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Applied Mathematical Methods by Bhaskar Dasgupta

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48

Variational Calculus*

A book or a course of the nature of the current one is appropriately concluded with an exposure to the topic of variational calculus, or the calculus of variations. With its spirit in optimization, formulations in terms of differential equations, operational tools coming from linear algebra and numerical methods, and wide-ranging applications in diverse fields from classic developments of theoretical physics to commercially booming finite element analysis softwares; variational calculus offers a great unifying theme of applied mathematics. In this chapter, we take up a short tour of this stimulating area. After a brief introduction to its basic ideas, we discuss at length the derivation of Euler’s equation in various ...

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