Nabla / del (∇) in LaTeX
\nabla produces the del (nabla) operator, the vector-calculus operator behind the gradient, divergence, curl and Laplacian.
LaTeX command
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The command \nabla renders the inverted-triangle del symbol. On a scalar field it is the gradient, \nabla f. Combined with \cdot it is the divergence of a vector field, \nabla \cdot \mathbf{F}, and with \times it is the curl, \nabla \times \mathbf{F}. The \cdot and \times are essential and change the meaning entirely.
The Laplacian is \nabla^2, sometimes written \Delta by other authors, so stay consistent within a document; \nabla \cdot \nabla is the same operator spelled out. Mark vector fields with \mathbf (or \vec) so \mathbf{F} reads as a vector rather than a scalar.
\nabla needs no package in LaTeX or KaTeX. Note that it is the upside-down form of the Greek capital \Delta; they are different symbols with different meanings, so do not swap one for the other.
Examples
$\nabla f$gradient of a scalar field
$\nabla \cdot \mathbf{F}$divergence
$\nabla \times \mathbf{F}$curl
$\nabla^2 \phi = 0$Laplace's equation
$\nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right)$gradient in components
Tips and common mistakes
\nablaf is the gradient,\nabla \cdot \mathbf{F}the divergence,\nabla \times \mathbf{F}the curl; the\cdotand\timesare essential.- The Laplacian is
\nabla^2; some authors use\Delta, so be consistent. - Mark vector fields with
\mathbf(or\vec) so\mathbf{F}reads as a vector. \nablais the inverted\Delta; they are different symbols, do not swap them.
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What is the LaTeX command for the nabla / del symbol?
\nabla, which needs no package in LaTeX or KaTeX.
How do I write gradient, divergence and curl?
Gradient is \nabla f, divergence \nabla \cdot \mathbf{F}, curl \nabla \times \mathbf{F}. Keep the \cdot and \times, as they distinguish the three.
How do I write the Laplacian?
Use \nabla^2 (for example \nabla^2 \phi), or \Delta if that is your convention; \nabla \cdot \nabla is the same operator written out.