定理表

{PDE 常用符号}

• $\nabla$ 梯度算子, 对每一分量求偏导的向量 eg. $(\frac{\partial}{\partial x},\frac{\partial}{\partial y},\frac{\partial}{\partial z})$.
• $\text{div}$ 散度, 理解为 $\text{div}=\nabla\cdot$, 即先算梯度再做点积, eg. $\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}+\frac{\partial u}{\partial z}$
• \text{curl} 旋度, 理解为 $\text{curl}=\nabla\times$, 即先算梯度, 再做叉积
• $\Delta$ 拉普拉斯算子, 针对空间变量, 对每一维的二阶偏导求和, $\Delta = \sum\limits_{i=1}^n \dfrac{\partial ^2}{\partial x_i^2}$