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    (Original post by Evil Monkey)
    Awwh that's so cute, you actually think you're smart just because you can throw some more technical words in to confuse the OP!

    He never even asked about keeping it real valued. Maybe if he had it'd give him something a bit more to look at, but it's actually completely useless in every way. Every other answer, that just tries to be helpful instead, works regardless of where you're applying it. So really, I would love to be wrong, what were you trying to do here...
    Actually, there isn't going to be any general answer to the question. Jake22's "Differentiation is essentially about linear approximation of functions." is better, but that doesn't cover e.g. Lie derivatives and exterior derivatives on manifolds, or formal derivatives in polynomial rings. Actually I'm not even convinced that covariant derivatives should be understood as linear approximation of functions...
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    (Original post by mcgoohan)
    What are all the d's and what's lim?
    Apart from knowing that it finds the gradient of a curve, i haven't a clue what it is.
    Integrations sister.
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    The act of finding the derivative in mathematics is called differentiation...

    What is a derivative?
    In calculus, the derivative is a measure of how a function changes as its input changes
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    (Original post by MUN123)
    It seems like Maths is not for me, because I just don't get the whole idea of defferentiation and Intergration. In my opinion both are useless and will not help me in the real world.
    Many modern luxuries you enjoy, e.g: cell phone, had calculus used in its design, programming manufacture etc...

    If you are an oil company, and want to know how fast your oil supplies will last at the current rate of flow. (Integrate over volume).

    If you are a disease expert and want to know the rate at which a particular disease is spreading, and how many people will be affected. (Integrate rate over area).

    A chemist would want to know how many molecules of gas are above the required activation energy for a given reaction, at the current temperature. (Integrate bell curve from current temperature to infinity).


    go here for a list of applications of calculus...
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    (Original post by kfkle)
    The derivative of a real-valued function f in a domain D is the Lagrangian section of the cotangent bundle T^*(D) that gives the connection form for the unique flat connection on the trivial \boldsymbol R-bundle D \times \boldsymbol R for which the graph of f is parallel.

    Is this straight out of 'Maths made Difficult'?
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    It is finding the gradient of the curve.

    Integration is finding the area under the curve.

    Simple.
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    (Original post by j.alexanderh)
    Is this straight out of 'Maths made Difficult'?
    I've heard of that book! I've never found a copy to read though, and it seems to be out of print...
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    (Original post by Zhen Lin)
    I've heard of that book! I've never found a copy to read though, and it seems to be out of print...
    Same here, I've searched pretty thoroughly for it and all I've found is an illicit pdf of part of it and a ridiculously expensive second hand copy on Amazon.
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    (Original post by j.alexanderh)
    Same here, I've searched pretty thoroughly for it and all I've found is an illicit pdf of part of it and a ridiculously expensive second hand copy on Amazon.
    It is actually from the first few paragraphs of a paper on the nature of mathematics. I haven't got round to reading the whole thing yet, but it looks very interesting. find it here.

    (Original post by Zhen Lin)
    I've heard of that book! I've never found a copy to read though, and it seems to be out of print...
    I can give you a direct link to the pdf, it's around 25MB. Send me a pm if you are interested.
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    (Original post by electriic_ink)
    Lim describes what happens to a function, f(x) as x gets close to a particular value eg:

     \displaystyle{\lim_{x->12} (x+1)} = 13 because as x gets closer to 12, x+1 gets closer to 13.

    \displaystyle{\lim_{x->2} \frac{1}{x-2}} = \infty because as x gets close to 2, 1/(x-2) approaches infinity.

    This one's a bit more interesting :p:
    \displaystyle{\lim_{x->0} \frac{\sin x}{x}} = 1
    think he was looking for a simpler answer
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    Are people who are good at maths clever human beings?
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    (Original post by Me-A-Doctor?)
    think he was looking for a simpler answer
    How could I have explained what a limit is any more simply?
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    (Original post by MUN123)
    Are people who are good at maths clever human beings?
    What on Earth is this post all about? Of course good mathematicians are clever people...
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    Differentiation is the method employed to find the derivative of a function.

