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Thread: Basic Concept in Analysis

  1. #1
    Jun 2010

    Basic Concept in Analysis

    So I remember in Calculus I they told me that (d/dx)f(x) is just a short-hand for lim_(x-->a)... etc. Then they pulled a fast one that I didn't notice at the time, and has annoyed me ever since. They split off the dx and used it in integrals, and never explained how this was valid. In general I don't get the validity of reasoning with an infinitesimal like d. Is there anywhere I can read about this? I took a course in introductory Analysis and still don't feel comfortable with it.
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  2. #2
    Senior Member
    Nov 2010
    Staten Island, NY
    Sure - in any calculus book, or you can find it on the web. You want to read the section on differentials. Then read about Riemann sums, the limit definition of the definite integral, and the fundamental theorem of calculus.

    If you already have a decent understanding of calculus, you can probably get through this stuff in a few hours.

    If you want a deeper understanding, then read the same sections in an advanced calculus or real analysis book.
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