Taylorova veta, aproximace fce f(x,y)

> restart:

> with(plots):

> f:=(x,y)->sin(x)*sin(y);

zobrazeni fce f(x,y)

> fce:=plot3d(f(x,y), x=-Pi..Pi, y=-Pi..Pi, orientation=[45,60], style=contour, color=red):

nacteni knihovny mtaylor

> readlib(mtaylor):

vytvoreni taylorovych aproximaci 1..15 radu

> tayloruvpom:=seq(mtaylor(f(x,y), [x=0,y=0], 2*k),k=1..8):

> tayloruv:=seq(unapply(tayloruvpom[k],x,y),k=1..8):

zobrazeni textu

> vysl:=seq(plot3d(tayloruv[k](x,y), x=-Pi..Pi, y=-Pi..Pi, orientation=[45,60], style=patchcontour),k=1..8):

> tayl:=display(vysl, insequence=true, view=-2..2):

> display(fce,tayl, view=-2..2);

> chyba:=seq((abs(tayloruvpom[i]-f(x,y))),i=1..8):

> chybap:=seq(plot3d(chyba[i],x=-Pi..Pi, y=-Pi..Pi),i=1..8):

> display(chybap,insequence=true,view=-2..2);