Example · Undergraduate
Terms
| Term | This example | Why |
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| gradient |
$\nabla f(x, y, z) = (2x, 2y, 0)$
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| Jacobian |
$Df(x, y, z) = \begin{bmatrix} 2x & 2y & 0 \end{bmatrix}$
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The Laplacian of $f$ is the sum of its second partial derivatives, $2 + 2 + 0 = 4$, and its Jacobian is the row of its first partial derivatives.
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| laplacian |
$\Delta f = 2 + 2 + 0 = 4$
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The sum of the second partial derivatives with respect to $x$, $y$, and $z$.
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