[物理学与PDEs]书中出现的向量公式汇总

P 11

 

1. $\rot (\phi{\bf A})=\n \phi\times{\bf A}+\phi\ \rot{\bf A}$.

 

2. $-\lap {\bf A}=\rot\rot {\bf A}-\n \Div{\bf A}$.

 

P 20

 

3. $\Div({\bf E}\times {\bf B})=\rot {\bf E}\cdot {\bf B}-{\bf E}\cdot \rot{\bf B}$.

 

P 22

 

4. $\Div({\bf E}\otimes{\bf E})=(\Div{\bf E}){\bf E}+\rot {\bf E}\times {\bf E}+\cfrac{1}{2}\n {\bf E}^2$.

 

P 23

 

5. $\n (E^2)=\Div(E^2{\bf I})$.

 

P 53

 

6. $\Div({\bf E}\times{\bf H})={\bf H}\cdot\rot{\bf E}-{\bf E}\cdot\rot {\bf H}.$