Operator questions

  • Thread starter Savant13
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  • #1
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Main Question or Discussion Point

I'm looking into vector calculus right now, and I have a few questions.

* is the dot operator

What is the difference between \nabla * F and F * \nabla ?

What is \nabla ^2 F, where F is a vector field?
 

Answers and Replies

  • #2
dx
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∇⋅F is ∂(F_x)/∂x + ∂(F_y)/∂y + ∂(F_z)/∂z which is a scalar function. F⋅∇ is (F_x)(∂/∂x) + (F_y)(∂/∂y) + (F_z)(∂/∂z) which is an operator.

∇²F for a vector field F is just the vector field with components ∇²(F_x), ∇²(F_y) and ∇²(F_z).
 
  • #3
85
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How did you get the symbols to work?
 
  • #4
1,707
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f*del can be thought of as the directional derivative in the direction of f
 

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