Laplace Operator (Laplacian) in Spherical Coordinates – PROOF
In this video I derive the Laplace Operator or Laplacian in spherical coordinates by applying the Laplacian in polar coordinates twice: once for the azimuthal (ф) angle and once for the polar angle (θ). Adding the two polar Laplacians, cancelling out terms, and writing the partial derivatives in terms of the spherical coordinates, we obtain the Laplace Operator in spherical coordinates!
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#math #polarcoordinates #calculus #sphericalcoordinates #multivariablecalculus
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