2.19 偏微分作用素

  $\displaystyle \frac{\partial}{\partial x}f= \frac{\partial f}{\partial x}$    
  $\displaystyle \left(\frac{\partial}{\partial x}\right)^2f= \frac{\partial}{\par...
...al}{\partial x}\frac{\partial f}{\partial x}= \frac{\partial^2 f}{\partial x^2}$    
  $\displaystyle \left( \alpha\frac{\partial}{\partial x}+ \beta\frac{\partial}{\p...
...l y}f = \alpha\frac{\partial f}{\partial x}+ \beta\frac{\partial f}{\partial y}$    
  $\displaystyle \frac{\partial}{\partial x}g\frac{\partial}{\partial x}f= \frac{\...
...g}{\partial x}\frac{\partial f}{\partial x}+ g\frac{\partial^2 f}{\partial x^2}$    

  $\displaystyle \frac{\partial}{\partial x}\frac{\partial}{\partial x} = \left(\frac{\partial}{\partial x}\right)^2= \frac{\partial^2}{\partial x^2}$    
  $\displaystyle \frac{\partial}{\partial x}g\frac{\partial}{\partial x} = \frac{\...
...ial g}{\partial x}\frac{\partial}{\partial x}+ g\frac{\partial^2}{\partial x^2}$    



Kondo Koichi
平成18年1月18日