A simple calculus question

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  • #1
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i just want simple explanation of this.
velocity v is a function of r and t.
then my professor, in order to derive relationship of something, he wrote:
[tex]\frac{dv}{dt}=\frac{\partial v}{\partial r}+\frac{\partial v}{\partial t}[/tex]
then assuming small spatial variation,
[tex]\frac{dv}{dt} \approx \frac{\partial v}{\partial t}[/tex]
my question: is the first equation above OK?
is it standard calculus? i am weak in this. please help.


thanks.
 

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  • #2
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look up the chain rule; when v = v(r(t),t),


[tex]\frac{dv}{dt}=\frac{\partial v}{\partial r}\frac{dr}{dt}+\frac{\partial v}{\partial t}[/tex]

then you can see the following argument makes more sense?
 
  • #3
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thanks. i just want to clarify again, does it mean dr/dt is small, i.e. small velocity?
 
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