Normal Derivative

normal derivative

[′nȯr·məl di′riv·əd·iv]
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 ?
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.
h]([OMEGA] [GAMMA]) if and only if v and its normal derivative vanish on [GAMMA].
Sampo shares, normal derivative, stock lending or other contracts may be entered
At the outlet, the uniform axial velocity was used to ensure continuity, and tangential velocities were computed from a zero normal derivative condition.
m, i] and can have nonzero trace of the normal derivative onto [[gamma].
k] the values of normal derivative at the midpoints of [[[delta].
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].
The book is unique for its presentation of a new theory for the tangential and normal derivatives of flow properties (such as pressure and velocity) just downstream of an infinitesimally thin, curved shock wave.
They exhibited significant differences only in the immediate proximity of the aperture, but in this region their physical properties were obscured by the fact that they or their normal derivatives, or both, do not reproduce the assumed incident field.
The Kirchhoff and Rayleigh-Sommerfeld integral equations (1) and (2) are alternative forms of the theorem of Helmholtz (5), which expresses Huygens' principle in terms of a scalar wave function U and its normal derivatives without assuming specific attributes of this function, except that it is continuous and twice differentiable with continuous derivatives and obeys the homogeneous wave equation,