The direct method is a technique used in the calculus of variations to find the extremal functions of a functional, typically expressed as an integral. This method directly evaluates the functional to identify minimizers or maximizers by applying conditions like the Euler-Lagrange equation, often leading to a more straightforward solution than indirect methods. It focuses on constructing appropriate variations of functions and analyzing their behavior to derive conclusions about the optimal paths or shapes that minimize or maximize the given functional.
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