Sunday, 5 April 2015

multivariable calculus - What does it mean that a differential can be integrated but it's final state depends on it's path?

An example would help here, but my problem is attempting to understand intuitively the difference between an exact and inexact differential. Maybe one of my problems may be the very definition of differential.



I assume differential is not the same as derivative. It is the change in y but how then can this be integrated? Don't you need dy/dx ? and what does it mean for it's integral to be path dependent vs. one which may be path independent.



The books are jumping around using "state" instead of path so I assume they are the same here. Not sure though. If the integral turns out to be path independent it is said to be exact. Wish I could get some intuition here with some simple problems with concrete example.

No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...