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Math Help - del operator, divergence , and the curl

  1. #1
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    del operator, divergence , and the curl

    In physics the del operator is fundamental.The basic laws of Electromagnetism are defined using it.I wanted to know the actual significance of the curl ( \nabla \times )and divergence.I also intended this post to be a starter for a discussion about mathematical fields,their difference and applications(in physics or other subjects).
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  2. #2
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    One reason why \nabla is so important is that it is invariant under rigid motions: rotating or translating the coordinate system does not change the form of \nabla. Roughly speaking, the "divergence", \nabla\cdot \vec{v}, measures how much a vector field "spreads out" (diverges) while the "curl", \nabla\times\vec{v} measure its tendency to rotate- hence the names "divergence" and "curl".
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