達朗貝爾原理{d}{dt}}\left({\frac {\partial \mathbf {r} _{i}}{\partial q_{j}}}\right)=\left({\frac {\partial }{\partial t}}+\sum _{k}{\dot {q}}_{k}{\frac {\partial }{\partial
扩散方程 {\displaystyle {\frac {\partial \phi ({\vec {r}},t)}{\partial t}}=\sum _{i=1}^{3}\sum _{j=1}^{3}{\frac {\partial }{\partial x_{i}}}\left(D_{ij}(\phi
福克-普朗克方程{\frac {\partial f}{\partial t}}=-\sum _{i=1}^{N}{\frac {\partial }{\partial x_{i}}}\left[D_{i}^{1}(x_{1},\ldots ,x_{N})f\right]+\sum _{i=1}^{N}\sum _{j=1}^{N}{\frac
守恆量 {d{\mathcal {L}}}{dt}}=\sum _{i}{\frac {\partial {\mathcal {L}}}{\partial q_{i}}}{\dot {q}}_{i}+\sum _{i}{\frac {\partial {\mathcal {L}}}{\partial {\dot {q}}_{i}}}{\ddot
外微分 I ∂ x i d x i ∧ d x I . {\displaystyle d{\omega }=\sum _{i=1}^{n}{\frac {\partial f_{I}}{\partial x_{i}}}dx_{i}\wedge dx_{I}.} 对于一般的k-形式 ΣI fI dxI (其中多重指标I取遍所有{1