Differential Notation

nobodythere

I understand this formula perfectly:

[U]f(x+h) - f(x)[/U]
      h

I get why it gives the tangent of the line etc etc etc.

But I can't seem to figure out why things are written in the form df/dx, and why those things can be treated like fractions. I got by with this in the leaving no problem (involved learning a little bit off) but now in college they're throwing these things all over the shop and it's a little hard to follow.

Can anyone explain this please?

ecksor

A search for "Leibniz notation" might get you some more information.

danmcn

the first expression you mention is Newton's notation.
the df/dx expression is part of Leibniz's notation for calculus.
They are exactly equivalent.

the idea is that df and dx are infinitesimally small "elements".
Suppose we take f(t) is a function of time, then dt is a infinitesimally small element of time and df is an infinitesimally small element of the function, then it stands to reason that df/dt is an infinitesimally small element of the CHANGE of the function wrt time.

important to note that df and dt are generally not invariant, they are functions too.
eg df(t)=t.dt
=>df/dt=t

its probably hard to grasp from this little note, but look up "Leibniz notation" as ecksor said, or even "differentials" in a book or on the net.

nobodythere

Ah I see... So it's kinda the same formula in a different way. I totally get it now... Thanks very much