Handleiding Maple 10 Hoofdstuk 2 Grafieken Versie Maple 10

x^2+y^2; Klik met de rechter muis op de formule in de uitvoer, kies dan op Plots en vervolgens op Plot Builder. Er komt dan een applet tevoorschijn waarin de instellingen mogelijk zijn die je wilt. De instellingen worden vertaald naar de volgende inputregel waarna eventueel editen tot de mogelijkheden behoort. plot3d(x^2+y^2, x = -5 .. 5, y = -5 .. 5, axes = boxed, title = "voorbeeld", axis[1] = [mode = linear, color = COLOR(RGB,0,1/5,1)], axis[2] = [mode = linear, color = COLOR(RGB,0,1/5,1)], orientation = [50, 60]); plot3d(x^2+y^2, x = -5 .. 5, y = -5 .. 5, axes = boxed, title = "voorbeeld", axis[1] = [mode = linear, color = COLOR(RGB,0,1/5,1)], axis[2] = [mode = linear, color = COLOR(RGB,0,1/5,1)]); plot3d(x^2+y^2, x = -5 .. 5, y = -5 .. 5, axes = boxed, title = "voorbeeld", axis[1] = [mode = linear, color = COLOR(RGB,0,1/5,1)], axis[2] = [mode = linear, color = COLOR(RGB,0,1/5,1)]); plot3d(x^2+y^2, x = -5 .. 5, y = -5 .. 5);

with(plots): Interactive(x^2+y^2); Het commando interactive mag ook met een kleine letter. Met deze manier om de Plot Builder te bereiken, krijg je alleen de figuur in de uitvoer na Plot en niet de invoerregel voor het script van de figuur maar wel als je op Command klikt.

restart; f:=sin(x)*exp(-x/4); plot(f,x=0..10);

restart;f:=sin(x)*exp(-x/4): g:=exp(-x/4); h:=-exp(-x/4); plot({f,g,h},x=0..10); plot([f,g,h],x=0..10,color=[yellow,green,red]);

restart; plot([Heaviside(t),1.5*Heaviside(t-1),sin(t)*Heaviside(t-2)],t=-1..5,thickness=2);

with(plots):p1:=plot([Heaviside(t),1.5*Heaviside(t-1),sin(t)*Heaviside(t-2)],t=-1..5,color=black,linestyle=2): p1a:=plot([Heaviside(t),1.5*Heaviside(t-1),sin(t)*Heaviside(t-2)],t=-1..5,color=black,thickness=2,discont=true): p2:=textplot([2,1.35,"1.5 Heaviside(t-1)"],align={ABOVE,RIGHT}): p3:=textplot([3.38,0.85,"Heaviside(t)"],align={ABOVE,RIGHT}): p4:=textplot([2.9,0.37,"sin(t) Heaviside(t-2)"],align={ABOVE,RIGHT}): display({p1,p1a,p2,p3,p4});

restart:f:=PIECEWISE([0,x<0],[x^2,x<=1],[1,1<x]); plot(f,x=-1..3); convert(f,Heaviside);

restart;f:=abs(x^2-3*x-5); plot(f,x=-4..6); convert(f,piecewise);

plot(f,x=-4..6,color=black,thickness=2,title="absolutewaardefunctie: | f(x) |");

restart; x:=t^3-3*t; y:=t^2-1; plot([x,y,t=-3..3]); plot([[x,y,t=-3..3],[t,t,t=-3..8]],color=black,thickness=[1,2]);

with(plots):p1:=plot([[x,y,t=-3..3],[t,t,t=-3..8]],color=black,thickness=[1,2]): p2:=plot({[subs(t=3,x),subs(t=3,y)],[subs(t=-1,x),subs(t=-1,y)],[subs(t=0,x),subs(t=0,y)],[subs(t=sqrt(3),x),subs(t=sqrt(3),y)],[subs(t=-3,x),subs(t=-3,y)]},style=point,symbolsize=20,color=black):p3:=textplot({[subs(t=3,x)+1,subs(t=3,y),"t=3"],[subs(t=-3,x)+1,subs(t=-3,y),"t=-3"],[subs(t=-1,x)+1,subs(t=-1,y),"t=-1"],[subs(t=sqrt(3),x)+1,subs(t=sqrt(3),y),"t=sqrt(3) of t=-sqrt(3)"]},align={RIGHT,ABOVE},color=black):p4:=textplot([subs(t=0,x)+1,subs(t=0,y),"t=0"],align={RIGHT,BELOW}): display({p1,p2,p3,p4},title="parameterkromme met parameter t die loopt van t=-3 tot t=3");

