| 书目名称 | Variational Calculus and Optimal Control | | 副标题 | Optimization with El | | 编辑 | John L. Troutman | | 视频video | | | 丛书名称 | Undergraduate Texts in Mathematics | | 图书封面 |  | | 描述 | Although the calculus of variations has ancient origins in questions of Ar istotle and Zenodoros, its mathematical principles first emerged in the post calculus investigations of Newton, the Bernoullis, Euler, and Lagrange. Its results now supply fundamental tools of exploration to both mathematicians and those in the applied sciences. (Indeed, the macroscopic statements ob tained through variational principles may provide the only valid mathemati cal formulations of many physical laws. ) Because of its classical origins, variational calculus retains the spirit of natural philosophy common to most mathematical investigations prior to this century. The original applications, including the Bernoulli problem of finding the brachistochrone, require opti mizing (maximizing or minimizing) the mass, force, time, or energy of some physical system under various constraints. The solutions to these problems satisfy related differential equations discovered by Euler and Lagrange, and the variational principles of mechanics (especially that of Hamilton from the last century) show the importance of also considering solutions that just provide stationary behavior for some measure of performa | | 出版日期 | Textbook 1996Latest edition | | 关键词 | Calculus; Convexity; Konvexe Funktion; Optimal control; Variationsrechnung; linear optimization; optimizat | | 版次 | 2 | | doi | https://doi.org/10.1007/978-1-4612-0737-5 | | isbn_softcover | 978-1-4612-6887-1 | | isbn_ebook | 978-1-4612-0737-5Series ISSN 0172-6056 Series E-ISSN 2197-5604 | | issn_series | 0172-6056 | | copyright | Springer Science+Business Media New York 1996 |
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发表于 2025-3-21 17:46:07
