Аннотация
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.
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