The calculus of variations

Bruce van Brunt - Collection Universitext

304 pages, parution le 13/11/2003

Ajouter à une liste

Indisponible

Résumé

The calculus of variations has a long history of interaction with other branches of mathematics, such as geometry and differential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations.This book is an introductory account of the calculus of variations suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering. The mathematical background assumed of the reader is a course in multivariable calculus, and some familiarity with the elements of real analysis and ordinary differential equations.

The book focuses on variational problems that involve one independent variable. The fixed endpoint problem and problems with constraints are discussed in detail. In addition, more advanced topics such as the inverse problem, eigenvalue problems, separability conditions for the Hamilton-Jacobi equation, and Noether's theorem are discussed. The text contains numerous examples to illustrate key concepts along with problems to help the student consolidate the material. The book can be used as a textbook for a one semester course on the calculus of variations, or as a book to supplement a course on applied mathematics or classical mechanics.

Bruce van Brunt is Senior Lecturer at Massey University, New Zealand. He is the author of The Lebesgue-Stieltjes Integral, with Michael Carter, and has been teaching the calculus of variations to undergraduate and graduate students for several years.

Introduction
The First Variation
Some Generalizations
Isoperimetric Problems
Applications to Eigenvalue Problems
Holonomic and Nonholonomic Constraints
Problems with Variable Endpoints
The Hamiltonian Formulation
Noether's Theorem
The Second Variation
Appendix A: Some Results from Analysis and Differential Equations
Appendix B: Function Spaces
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Bruce van Brunt
Collection	Universitext
Parution	13/11/2003
Nb. de pages	304
Format	16 x 24
Couverture	Relié
Poids	555g
Intérieur	Noir et Blanc
EAN13	9780387402475
ISBN13	978-0-387-40247-5