# Tagged Questions

Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on an infinite dimensional spaces.

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### Pontryagin's maximum principle

So I've been doing some optimal control theory lately. It's really interesting but I've spent the whole day trying to wrap my head around pontryagin's maximum principle. There's a lot of mathematical ...
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### Best Differential Equation, Partial Differential Equation and Calculus of Variations books?

Electrical Engineer here thinking of switching to physics. What are the best Differential Equation, Partial Differential Equation and Calculus of Variations books? Ideally they explain the topic ...
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### what is difference between variations of the work and virtual work

virtual work part https://en.wikipedia.org/wiki/Virtual_work I really want to know that both equations are same or not.(mathematically)(I think that they are the same.) Thanks for reading.
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### Two Approaches Two Different Solutions: Optimal Controls vs. Different Method

If I try to solve a problem two different ways, I get two different answers which generally means I am committing some horrible sin! Given the problem, \begin{align} \min_u\ S &= \int dt\ L(x, u) ...
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### Independence of function and its derivative in calculus of variations

It's common to see in calculus of variation that the integrand $f$ of functional $F[y]=\int f(y,y',x)dx$ is a function of $y,y'$ and $x$. Why do we regard the derivative $y'$ as an independent ...
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### Determining whether the extremal problem has a weak minimum or strong minimum or both

The extremal of the functional $\int_{0}^{\alpha}{\left((y')^2 - y^2\right)dx}$ that passes through (0,0) and (${\alpha}$,0) has a weak minimum if ${\alpha}$ < $\pi$ strong minimum if ${\alpha}$ ...
### Probability if variable has $15\%$ CV
I have a relatively simple question, but I am not sure if I understand it right. I have estimated through my calculations the value $X$. $X$ depends on many things, but one of them is $Y$ and I know ...