Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §15.3 Green’s Theorem, #39 · Multivariable Calculus · Green, Stokes & divergence

The real part of … is

The real part of $(x + i y)^{3} = x^{3} + 3 i x^{2} y - 3 x y^{2} - i y^{3}$ is $f = x^{3} - 3 x y^{2}$ . Its gradient field is $F = grad f =$ ____. The divergence of $F$ is ____. Therefore $f$ satisfies Laplace's equation $f_{xx} + f_{y y} = 0$ (check that it does).

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §15.3 Green’s Theorem, #39

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