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

IEVref: | 102-05-06 | ID: | |

Language: | en | Status: Standard | |

Term: | scalar surface element | ||

Synonym1: | |||

Synonym2: | |||

Synonym3: | |||

Symbol: | dA
| ||

Definition: | at a given point of a given surface, area of a surface element containing the point and contained in a sphere of infinitesimal radius Note 1 to entry: For a surface defined by (fu, v) where $(u,v)\in \text{U}\subseteq {R}^{\text{2}}$, the scalar surface element is given by $\left|\frac{\partial f}{\partial u}\times \frac{\partial f}{\partial v}\right|\cdot \mathrm{d}u\mathrm{d}v$. Note 2 to entry: For a surface defined by the equation $\sqrt{1+{\left(\frac{\partial f}{\partial x}\right)}^{2}+{\left(\frac{\partial f}{\partial y}\right)}^{2}}\mathrm{d}x\mathrm{d}y$. | ||

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: |

Note 1 to entry: For a surface defined by ** r** =

$\left|\frac{\partial f}{\partial u}\times \frac{\partial f}{\partial v}\right|\cdot \mathrm{d}u\mathrm{d}v$.

Note 2 to entry: For a surface defined by the equation *z* = *f*(*x*, *y*), the scalar surface element is given by

$\sqrt{1+{\left(\frac{\partial f}{\partial x}\right)}^{2}+{\left(\frac{\partial f}{\partial y}\right)}^{2}}\mathrm{d}x\mathrm{d}y$.