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Finding the Best Function: A Way to Explain Calculus of Variations to Engineering and Science Students

In many practical problems, we need to find the most appropriate function: e.g., we need to find a control strategy u(t) that leads to the best performance of a system, we need to find the shape of the car which leads to the smallest energy losses, etc. Optimization over an unknown function can be described by the known Euler-Lagrange equations. The traditional way of deriving Euler-Lagrange equations when explaining them to the engineering and science students is, however, somewhat over-complicated. We provide a new, simpler way to deriving these equations, a way in which we directly use the fact that when the optimum is attained, all partial derivatives are equal to 0.