Fourier's Law gives the rate of heat transfer through a material as proportional to the negative result of this operator applied to a temperature field.
On Riemannian manifolds, this operator gives a field equivalent to the musical isomorphism sharp of the function's differential. Fourier's Law gives the rate of heat transfer through a material as proportional to the negative result of this operator applied to a temperature field. The Jacobian of this operator is the Hessian, and the Jacobian is itself formed of transposes of this operator. The curl of the result of this operator is always zero, and it's divergence is equal to zero for harmonic functions and known as the Laplacian, which is sometimes symbolized by this operator squared. FTP, name this operator which points in the direction of steepest ascent for a scalar field and returns a vector consisting of a function's partial derivatives, generally symbolized with a nabla, a down-pointing triangle.
On Riemannian manifolds, this operator gives a field equivalent to the musical isomorphism sharp of the function's differential.
{Gradient} (prompt on “del” or “nabla”)