Hi, thx, but the correct URL is http://sagenb.org/home/pub/298/
H On Mar 8, 10:37 pm, "ma...@mendelu.cz" <ma...@mendelu.cz> wrote: > Dear readers of this group, I wrote a simple sagelet which describes > approximation of a function in two variabels using differential. The > sagelet is published athttp://www.sagenb.org/home/pub/298/ > > I hope, somebody finds it useful in her/his courses. > > Any suggestions are welcomed. > > Robert Marik > > --------------- > code: > > x,y=var('x y') > html('<h2>Explaining approximation of a function in two \ > variables by differential</h2>') > html('Points x0 and y0 are values where the exact value of the > function \ > is known. Deltax and Deltay are displacements of the new point. Exact > value \ > and approximation by differential at shifted point are compared.') > @interact > def _(func=input_box('sqrt(x^3+y^3)',label="f(x,y)=",type=str), x0=1, > y0=2, \ > deltax=slider(-1,1,0.01,0.2),\ > deltay=slider(-1,1,0.01,-0.4), xmin=0, xmax=2, ymin=0, ymax=3): > f=sage_eval('lambda x,y: ' + func) > derx(x,y)=diff(f(x,y),x) > dery(x,y)=diff(f(x,y),y) > tangent(x,y)=f(x0,y0)+derx(x0,y0)*(x-x0)+dery(x0,y0)*(y-y0) > A=plot3d(f(x,y),(x,xmin,xmax),(y,ymin,ymax),opacity=0.5) > B=plot3d(tangent(x,y),(x,xmin,xmax), > (y,ymin,ymax),color='red',opacity=0.5) > C=point3d((x0,y0,f(x0,y0)),rgbcolor='blue',size=9) > CC=point3d((x0+deltax,y0+deltay,f > (x0+deltax,y0+deltay)),rgbcolor='blue',size=9) > D=point3d((x0+deltax,y0+deltay,tangent > (x0+deltax,y0+deltay)),rgbcolor='red',size=9) > exact_value_ori=f(x0,y0).n(digits=10) > exact_value=f(x0+deltax,y0+deltay) > approx_value=tangent(x0+deltax,y0+deltay).n(digits=10) > abs_error=(abs(exact_value-approx_value)) > html(r'Function $ f(x,y)=%s \approx %s $ '%(latex(f(x,y)),latex > (tangent(x,y)))) > html(r' $f %s = %s$'%(latex((x0,y0)),latex(exact_value_ori))) > html(r'Shifted point $%s$'%latex(((x0+deltax),(y0+deltay)))) > html(r'Value of the function in shifted point is $%s$'%f > (x0+deltax,y0+deltay)) > html(r'Value on the tangent plane in shifted point is $%s$'%latex > (approx_value)) > html(r'Error is $%s$'%latex(abs_error)) > show(A+B+C+CC+D) --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
