Geometricky vyznam parcialnich derivaci

> restart:

> with(plots):

zadana funkce

> fce:=(x,y)->3*(sin(x)*sin(y)/(x*y));

> f1:=plot3d(fce(x,y),x=-2..2,y=-2..2,style=patchnogrid,lightmodel=light2, scaling=constrained, orientation=[-51,67]):

souradnice z pruseciku v bode [x,y]

> bod_xy:=seq([-2+10*k/31,-2+10*k/31],k=1..12):

> bod_z:=seq(eval(eval(fce(x,y),x=bod_xy[k][1]),y=bod_xy[k][2]),k=1..12):

> body:=seq([bod_xy[k][1],bod_xy[k][2],bod_z[k]],k=1..12):

sekvence zobrazeni techto pruseciku

> body_pos:=seq(implicitplot3d( (x-body[k][1])^2 + (y-body[k][2])^2 + (z-body[k][3])^2 = 1/60,x=-2..2,y=-2..2,z=0..31/10,
color=black, grid=[40,40,40]),k=1..12):

vykreslovani pruseciku

> body_p:=display(body_pos,insequence=true):

> vysl_b:=[seq(body_pos[13-k],k=2..11),seq(body_pos[k],k=1..12)]:

> vysl_body:=display(vysl_b,insequence=true):

tecna v bode [x,y,z]

> smerx:=seq(limit((fce(body[k][1]+h,body[k][2])-fce(body[k][1],body[k][2]))/h,h=0),k=1..12):

> tecna:=seq(spacecurve(evalm([body[k][1],body[k][2],fce(body[k][1],body[k][2])]+t*[1,0,smerx[k]]), t=-1..1, color=brown, thickness=3),k=1..12):

> tecna_p:=display(tecna, insequence=true):

> vysl_t:=[seq(tecna[13-k],k=2..11),seq(tecna[k],k=1..12)]:

> vysl_tecny:=display(vysl_t,insequence=true):

plochy, kolme na osy x a y, obsahujici tecny

> plochy:=seq(plot3d([body[k][1]+1*t, body[k][2]+0*t,z], t=-1..1, z=0..3, grid=[12,12], style=wireframe, thickness=2,color=gray),k=1..12):

> plochy_p:=display(plochy,insequence=true):

> vysl_p:=[seq(plochy[13-k],k=2..11),seq(plochy[k],k=1..12)]:

> vysl_plochy:=display(vysl_p,insequence=true):

vysledna animace

> display(f1,vysl_body, vysl_tecny, vysl_plochy);

>