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This is considered the oldest problem in the Calculus of Variations. Proposed by Johann Bernoulli in 1696: Given a point 1 higher than a point 2 in a vertical plane, determine a (smooth) curve from 1 ! 2 along … n important role in the calculus of variations. A similar situation is encountered in elementary analysis, where, in dealing with functions of n variables, it is convenient to use the concept of an ^-dimensional … This section is also the opening to control theory|the modern form of the calculus of variations. Its constraints are di erential equations, and Pontryagin's maximum principle yields solutions. CALCULUS OF VARIATIONS In calculus, one studies min-max problems in which one looks for a number or for a point that minimizes (or ma. imizes) some quantity. The calculus of variations is about min-max … The calculus of variations is a technique in which a partial differential equation can be reformulated as a minimization problem. In the previous section, we saw an example of this technique.
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