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Sinopsis
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.
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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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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
"Sobre este título" puede pertenecer a otra edición de este libro.
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Lectures on the Calculus of Variations (Classic Reprint)
Impresión bajo demandaLibrería: Revaluation Books, Exeter, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
Paperback. Condición: Brand New. 292 pages. 9.00x6.00x0.66 inches. This item is printed on demand. Nº de ref. del artículo: zk1440066264
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