Translation of "Differentialoperator" in English

In vector calculus, the surface gradient is a vector differential operator that is similar to the conventional gradient.

In mathematics and physics, the vector Laplace operator, denoted by formula_1, named after Pierre-Simon Laplace, is a differential operator defined over a vector field.

In differential geometry, the Atiyah–Singer index theorem, proved by , states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data).

So in local coordinates it acts as a differential operator, taking smooth sections of "E" to smooth sections of "F".

I could write the derivative operator on both sides, but I think you know that at this point, so that's the next step.

The question he asked was a fascinating one: what does the differential operator D n mean when n is not an integer?

He replaced the differential operator d /dx by a variable p transforming a differential equation into an algebraic equation.