What Does the Notation \(\frac{\partial u}{\partial t}(x,0)\) Indicate in PDEs?

[yungman]

What is the meaning of $$\;\;\frac{\partial u}{\partial t}(x,0)$$

Is it equal to $$\;\;\frac{\partial u(x,t)}{\partial t}\;\;first\;then\;set\;t=0$$

or $$\;\;\;\frac{\partial u(x,0)}{\partial t}\;\;$$ Which is setting t=0 in u(x,t) first then differentiate?

 

[Lord Crc]

Well, if you set t=0 and then differentiate with respect to t, you're not going to get much...

 

[yungman]

Well, if you set t=0 and then differentiate with respect to t, you're not going to get much...

Thanks

I just want to make double sure. Don't want to take anything for granted.

 

[Lord Crc]

Good point :)