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A nice application in fluid mechanics is Kelvin's circulation theorem. You could also discuss how it fails to hold, if there are obstacles in the fluid flow. In the same spirit stokes theorem is applied in the canonical formalism of classical mechanics to find the poincare-cartan integral invariants.

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A nice application in fluid mechanics is Kelvin's circulation theorem. In the same spirit stokes theorem is applied in the canonical formalism of classical mechanics to find the poincare-cartan integral invariants.