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Can someone give me an intuitive definition for differentials?

  1. Sep 10, 2007 #1
    Can someone give me an intuitive definition for differentials? My prof said to brush up on them because we'll be seeing them lots in thermo. I don't need all the theory because I'll be seeing them in november in calc. Right now I just have to work with them. Are they just infinitely small differences?
     
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  3. Sep 10, 2007 #2

    mathwonk

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    read tenenbaum and pollard, ode, first few pages.
     
  4. Sep 10, 2007 #3
    This picture show what differential is for a function f(x)
    http://www.bymath.com/studyguide/ana/sec/ana4a.gif
    Basically, it is the change in the linear approximation for a function for a change in x, dx.

    dy/dx = f '(x) -> differential dy = f '(x) dx
    When dx is small dy is a good approximation for f(x + dx) - f(x);
     
  5. Sep 10, 2007 #4

    mathwonk

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    consider for a smooth curve y=f(x), its family of tangent lines. the differential of f, df, is the family of linear functions whose graphs are those tangent lines.

    so that picture depicted the graph of df(x0), the graph of one of the linear functions making up the differential.
     
  6. Sep 12, 2007 #5
    Loomis and Sternberg, chapter 3 section 5 and following sections.
    You'll have to do some preliminary reading in order to get to this point. Their text is freely available.

    Even if you don't do more than look at it now, it'll serve you well in November.
     
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