Smerova derivace

> restart:

> with(plots):

zadana funkce

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

> f1:=plot3d(fce(x,y),x=-Pi..Pi,y=-Pi..Pi,style=patchnogrid,lightmodel=light4, axes=frame, orientation=[41,61], scaling=constrained):

> bod:=[2/3,-1/10];

prusecik s funkci v bode [x,y]

> bod_z:=eval(eval(fce(x,y),x=bod[1]),y=bod[2]):

zobrazeni tohoto pruseciku

> bod_h:=implicitplot3d( (x-bod[1])^2 + (y-bod[2])^2 + (z-bod_z)^2 = 1/25,x=-Pi..Pi,y=-Pi..Pi,z=0..3,
color=black, grid=[50,50,50]):

smery

> smery:=[[1,1],[1/2,1],[0,1],[-1/2,1],[-1,1],[-1,1/2],[-1,0],[-1,-1/2],[-1,-1],[-1/2,-1],[0,-1],[1/2,-1],[1,-1],[1,-1/2],[1,0],[1,1/2]]:

> smery_h:=seq(limit((fce(bod[1]+t*smery[k][1], bod[2]+t*smery[k][2])-fce(bod[1],bod[2]))/t, t=0),k=1..16):

tecny v bode [x,y]

> tecny:=seq(spacecurve(evalm([bod[1],bod[2], fce(bod[1],bod[2])]+t*[smery[k][1],smery[k][2],smery_h[k]]), t=-2..2, thickness=3,color=red),k=1..16):

> tecny_h:=display(tecny, insequence=true):

plochy, kolme na osy x a y, obsahujici tecny

> plochy:=seq(plot3d([bod[1]+smery[k][1]*t, bod[2]+smery[k][2]*t,z], t=-Pi..Pi, z=0..3, grid=[24,12], style=wireframe, color=gray),k=1..16):

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

> display(bod_h, tecny_h,f1,plochy_h);

!!!pozor na prohozeni osy x a y