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Lectures On The Calculus Of Variations(1st Edition)
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Oskar Bolza
Cover Type:Hardcover
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ISBN: 1440066264, 978-1440066269
Book publisher: Forgotten Books
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Book Summary: Calculus of Variations during the last thirty years may be characterized as follows: 1. A critical revision of the foundations and demonstrations of the older theory of the first and second variation according to the modern requirements of rigor, by WEIEB- STKASS, ERDMANN, Du BOIS-REYMOND, SCHEEFFEB, SCHWABZ, and others. The result of this revision was: a sharper formulation of the problems, rigorous proofs for the first three necessary conditions, and a rigorous proof of the sufficiency of these conditions for what is now called a weak extremum. 2. WEIEBSTBASS Sextension of the theory of the first and second variation to the case where the curves under consideration are given in parameter-representation. This was an advance of great importance for all geometrical applications of the Calculus of Variations; for the older method implied for geometrical problems a rather artificial restriction. 3. WEIEBSTBASS Sdiscovery of the fourth necessary condition and his sufficiency proof for a so-called strong extremum, which gave for the first time a complete solution, at least for the simplest type of problems, by means of an entirely new method based upon what is now known as WEIEBSTBASS Sconstruction. These discoveries mark a turning-point in the history of the Calculus of Variations. Unfortunately they were given by WEIEBSTBASS only in his lectures, and thus became known only very slowly to the general mathematical public.(Typographical errors above are due to OCR software and don't occur in the book.)About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digita
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