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Vector Laplacian Proof

This post categorized under Vector and posted on August 13th, 2019.

As a special case the square of a triple product is a Gram determinant. Scalar or pseudoscalar. Although the scalar triple product gives the volume of the parallelepiped it is the signed volume the sign depending on the orientation of the frame or the parity of the permutation of the vectors.In mathematics and physics the vector Laplace operator denoted by named after Pierre-Simon Laplace is a differential operator defined over a vector field. The vector Laplacian is Vector Laplacian In some cases it is possible to relate a velocity field to a scalar function called the velocity potential. When we examine the divergence of the velocity field we obtain a new operation on the scalar phi called the Laplacian.

31.08.2016 Laplacian in spherical coordinates is not simply the second derivative wrt [itex] r [itex] and you have ignored the [itex] vecr [itex].If you keep in mind that a 0-form is a function and a 1-form is a row-vector field all the familiar operations of vector calculus can be written in terms of the ones above. The gradient of a function f is the 1-form df. The curl of a 1-form A is the 1-form star dA. The divergence of Stack Exchange network consists of 175 Q&A communities including Stack Overflow the largest most trusted online community for developers to learn share their knowledge and build their careers.

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