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This section is also the opening to control theory—the modern form of the calculus of variations. Its constraints are differential equations, and Pontryagin's. In calculus of variations the basic problem is to find a function y for which the functional I(y) is maximum or minimum. We call such functions as extremizing (ii) To illustrate the application of the calculus of variations in several fields outside the realm of pure mathematics. (By far the greater. This format ensures that mathematical notation is presented accurately and clearly. The PDF of this extract thus shows the content exactly as it would be seen The history of the calculus of variations dates back several thousand years, mathematical tool used to define variations or laws of evolution,