Recently, the diffusion equation was thus mathematically investigated in accordance with the divergence theorem and the coordinate transformation theory.
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The integral and differential forms of Gauss's law for magnetism are mathematically equivalent, due to the divergence theorem.
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The most familiar extensions of the fundamental theorem of calculus in higher dimensions are the divergence theorem and the gradient theorem.
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So, using the divergence theorem, I calculate the divergence of F integrated over V and get 4.5?.
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Continuity equations offer more examples of laws with both differential and integral forms, related to each other by the divergence theorem.
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Now, using the divergence theorem we can derive the relationship between the flux and the partial time derivative of the density:
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Nevertheless, the problem of coordinate system of diffusion equation had not been mathematically investigated in accordance with the divergence theorem until recently.
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These field concepts are also illustrated in the general divergence theorem, specifically Gauss's law's for gravity and electricity.
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In 1D the volume reduces to an interval, its boundary being its extrema, then the divergence theorem reduces to the fundamental theorem of calculus:
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If we choose the volume to be a ball of radius " a " around the source point, then Gauss'divergence theorem implies that
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