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Math Help - Taylor Expansion

  1. #1
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    Taylor Expansion

    I have a couple of questions relating to Taylor expansions.

    1) I have a function f(s) and I'm trying to use a Taylor expansion to look at the change in value of f over a small change in s,  \delta s, how would I represent
    f(s + \delta s) as a Taylor expansion?

    2) If I have a function of 2 variables, how would I find a Taylor expansion for f(s,t)?
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  2. #2
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    Quote Originally Posted by bigdoggy View Post
    I have a couple of questions relating to Taylor expansions.

    1) I have a function f(s) and I'm trying to use a Taylor expansion to look at the change in value of f over a small change in s,  \delta s, how would I represent
    f(s + \delta s) as a Taylor expansion?

    2) If I have a function of 2 variables, how would I find a Taylor expansion for f(s,t)?
    1) f(s + \delta s) = f(s) + f'(s) \delta s + \frac{f''(s)}{2!} (\delta s)^2 + \frac{f'''(s)}{3!} (\delta s)^3 + \cdots

    2) f(x,y) = f(a,b) + f_x(a,b)(x-a) + f_y(a,b)(y-b)  + \frac{1}{2!} f_{xx}(a,b)(x-a)^2 + f_{xy}(a,b)(x-a)(y-b) + \frac{1}{2!} f_{yy}(a,b)(y-b)^2 + \cdots
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  3. #3
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    Quote Originally Posted by Danny View Post
    1) f(s + \delta s) = f(s) + f'(s) \delta s + \frac{f''(s)}{2!} (\delta s)^2 + \frac{f'''(s)}{3!} (\delta s)^3 + \cdots

    2) f(x,y) = f(a,b) + f_x(a,b)(x-a) + f_y(a,b)(y-b)  + \frac{1}{2!} f_{xx}(a,b)(x-a)^2 + f_{xy}(a,b)(x-a)(y-b) + \frac{1}{2!} f_{yy}(a,b)(y-b)^2 + \cdots
    thanks, but why is this?
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  4. #4
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    Quote Originally Posted by bigdoggy View Post
    thanks, but why is this?
    Which one are you refering to?
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