Clarification of PDE notation

[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 :)

 

[blue_raver22]

The notation \frac{\partial u}{\partial t}(x,0) means taking the partial derivative of the function u with respect to t at the specific point (x,0). This notation does not imply any specific order of operations, as both options mentioned in the question are valid interpretations. However, in most cases, it is more common to first set t=0 and then differentiate, as this allows for a clearer understanding of the function at the specific point in question. Ultimately, the specific interpretation of this notation may depend on the context in which it is being used and the preferences of the author.