Hence the Laplacian ?f ] " div grad f maps the scalar function f to a scalar function.
12.
Hence the Laplacian ?f ] " div grad f maps the scalar function f to a scalar function.
13.
For a laboratory plasma, ? is a constant and ? is a scalar function of spatial coordinates.
14.
The 1-forms are the cotangent vectors, while the 0-forms are just scalar functions.
15.
This allows the abstraction of the notion of a directional derivative of a scalar function to general manifolds.
16.
A scalar function whose contour lines define the streamlines is known as the "'stream function " '.
17.
This map is the one that relates covectors to infinitesimal displacements, mentioned above; some covectors are the exterior derivatives of scalar functions.
18.
Most theorems on integration and differentiation of scalar functions can be generalized to vector-valued functions, often using essentially the same proofs.
19.
Where V is the volume of the object in the fluid and P is the scalar function that describes the pressure at all locations in space.
20.
This square root satisfies the following relation involving the " L " 2-norm for suitable scalar functions " f ":
