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Mathematics | Calculus of Variations I

Calculus of Variations I

Giaquinta, Mariano, Hildebrandt, Stefan

1996, XXIX, 474 p.

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  • About this book

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.

Content Level » Research

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

Related subjects » Geometry & Topology - Mathematics - Theoretical, Mathematical & Computational Physics

Table of contents 

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.

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