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The Calculus of Variations: An Introduction

  • Rodney Coleman
Chapter
Part of the Universitext book series (UTX)

Abstract

If \(\mathcal{E}\) is a normed vector space composed of mappings, for example, the space of continuous real-valued functions defined on a compact interval, then we refer to a real-valued mapping F defined on a subset S of \(\mathcal{E}\) as a functional. The calculus of variations is concerned with the search for extrema of functionals. In general, the set S is determined, at least partially, by constraints on the mappings and the functional F is defined by an integral. The elements of S are often said to be F-admissible(or admissible if there is no possible confusion).

References

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    Troutman, J. L.: Variational Calculus and Optimal Control, 2nd edn. Springer-Verlag, Berlin (1996)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Rodney Coleman
    • 1
  1. 1.Laboratoire Jean KuntzmannGrenobleFrance

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