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Stokes' Theorem:
\[
\int \int (\vec{\nabla} \times \vec{A}) \vec{df} = \oint \vec{A} \vec{dl}
\]
Euler-Lagrange Equations:
\[
\frac{d}{dx} \left(\frac{\partial F}{\partial y'_i} \right)
- \frac{\partial F}{\partial y_i} = 0
\]
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