In the Helmholtz equation, applying it to a function yields the same function multiplied by a scale factor, and in flat space-time, it generalizes to the d'Alembertian.
In the Helmholtz equation, applying it to a function yields the same function multiplied by a scale factor, and in flat space-time, it generalizes to the d'Alembertian. Its square appears in the von Karman equations and is known as the biharmonic operator, and applying this operator to one over x yields a delta function of x. In cylindrical coordinates, the solutions generated by applying this operator to a scalar function and setting the result to zero are the Bessel functions, and when applied to electric charge density, this operator yields the total enclosed charge in Gauss's law. For ten points, identify this vector operator obtained by taking the divergence of a gradient of a scalar function, which is denoted by the square of an upside- down capital delta.
In the Helmholtz equation, applying it to a function yields the same function multiplied by a scale factor, and in flat space-time, it generalizes to the d'Alembertian.
{Laplacian} (or {del-squared} before mention)