(Untitled) | (Untitled) | (Untitled) | (Untitled) | (Untitled) | Examples |

IEVref: | 102-05-28 | ID: | |

Language: | en | Status: Standard | |

Term: | Laplacian, <of a scalar field> | ||

Synonym1: | |||

Synonym2: | |||

Synonym3: | |||

Symbol: | |||

Definition: | scalar Δf associated at each point of a given space region with a scalar f, equal to the divergence of the gradient of the scalar field Δ Note 1 to entry: In orthonormal Cartesian coordinates, the Laplacian of a scalar field quantity is: $\Delta \text{\hspace{0.05em}}f=\frac{{\partial}^{2}f}{\partial \text{\hspace{0.17em}}{x}^{2}}+\frac{{\partial}^{2}f}{\partial \text{\hspace{0.17em}}{y}^{2}}+\frac{{\partial}^{2}f}{\partial \text{\hspace{0.17em}}{z}^{2}}$. Note 2 to entry: The Laplacian of the scalar field | ||

Publication date: | 2008-08 | ||

Source: | |||

Replaces: | |||

Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO | ||

CO remarks: | |||

TC/SC remarks: | |||

VT remarks: | |||

Domain1: | |||

Domain2: | |||

Domain3: | |||

Domain4: | |||

Domain5: |

Δ*f* = div **grad** *f*

Note 1 to entry: In orthonormal Cartesian coordinates, the Laplacian of a scalar field quantity is:

$\Delta \text{\hspace{0.05em}}f=\frac{{\partial}^{2}f}{\partial \text{\hspace{0.17em}}{x}^{2}}+\frac{{\partial}^{2}f}{\partial \text{\hspace{0.17em}}{y}^{2}}+\frac{{\partial}^{2}f}{\partial \text{\hspace{0.17em}}{z}^{2}}$.

Note 2 to entry: The Laplacian of the scalar field *f* is denoted Δ*f* or ∇^{2}*f*, where Δ is the Laplacian operator.