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Titlebook: A History of the Calculus of Variations from the 17th through the 19th Century; Herman H. Goldstine Book 1980 Springer-Verlag New York Inc

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发表于 2025-3-21 17:23:09 | 显示全部楼层 |阅读模式
期刊全称A History of the Calculus of Variations from the 17th through the 19th Century
影响因子2023Herman H. Goldstine
视频videohttp://file.papertrans.cn/142/141227/141227.mp4
学科分类Studies in the History of Mathematics and Physical Sciences
图书封面Titlebook: A History of the Calculus of Variations from the 17th through the 19th Century;  Herman H. Goldstine Book 1980 Springer-Verlag New York Inc
影响因子The calculus of variations is a subject whose beginning can be precisely dated. It might be said to begin at the moment that Euler coined the name calculus of variations but this is, of course, not the true moment of inception of the subject. It would not have been unreasonable if I had gone back to the set of isoperimetric problems considered by Greek mathemati­ cians such as Zenodorus (c. 200 B. C. ) and preserved by Pappus (c. 300 A. D. ). I have not done this since these problems were solved by geometric means. Instead I have arbitrarily chosen to begin with Fermat‘s elegant principle of least time. He used this principle in 1662 to show how a light ray was refracted at the interface between two optical media of different densities. This analysis of Fermat seems to me especially appropriate as a starting point: He used the methods of the calculus to minimize the time of passage cif a light ray through the two media, and his method was adapted by John Bernoulli to solve the brachystochrone problem. There have been several other histories of the subject, but they are now hopelessly archaic. One by Robert Woodhouse appeared in 1810 and another by Isaac Todhunter in 1861.
Pindex Book 1980
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Jacobi and His School, did not become loyal republicans, renouncing xenophobia, authoritarianism, and . in favor of philo-Semitism, parliamentary democracy, and pro-metropolitan sentiment. The . may have acquiesced to the need for defense against foreign invasion, but such support was half-hearted at best, and revoked at
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0172-570X e name calculus of variations but this is, of course, not the true moment of inception of the subject. It would not have been unreasonable if I had gone back to the set of isoperimetric problems considered by Greek mathemati­ cians such as Zenodorus (c. 200 B. C. ) and preserved by Pappus (c. 300 A.
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https://doi.org/10.1007/b138204ttle or no indication as to why they are so. I do not know why he chose this means of announcing his results, unless he was anxious to publish before someone preceded him. In any case let us look at some results in connection with the second variation that should help to illuminate Jacobi’s paper.
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