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    someone said on another thread this was c1 stuff??

    I've done C1, and have no idea what 'first principles' are??
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    Don't worry... it isn't in every exam board and even the ones it's in it isn't covered properly.

    Basically, it is a discussion of the fact that

    \displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}
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    (Original post by SimonM)
    Don't worry... it isn't in every exam board and even the ones it's in it isn't covered properly.

    Basically, it is a discussion of the fact that

    \displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

    Wooo that makes some sense!! but still confused.

    I know how to differentiate but someone said 'from first principles' might come up at an interview. I will just differentiate as normal i just???

    +rep
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    (Original post by kam_007)
    Wooo that makes some sense!! but still confused.

    I know how to differentiate but someone said 'from first principles' might come up at an interview. I will just differentiate as normal i just???

    +rep
    Ok, if at an interview it says "first principles" then tell them you've not done it. But say you've read the definition somewhere and have a go at doing it that way. They're unlikely to ask anything difficult probably,

    Differentiate x^2 with respect to x from first principles

    All you'd have to do would be to say

    \displaystyle \begin{array}{lcl} \displaystyle f'(x) &=& \displaystyle \lim_{h \to 0} \frac{(x+h)^2-x^2}{h} 

\\ \displaystyle &=& \displaystyle  \lim_{h \to 0} \frac{x^2+2 xh +h^2-x^2}{h}  

\\ \displaystyle &=& \displaystyle \lim_{h \to 0} \frac{h(2x+h)}{h}  

\\ \displaystyle &=& \displaystyle \lim_{h \to 0} 2x+h 

\\ \displaystyle & =& 2x \end{array}
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    (Original post by SimonM)
    Ok, if at an interview it says "first principles" then tell them you've not done it. But say you've read the definition somewhere and have a go at doing it that way. They're unlikely to ask anything difficult probably,

    Differentiate x^2 with respect to x from first principles

    All you'd have to do would be to say

    \displaystyle f'(x) = \lim_{h \to 0} \frac{(x+h)^2-x^2}{h} =  \lim_{h \to 0} \frac{x^2+2 xh +h^2-x^2}{h} = \lim_{h \to 0} \frac{h(2x+h)}{h} = \lim_{h \to 0} 2x+h = 2x
    I can not imagine that that is easier, or any more efficient that the normal way but thanks very much!
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    (Original post by kam_007)
    I can not imagine that that is easier, or any more eddicient that the normal way but thanks very much!
    Why does the "normal" way work?
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    I knew as soon as i wrote it some uber cool maths guy was going to call me on it!:p:

    Umm just seems easier:o:

    :cool: wow i think if i answer a question like that at an interview im in for an unconditional offer:eek:

    :rolleyes:
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    (Original post by kam_007)
    :cool: wow i think if i answer a question like that at an interview im in for an unconditional offer:eek:
    I doubt it. Many candidates will be comfortable with some much more complex topics than that. As an interesting aside however, some friends of mine suggested that I should try to bring up formal differentiation during my interview (not from first principles)
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    this explains it pretty well:
    http://www.projectalevel.co.uk/maths...ationfirst.htm
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    We say f:[a,b]\to \mathbb R is differentiable at c \in (a,b) with derivative f'(c) if for each \epsilon > 0 there exists \delta > 0 such that x \in [a,b], |x-c|<\delta \implies |\frac{f(x)-f(c)}{x-c}-f'(c)|<\epsilon
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    (Original post by Gaz031)
    We say f:[a,b]\to \mathbb R is differentiable at c \in (a,b) with derivative f'(c) if for each \epsilon > 0 there exists \delta > 0 such that x \in [a,b], |x-c|<\delta \implies |\frac{f(x)-f(c)}{x-c}-f'(c)|<\epsilon

    That looks so wiked... but i don't understand any of it!!!:o:
    Im feeling really very dumb:shifty:
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    You shouldn't feel dumb. You would never get taught this stuff at A-Level
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    (Original post by kam_007)
    That looks so wiked... but i don't understand any of it!!!:o:
    Im feeling really very dumb:shifty:
    Don't feel dumb, that sort of definition is very useful for analysis, but for a slightly lower level understanding, feel happy using the definition given at the top.
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    Heh no need to feel stupid - it's pretty much just the second post but with the actual definition of what a limit put in. Aaah - need to go write my project!
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    (Original post by SimonM)
    Don't feel dumb, that sort of definition is very useful for analysis, but for a slightly lower level understanding, feel happy using the definition given at the top.
    Yupp i get your one

    im so glad i doing physics now.... i don't think i could hack straight maths now.

    :yep:
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    How amusing that I got negative rep for my post which gave the definition of what it means for a real valued function on a closed interval to be differentiable.

    Sadly it seems that many of the posters on this board are here to cram for exams and don't care about anything else, making them, in actual fact, pretty lousy mathematicians.

    You should also sign your name when you leave rep. It's poor manner not to.

    Thank god I don't waste my time trying to post here regularly anymore.
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    We say is differentiable at with derivative if for each there exists such that
    Thats wrong, the OP asked for differentiation from first priniciples, you only showed it in the real numbers, you need to include complex numbers.
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    (Original post by Simplicity)
    Thats wrong, the OP asked for differentiation from first priniciples, you only showed it in the real numbers, you need to include complex numbers.
    What?
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    (Original post by SimonM)
    What?
    Good point. (And im not being sarcastic.)
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    (Original post by Simplicity)
    Thats wrong, the OP asked for differentiation from first priniciples, you only showed it in the real numbers, you need to include complex numbers.
    Or for functions f\colon \mathbb R^{m}\to \mathbb R^{n}, or real valued functions on Banach spaces, or between smooth manifolds. Actually there's a paper by Cheeger that says, with certain assumptions, you can define a notion of differentiability for real valued functions on a metric measure space and then Lipschitz functions are differentiable almost everywhere.

    Looking back my post was very relevant!
 
 
 
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