A Brief Survey of the History of the Calculus of Variations and its Applications
A Brief Survey of the History of the Calculus of Variations and its Applications
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发表时间：
2004-02
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通讯作者：
James C. Ferguson
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作者：
James C. Ferguson
本文追溯了变分法理论的发展过程。从它起源于希腊思想家的工作，一直延续到文艺复兴，我们看到物理学的进步是数学理论发展的催化剂。从18世纪世纪起，建立一个严格的框架变分法的任务进行了研究，最终在希尔伯特的工作狄利克雷问题和最优控制理论的发展。最后，我们对该理论在不同问题上的一些应用进行了简要的介绍。
In this paper, we trace the development of the theory of the calculus of variations. From its roots in the work of Greek thinkers and continuing through to the Renaissance, we see that advances in physics serve as a catalyst for developments in the mathematical theory. From the 18th century onwards, the task of establishing a rigourous framework of the calculus of variations is studied, culminating in Hilbert's work on the Dirichlet problem and the development of optimal control theory. Finally, we make a brief tour of some applications of the theory to diverse problems.