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I'm trying to do some practice for an electromagnetism course, and am trying to calculate the grad, curl and div of a vector $A = (2xy, 3zx, yx^2)$

I know:

Div = $\nabla . A$

Curl = $\nabla \times A$

Grad = $\nabla A$

I have worked out the first two, but I seem to be having a mind blank and I'm getting myself all confused with the Grad component if someone could clarify this?

Also if someone could explain when I might need to use the Laplace Operator? What is it used for?

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You can only use the gradient on scalar functions, not on vector fields. –  dinosaur Feb 21 at 12:49
Okay that's why I'm getting confused then! Any chance you could give me an example? –  Sarah Jayne Feb 21 at 12:50
@dinosaur actually you can. The result is a tensor field –  David H Feb 21 at 12:50
@DavidH yes, but I don't think that this is what Sarah had in mind here. –  dinosaur Feb 21 at 14:06
@SarahJayne for example consider $f(x,y)=x^2+y^2$. This is a scalar function and you can calculcate $\nabla f(x,y)=\left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}\right) = (2x,2y)$. –  dinosaur Feb 21 at 14:07

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