Re: Taylor polynomials in mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg108175] Re: Taylor polynomials in mathematica
- From: dh <dh at metrohm.com>
- Date: Tue, 9 Mar 2010 06:28:19 -0500 (EST)
- References: <hmvq9c$18t$1@smc.vnet.net>
Hi Halla,
you had a bracket missing, hope I put it in the right place. Further,
the is a bug in y'[0]: y'[0]==d/(3 d^2)
Now, the second derivative at b==0 can be obtained by the derivative of
the first derivative and replacing values at b=0, like:
firstder={(b*x[b] - 3*((y[b])^3))/(9 (x[b])^2 (y [b])^2 - b^2),
(b*y[b] - 3*((x[b])^3))/(9 (x[b])^2 (y[b])^2 - b^2)}
secondderiv= D[firstderiv,b]//.{b -> 0, x[0] -> -c, y[0] -> -d, x'[0] ->
c/(3 d^2), y'[0] -> d/(3 d^2)}
Daniel
On 07.03.2010 10:05, Halla Gralla wrote:
> What I have is two unknown functions of b, x(b) and y(b). I do know their values in b=0, their first derivative and the value of their first derivatives in b=0.
>
> x(0) = -c
>
> x(0) = -d
>
> x'(b) = (b*x(b) - 3*((y(b))^3) / (9(x(b))^2(y(b))^2 - b^2)
>
> y'(b) = (b*y(b) - 3*((x(b))^3) / (9(x(b))^2(y(b))^2 - b^2)
>
> it follows that:
>
> x'(0) = c / 3d^2
>
> y'(0) = d / 3x^2
>
> Now I don't now how to find x''(b) or y''(b), which would be needed for a second ordered taylor polynomial, but mathematica knows (and perhaps does this automatically when setting up taylor polynomials?). Problem is, I don't know how to use mathematica very well. I need to make a "program" in mathematica where I can change values for n (order of taylor polynomial) and for c and d (which are constants in the functions).
>
> Any help? =))
>
--
Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>