Introduction to Electrodynamics · Problem 1.26

Vector Analysis — David J. Griffiths

Physics · vector-calculus-laplacian

Problem

Calculate the Laplacian of the following functions: (a) Ta=x2+2xy+3z+4T_a = x^2 + 2xy + 3z + 4. (b) Tb=sin⁡xsin⁡ysin⁡zT_b = \sin x \sin y \sin z. (c) Tc=e−5xsin⁡4ycos⁡3zT_c = e^{-5x} \sin 4y \cos 3z. (d) v=x2 x^+3xz2 y^−2xz z^\mathbf{v} = x^2\,\hat{\mathbf{x}} + 3xz^2\,\hat{\mathbf{y}} - 2xz\,\hat{\mathbf{z}}.

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