Normal Derivative

normal derivative

[′nȯr·məl di′riv·əd·iv]
(mathematics)
The directional derivative of a function at a point on a given curve or surface in the direction of the normal to the curve or surface.

Normal Derivative

 

of a function defined in space (or in a plane), the derivative in the direction of the normal to some surface (or to a curve lying in the plane). Let S be a surface, P a point on S, and f a function in some neighborhood of P. Then the normal derivative of f at P is equal to the limit of the ratio of the difference f(A) — f(P) over the distance from A to P, where A is a point on the normal to S at P that approaches P from one side of S (see Figure 1).

Figure 1

We distinguish between the derivative of f with respect to the outward-drawn and the inward-drawn normals to S, depending on the direction from which A approaches P. Consideration of normal derivatives is particularly important in the theory of boundary value problems.

References in periodicals archive ?
Here the outward normal derivative is [mathematical expression not reproducible]; then
To translate the condition to reference coordinates, we again use the chain rule to write the normal derivative as a combination of change of variables terms and derivatives in parameter space (by inverting the Jacobian of the mapping [f.
8) is a integral for determining the potential [PHI] on the flapping hydrofoil surface SB and the normal derivative [partial derivative]/[partial derivative][n.
Note that [partial derivative][OMEGA] is part of the interface because the boundary condition for the normal derivative is only enforced weakly through the penalty term in (1.
x] is the normal derivative of u at x, f : [OMEGA] [right arrow] R, and g, [g.
At the outlet, the uniform axial velocity was used to ensure continuity, and tangential velocities were computed from a zero normal derivative condition.
Then the Dirichlet-Neumann operator R([Lambda]) maps a function [Phi](x) defined on [Gamma] to the outward normal derivative of the solution u(x) of the problem
Here [partial derivative]/[partial derivative]v = v x [nabla] is the operator of normal derivative on [partial derivative]S, v is the outward unit normal vector to [partial derivative]S, and [f.
The function value and its normal derivative on the boundary, [PHI](Q) and ([partial derivative]/[partial derivative]n)[PHI](Q), are already known after the evaluation of (4).
where [DELTA] denotes the Laplacian operator and [partial derivative]/[partial derivative]v is the normal derivative at the boundary of [OMEGA].
j] to be the function whose normal derivative at p is 1 and takes the value zero for all other nodal variables, and (iii) [[delta].