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I would like to plot a real-valued function $f$ of two real variables $x,y$ but only over the region of the $x$-$y$ plane satisfying \begin{align} x>0, \qquad -x^{3/2} < y < x^{3/2}. \end{align} Is there a straightforward way to do this using Plot3D?

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RegionFunction option is what you're looking for:

Plot3D[Cos[x] + Sin[y], {x, -1, 5}, {y, -5, 5},
 RegionFunction -> (#1 > 0 && - #1^(3/2) < #2 < #1^(3/2) &)]

plot

The arguments provided to the function vary a bit depending on which plot function you are using, you can see under "Details" in the documentation. ("More Information" in older versions)

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  • $\begingroup$ Perfect thanks! $\endgroup$ – joshphysics Sep 13 '13 at 0:01
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The second iterator (for y) may depend on the first:

Plot3D[Cos[x] + Sin[y], {x, 0, 5}, {y, -x^(3/2), x^(3/2)}]

Mathematica graphics

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