt
      Pages 3-86
    3. Mariano Giaquinta, Stefan Hildebrandt
      Pages 87-144
    4. Mariano Giaquinta, Stefan Hildebrandt
      Pages 145-214
  3. The Second Variation and Sufficient Conditions

    1. Front Matter
      Pages 215-215
    2. Mariano Giaquinta, Stefan Hildebrandt
      Pages 217-263
    3. Mariano Giaquinta, Stefan Hildebrandt
      Pages 264-309
    4. Mariano Giaquinta, Stefan Hildebrandt
      Pages 310-399
  4. Back Matter
    Pages 400-474

About this book

Introduction

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.

Keywords

Calculus of Variations Convexity Gaussian curvature Hamiltonian Formalism Lagrangian Formalism Mean curvature Vector field calculus curvature differential equation differential geometry

Authors and affiliations

  • Mariano Giaquinta
    • 1
  • Stefan Hildebrandt
    • 2
  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Mathematisches InstitutUniversität BonnBonnGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03278-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08074-6
  • Online ISBN 978-3-662-03278-7
  • Series Print ISSN 0072-7830
  • About this book