Chapter 4. The Calculus of Variations
Published Online: 24 DEC 2007
DOI: 10.1002/9783527617210.ch4
Copyright © 2004 WILEY-VCH Verlag GmbH & Co. KGaA
Book Title
Methods of Mathematical Physics, Volume I
Additional Information
How to Cite
Courant, R. and Hilbert, D. (2007) The Calculus of Variations, in Methods of Mathematical Physics, Volume I, Wiley-VCH Verlag GmbH, Weinheim, Germany. doi: 10.1002/9783527617210.ch4
Publication History
- Published Online: 24 DEC 2007
- Published Print: 19 APR 1989
ISBN Information
Print ISBN: 9780471504474
Online ISBN: 9783527617210
- Summary
- Chapter
- References
Keywords:
- analysis;
- reflection;
- extremum;
- argument;
- quantity;
- brachistochrone
Summary
This chapter contains sections titled:
Problems of the calculus of variations
Direct solutions
The Euler equations
Integration of the Euler differencial equation
Boundary conditions
The second variation and the Legendre condition
Variational problems with subsidiary conditions
Invariant character of the Euler equations
Transformation of variational problems to canonical and involutory form
Variational calculus and the differential equations of mathematical physics
Reciprocal quadratic variational problems
Supplementary remarks and exercises