Extremum Problems of Functionals and Calculus of Variations

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Last note, Functionals, Euler’s Equation, and Equilibrium, reviewed the concept of functionals and the method that solves the extremum problems of the simplest integral form of functionals—the Euler’s equation. The derivation adopted in that post is a directional derivatives like method. This treatment was simply to bypass the review of calculus of variations at that time. Calculus of variations is the subject of mathematics directly concerns the extremum problems of functionals, which underlies quite a lot of mechanics laws. The notation \(\delta\) frequently appears in many principles of mechanics and numerical formulations of complex mechanics problems. This memento reviews the concept of calculus of variations.
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