Recent content by Flumpster

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    Relationship between Riemann Sum and the Integral

    Homework Statement The notation for a Riemann sum - Ʃ f(x*i)Δx - is very similar to the notation for the integral (the Ʃ becomes ∫, the f(x*i) becomes f(x) and the Δx becomes dx). \int f(x)dx = \lim_{n \to \infty}\sum_{k=0}^{n} f(x_i) Δx Is there a way to explicitly define the values on the...
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    A question about the derivative

    Thanks, Mark44 and SammyS :) Bennett.F.L, I'm sorry, I'm not sure what you mean. It's ok though, I think I got it.
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    A question about the derivative

    Homework Statement Generally the derivative has the limit x-- h applied to the whole thing like $$\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}$$ I'm guessing you can't express it as $$\frac{\lim_{h\to 0} f(x+h)-f(x)}{\lim_{h\to 0} h}$$ because the quotient rule for limits doesn't hold when...
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    Question about Indefinite integrals

    Thanks a lot everyone! :D
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    Question about Indefinite integrals

    Absolutely a typo. :) sorry! You'd be surprised at the quality of the instruction here - for example, one of my teachers didn't know what this f(x+h)-f(x) ---------- h lim h--> 0 was. I understand that the upper limit is x, I just mean that that I would expect the definition of the...
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    Question about Indefinite integrals

    Ok, here's what I meant: I was looking at ## \int_a^b f(t)dt = \int_0^b f(t)dt - \int_0^a f(t)dt = F(a) - F(b)## and I've been taught that F(x), or F(a) or so on, in this context, is an indefinite integral. Like this: $$\int f(x) dx$$ But that didn't make sense to me because I don't...
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    Question about Indefinite integrals

    Mark44 - You're right, I miss-copied. When I have access to a computer I'll try to explain what I meant. Thanks :)
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    Question about Indefinite integrals

    Homework Statement I hope this is in the right forum, because this is a question on theory and not related to a specific problem. I was reading onlne about the Fundamental Theorem of Calculus. On one site the author wrote: F(x) = \int_{0}^{x} f(t) dt Later, he wrote: \int_{a}^{b}...
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    Integral of a constant function with/without endpoint

    Thanks everyone! SammyS, thanks for writing it out like that, it made it a lot clearer to me. RGV, I'll look at that link, thanks. :)
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    Integral of a constant function with/without endpoint

    Thank you both for your answers :) I still haven't really managed to explain what I'm talking about...I'll have a look at related threads in the forum to see if I can clarify.
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    Integral of a constant function with/without endpoint

    I think you misunderstood me, I probably haven't been using the correct terminology. I dug up my calculus book, and I think what I'm thinking about is a step function. In the book, it says the following: "...if s(x) = c for all x in the closed interval [a,b], the ordinate set of s is a...
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    Integral of a constant function with/without endpoint

    Homework Statement / The Attempt at a Solution I know that given f(x)=c, the integral from a≤x≤b is c(b-a) (at least, I hope I know that! :D). Is the integral the same value if you don't include an endpoint? That is, if you were evaluating f(x) from a≤x<b? Intuitively I think it both...
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    Biology or Economics (A level)

    I'm familiar with the A-Level system, although I haven't taken Economics. I think that other than possible A-Levels universities will require in order to do physics/engineering (I imagine Math/Further Math, Physics and Chemistry will more than satisfy any prerequisites, although I haven't...
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    What physics background needed for quantum mechanics?

    I understand now. Thank you all for your awesome replies! You've really helped me a lot :)
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    What physics background needed for quantum mechanics?

    Jorriss - Thanks. I was worried that you have to do many classical mechanics courses in order to learn quantum mechanics - an intro course and an advanced course doesn't sound as bad as I thought. Oh, I actually am looking forward to Thermodynamics/Stat. Mechanics :) When I said I was less...
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