## A history of the calculus of variations from the 17th through the 19th century |

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### Contents

Fermat Newton Leibniz and | 1 |

Euler | 67 |

Lagrange and Legendre | 110 |

Copyright | |

5 other sections not shown

### Other editions - View all

A History of the Calculus of Variations from the 17th through the 19th Century H. H. Goldstine No preview available - 2011 |

### Common terms and phrases

analysis arbitrary constants assumes axis Bliss Bolza brachystochrone problem calculus of variations Caratheodory Clebsch coefficient concludes conjugate points considers const continuous continuous function curve 01 cycloid defined determinant discussion elegant end-conditions end-points envelope envelope theorem Euler Euler equation Euler-Lagrange equations evaluated expression extremum family of extremals Fermat Figure finds fixed follows frustum function geodesics given curve Hamilton-Jacobi Hamilton-Jacobi theory hence Hilbert implies integral integrand interval isoperimetric problem Jacobi James Bernoulli John Bernoulli Kneser Lagrange Lagrange's Legendre Leibniz maximum or minimum Mayer minimizing arc necessary condition Newton notation notes paper parameter partial derivatives partial differential equation point conjugate proceeds proof quantities relation remarks resistance result right-hand member satisfy says second variation Section side-conditions solution solve Suppose surface tangent theorem transversal vanish variable velocity Weierstrass writes