Taylor Polynomials



You can make animations in 3d using the draw package:

(%i14) load(draw)$
(%i15) tay(n, x, y) := block(
    [ts : taylor(exp(-x__^2-y__^2), [x__, y__], [0,0], n)],
    subst([x__=x, y__=y], ts)
)$
(%i16) with_slider_draw3d(
    n, 1+2*makelist(i,i,0,6),
    color = blue,
    explicit(exp(-x^2-y^2), x, -1, 1, y, -1, 1),
    color = red,
    explicit('(tay(n,x,y)), x, -1, 1, y, -1, 1),
    zrange=[0,1]
);

HTH,

Andrej



On Sun, Nov 30, 2008 at 4:20 PM, Thomas Lingefj?rd
<Thomas.Lingefjard at ped.gu.se> wrote:
> Dear all,
>
> I know how to make a dynamic view of a Taylor Polynomial in two
> dimensions by using the function with_slider(  in wxMaxima.
>
> Is there a similar way to show the approximating
> Taylor polynomial in three dimensions, for instance for the
> surface of f: exp(-x^2-y^2) at (0, 0)or at any other point?
>
> --
> V?nliga h?lsningar/  Bedste hilsner/  Best regards/  Bien cordialement/
>  Cordilamente/  Pozdrowienia/  Sch?ne Gr??e/  Sz?v?lyes ?dv?zlettel,
> Thomas
>
> *******************************************************
> Thomas Lingefj?rd
>
> Associate Professor, Mathematics Education
> UNIVERSITY of GOTHENBURG, Department of Education
>
> Box 300
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>
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