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  • What does the symbol nabla indicate? - Mathematics Stack Exchange
    First up, this question differs from the other ones on this site as I would like to know the isolated meaning of nabla if that makes sense Meanwhile, other questions might ask what it means in rel
  • vectors - Proof of $\nabla\times (\nabla\times \mathbf f)=\nabla . . .
    To give an example, in the derivation of the wave equation from maxwell's equations, the following identity is used: $$ \nabla\times (\nabla\times \mathbf f)=\nabla (\nabla\cdot \mathbf f)-\nabla^2\mathbf f \label {1} $$ I can prove it by direct calculation, but that would be very boring and mechanical
  • $\nabla$, $\cdot \nabla$, $\nabla \cdot$, $\nabla^2$ - What do they do . . .
    Finally, there's a $\nabla\cdot$ operator which seems to be the sum of the components of the first derivatives So in the absense of an explanation, I'm somewhat confused as to how the $\nabla$, $\cdot \nabla$, $\nabla \cdot$, and $\nabla^2$ operators actually work?
  • multivariable calculus - Del. $\partial, \delta, \nabla $: Correct . . .
    $\nabla$: Called Nabla or del This has four different uses, which can be easily distinguished while reading out loud, but it gets confusing when the first and last uses (grad and covariant derivative) get mixed up with $\partial$ and $\delta$ Gradient grad: $\vec {\nabla}\phi$ (phi is a scalar) Read as "nabla phi", or "del phi"
  • Is $\nabla$ a vector? - Mathematics Stack Exchange
    Cross product: $\nabla \times (Vector)=Vector$ From the above equation of cross product we can say that $\nabla$ is a vector (specifically vector operator) However, a vector generally has magnitude and an associated direction
  • How is $\nabla (u\cdot A) =u\cdot \nabla A+ u\times (\nabla \times A)
    OMG this is such ambiguous notation The thing is: $$\vec {a} \cdot (\nabla \vec {b}) \neq (\vec {a}\cdot \nabla) \vec {b}$$ The answer that I linked derived a formula involving $ (\vec {a}\cdot \nabla) \vec {b}$ This is why they got an extra cross product term I derived a formula involving $ \vec {a} \cdot (\nabla \vec {b}) $, which is why I didn't get the cross product term $ (\vec {a
  • Nabla and its rules - Mathematics Stack Exchange
    "Nabla" is a symbolic "vector differential operator" It can be written, symbolically, $\nabla= \frac {\partial} {\partial x}\vec {i}+ \frac {\partial} {\partial Y
  • Why $\\nabla \\cdot E = 0$ is used in the derivation of EM wave . . .
    For basic EM wave propagating in free space, all field lines pass into and out of any flux surface, as in the third image, so $\nabla \cdot \vec E = 0$ Only if your flux surface includes a source or sink (i e positive or negative charge) would the divergence be nonzero





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