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Lectures On The Calculus Of Variations(1st Edition)

Authors:

Oskar Bolza

lectures on the calculus of variations 1st edition oskar bolza 0486822362, 978-0486822365

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ISBN: 0486822362, 978-0486822365

Book publisher: Dover Publications

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Lectures On The Calculus Of Variations 1st Edition Summary: This pioneering modern treatise on the calculus of variations studies the evolution of the subject from Euler to Hilbert. The text addresses basic problems with sufficient generality and rigor to offer a sound introduction for serious study. It provides clear definitions of the fundamental concepts, sharp formulations of the problems, and rigorous demonstrations of their solutions. Many examples are solved completely, and systematic references are given for each theorem upon its first appearance. Initial chapters address the first and second variation of the integral, and succeeding chapters cover the sufficient conditions for an extremum of the integral and Weierstrass's theory of the problem in parameter-representation; Kneser's extension of Weierstrass's theory to cover the case of variable end-points; and Weierstrass's theory of the isoperimetric problems. The final chapter presents a thorough proof of Hilbert's existence theorem.

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