IEVref: 102-05-32 ID: Language: en Status: Standard Term: first Green formula Synonym1: Synonym2: Synonym3: Symbol: Definition: identity resulting from the divergence theorem applied to the vector field ${f}_{1}\text{\hspace{0.17em}}\mathrm{grad}\text{\hspace{0.17em}}{f}_{2}$, where f1 and f2 are two scalar fields given at each point of a three-dimensional domain V limited by a closed surface S $\underset{\text{V}}{\iiint }\left(\mathrm{grad}\text{\hspace{0.17em}}{f}_{1}\cdot grad\text{\hspace{0.17em}}{f}_{2}+{f}_{1}\text{\hspace{0.17em}}\Delta \text{ }{f}_{2}\right)dV=\underset{\text{S}}{∯}{f}_{1}\text{\hspace{0.17em}}grad\text{\hspace{0.17em}}{f}_{2}\cdot {e}_{\text{n}}dA$ where dV is the volume element, endA is the vector surface element and Δ is the Laplacian operatorNote 1 to entry: In English the first Green formula is sometimes called “first Green theorem” or “first Green identity”. 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: