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Physics: Path Integrals, Navier Stokes, Cartesian Coordinates, Conservation Laws

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I am not sure how to solve these. Questions involves calculating path integrals, Navier Stokes equation, Cartesian coordinates, and conservation laws. Examples similar to these would be very helpful.

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This solution involves calculations for questions of path integrals, Navier Stokes equation, Cartesian coordinates, and conservation laws.

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