    If you want to know more; aim for maths degree at uni and you'll discover many beautiful mathematics
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      (Original post by mcgoohan)
      What are all the d's and what's lim?
      Apart from knowing that it finds the gradient of a curve, i haven't a clue what it is.
      Differential calculus is the study of finding the instantaneous slope of a curve, not merely the slope between two points but the slope at a single point. The function that shows the slope at every point is called the derivative of the curve. Usually the instantaneous slope (at each particular point) is defined as the limit of slopes as the second point gets closer to the first. If you work in a framework with infinitesimals, however, the instantaneous slope can also be computed as the slope between two infinitesimally close points. For instance, in smooth infinitesimal analysis, the basic axiom is that

      f(x+d) = f(x) + f'(x)d

      for any nilsquare d^2 = 0; this may be where your d's come from. In standard calculus, the notion of d's are basically the cultural artifacts that remain from this kind of reasoning.
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      (Original post by Saichu)
      Differential calculus is the study of finding the instantaneous slope of a curve, not merely the slope between two points but the slope at a single point. The function that shows the slope at every point is called the derivative of the curve. Usually the instantaneous slope (at each particular point) is defined as the limit of slopes as the second point gets closer to the first. If you work in a framework with infinitesimals, however, the instantaneous slope can also be computed as the slope between two infinitesimally close points. For instance, in smooth infinitesimal analysis, the basic axiom is that

      f(x+d) = f(x) + f'(x)d

      for any nilsquare d^2 = 0; this may be where your d's come from. In standard calculus, the notion of d's are basically the cultural artifacts that remain from this kind of reasoning.
      I'm pretty sure Newton and Leibniz didn't use this sort of reasoning, and if they did, they didn't use this terminology... Moreover, to use this sort of analysis, you need to first extend the domain of your functions to include these infinitesimals. This, I think, is a non-trivial task. It's obvious enough how to do it for polynomials and power series, but what if I give you an arbitrary continuous, differentiable function?
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        (Original post by Zhen Lin)
        I'm pretty sure Newton and Leibniz didn't use this sort of reasoning, and if they did, they didn't use this terminology... Moreover, to use this sort of analysis, you need to first extend the domain of your functions to include these infinitesimals. This, I think, is a non-trivial task. It's obvious enough how to do it for polynomials and power series, but what if I give you an arbitrary continuous, differentiable function?
        It's a useful myth (with "sexed up" notation) that I'm very happy to perpetrate, like Newton's apple.

        1) In Robinson's Nonstandard Analysis, trivial; take the function in the nonstandard model denoted by the same constant symbol.

        2) In SIA (which is the one described above), not possible if the function isn't smooth, as the name suggests. Unfortunately, even if the function is smooth, I'm not 100% sure of a correspondence. However, my strongest guess would be that one doesn't need to specify the value of the function on the infinitesimals/other new elements, because none of them can be explicitly accessed anyway (e.g. the existence of a nonzero infinitesimal cannot even be proved). What's more important are the numbers that pop in to the Taylor-like equations as above, and those are determined by the classical derivatives.
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        (Original post by Saichu)
        Differential calculus is the study of finding the instantaneous slope of a curve, not merely the slope between two points but the slope at a single point. The function that shows the slope at every point is called the derivative of the curve. Usually the instantaneous slope (at each particular point) is defined as the limit of slopes as the second point gets closer to the first. If you work in a framework with infinitesimals, however, the instantaneous slope can also be computed as the slope between two infinitesimally close points. For instance, in smooth infinitesimal analysis, the basic axiom is that

        f(x+d) = f(x) + f'(x)d

        for any nilsquare d^2 = 0; this may be where your d's come from. In standard calculus, the notion of d's are basically the cultural artifacts that remain from this kind of reasoning.
        You just gave me a spark on solving a problem thanks for that!!
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        (Original post by Farhan.Hanif93)
        What on Earth is this post all about? Of course good mathematicians are clever people...
        I think that they are not clever but they try hard and they have motivations from their parents etc.
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        (Original post by electriic_ink)
        Lim describes what happens to a function, f(x) as x gets close to a particular value eg:

         \displaystyle{\lim_{x->12} (x+1)} = 13 because as x gets closer to 12, x+1 gets closer to 13.

        \displaystyle{\lim_{x->2} \frac{1}{x-2}} = \infty because as x gets close to 2, 1/(x-2) approaches infinity.

        This one's a bit more interesting :p:
        \displaystyle{\lim_{x->0} \frac{\sin x}{x}} = 1
        can you please explain that last one please?
       
       
       
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