设某量场由
给出,其中P、Q、R具有一阶连续偏导数,Σ是场内的一片有向曲面,n是Σ在点(x,y,z)出的单位法向量,则 ∬ Σ A ⋅ n d S {\displaystyle \iint \limits _{\Sigma }\mathbf {A} \cdot \mathbf {n} dS} 叫做向量场A通过曲面Σ向着指定侧的通量(或流量),而 ∂ P ∂ x + ∂ Q ∂ y + ∂ R ∂ z {\displaystyle {\frac {\partial P}{\partial x}}+{\frac {\partial Q}{\partial y}}+{\frac {\partial R}{\partial z}}} 叫做向量场A的散度,记作 div A,即