Taylor Expansion

**bigdoggy** · April 6th 2010, 05:06 AM

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)?

**Danny** · April 6th 2010, 06:35 AM

Originally Posted by bigdoggy

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) $f(x,y) = f(a,b) + f_x(a,b)(x-a) + f_y(a,b)(y-b)$ $+ \frac{1}{2!} f_{xx}(a,b)(x-a)^2 + f_{xy}(a,b)(x-a)(y-b) + \frac{1}{2!} f_{yy}(a,b)(y-b)^2 + \cdots$

**bigdoggy** · April 6th 2010, 11:56 AM

Originally Posted by Danny

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?

**Danny** · April 6th 2010, 12:15 PM

Originally Posted by bigdoggy

thanks, but why is this?

Which one are you refering to?

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