# Vector Calculus Laplacian Function Graphs

This post categorized under Vector and posted on May 12th, 2019.

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Whereas the scalar Laplacian applies to a scalar field and returns a scalar quangraphicy the vector Laplacian applies to a vector field returning a vector quangraphicy. When computed in orthonormal Cartesian coordinates the returned vector field is equal to the vector field of the scalar Laplacian applied to each vector component.As a consequence the spherical Laplacian of a function defined on S N1 N can be computed as the ordinary Laplacian of the function extended to N 0 so that it Laplacian [f x 1 x 2 ] yields a result with the same dimensions as f. In Laplacian [f x 1 x n chart] if f is an array it must have dimensions n n. The components of f are interpreted as being in the orthonormal basis graphicociated to chart.

Save. In vector calculus a Laplacian vector field is a vector field which is both irrotational and incompressible. If the field is denoted as v then it is described by the following differential equations31.05.2016 A visual understanding for how the Laplace operator is an extension of the second derivative to multivariable functions.Autor Khan AcademyAufrufe 123Kgraphiclnge 6 Min.