So when deriving the Euler-Lagrange equation for the simple case (the integrand is just a function of x, y(x), and y'(x) where y is defined on [a,b]) we're interested in those functions which connect two points (x_0, y(x_0)) and (x_1, y(x_1)). But these functions don't form a function space in themselves. So are we just looking at all functions on [a,b] with continuous second derivatives and out of those, considering the ones which satisfy the boundary conditions we're interested in?(adsbygoogle = window.adsbygoogle || []).push({});

This must be the case, because in the derivation we then increment y(x) by an h(x) where h(x_0)=h(x_1)=0. This wouldn't make sense unless we were considering a larger space than just those functions satisfying the boundary conditions. Just let me know if I'm on the right track here.

Thanks,

Kevin

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# Calc of Variations quickie

Can you offer guidance or do you also need help?

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