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Symbol Question

  1. Jan 6, 2009 #1
    I have seen the symbol dx in differential equations, but recently I saw it appear in various other equations that I previously thought included Δx instead of dx.

    Are those two symbols the same? I mean, is Δx = dx = xfinal - xinitial ?

    This may be the wrong thread, but I am still a newcomer, and plus I thought I saw another such question around here before!

  2. jcsd
  3. Jan 6, 2009 #2


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    Welcome to PF!

    Hi karkas! Welcome to PF! :smile:

    ∆x is an actual difference.

    dx is an infinitesimal difference.

    dx/dt = lim{∆x(t)/∆t} = lim{[x(t+∆t) - x(t)]/∆t}.

    (for linear functions, of course, it makes no difference)

    So Δx = xfinal - xinitial is correct :smile:

    but dx = xfinal - xinitial is wrong :cry:
  4. Jan 6, 2009 #3
    Thanks Tiny - tim!

    Yet I still don't understand something (probably it's because we're taught everything in Greek and I am still not adept with English terminology).

    If I say that the speed is v = Δx/Δt and v = dx/dt is the same thing if there is no force disrupting the linear movement?
  5. Jan 6, 2009 #4


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    hmm … mathematical symbols should be an international language! :smile:

    Yes, v = dx/dt is always correct …

    but if there's no acceleration, then v = ∆x/∆t is also correct.

    However, when you write dx/dt, you don't need to explain it,

    but when you write ∆x/∆t, you need to specify a particular interval. :wink:
  6. Jan 6, 2009 #5
    In physics and engineering, cap delta is frequently used to denote a finite change, a little bit of something. Thus cap delta x denotes a finite change in x.

    It is common in setting up a problem to write things in terms of finite differences before passing to the limit when these differences, in the form of ratios, become derivatives.
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