restart; x:=1-t^2; y:=2^t; with(plots): animatecurve([x,y,t=-3..3]);

restart; interface(warnlevel=0): with(plots): x,y,z:=t^3-3*t,t^2-1,t; spacecurve([x,y,z],t=-3..3,thickness=4,axes=boxed,labels=[X,Y,Z],color=black,orientation=[75,80]); tubeplot([x,y,z],t=-3..3,labels=[X,Y,Z],radius=0.4,axes=boxed,orientation=[75,80],labelfont=[TIMES,BOLDITALIC,12],title="Ruimtekromme");

restart; interface(warnlevel=0):with(plots): R1 := cos(2*phi); R2:=2*exp(-phi/4); polarplot([R1,phi,phi=0..2*Pi],color=black,scaling=constrained); polarplot([[R1,phi,phi=-Pi/4..Pi/4],[R1,phi,phi=3*Pi/4..5*Pi/4], [r2,phi,phi=0..2*Pi]],color=[red,blue,green],thickness=[1,1,2],scaling=constrained);

restart; interface(warnlevel=0):with(plots): R1 := cos(2*phi); R2:=2*exp(-phi/4); p1:=polarplot([[R1,phi,phi=-Pi/4..Pi/4],[R1,phi,phi=3*Pi/4..5*Pi/4], [R2,phi,phi=0..2*Pi]],color=[red,blue,green],thickness=[1,1,2],scaling=constrained): p2:=textplot({[1.21,1.21,"R2"],[0.48,0.31,"R1 (deel 1)"],[-0.72,0.34,"R1 (deel 2)"]},align={RIGHT,ABOVE}): display({p1,p2},title="meer polarplot-grafieken in \303\251\303\251n figuur",color=black);

restart; interface(warnlevel=0):with(plots): r:=2*sqrt(2*cos(2*phi)); polarplot([r,phi,phi=0..2*Pi],numpoints=1000, scaling=constrained,style=point); polarplot([r,phi,phi=0..2*Pi], scaling=constrained,style=point); polarplot([r,phi,phi=0..2*Pi], scaling=constrained,style=point,adaptive=false);

restart;interface(warnlevel=0): with(plots): r:=exp(-phi/4): phi:=0.5+2*t; polarplot([r,phi,t=0..10],scaling=constrained);

restart;interface(warnlevel=0): with(plots): r:=exp(-phi/4); phi:=0.5+2*t; p1:=polarplot([r,phi,t=0..10],scaling=constrained,color=black,thickness=2,title="polaire figuur van r(phi) waarbij de hoek een functie is van de tijd en t loopt van 0 tot 10"): p2:=textplot([0.7,0.4,"t = 0"]): display({p1,p2});

restart; with(plots): polarplot([3,phi,phi=0..2*Pi],scaling=constrained);

restart; with(plots): C:=y^2*(x+1)=x^2-y; smartplot[x, y]( C ); implicitplot(C,x=-2..10,y=-4..4,title=" impliciete functie",color=black);

restart; interface(warnlevel=0):with(plots): C:=1/4*x^2+y^2=2; implicitplot(C,x=-10..10,y=-10..10,scaling=constrained);

implicitplot(C,x=-10..10,y=-10..10,scaling=constrained,color=black,thickness=2, title="Ellips geplot in een te groot interval zodat deze hoekig wordt");

Voorbeeld 2.18 Ruimte-figuur van de functie f(x,y)=x\302\262y tesamen met het 0-niveau restart; f:=x^2*y; plot3d({f,0},x=-10..10,y=-10..10,axes=boxed,title="Ruimtefiguur met nul-niveau",orientation=[30,75]); plot3d(Vector([x,y,f]),x=-10..10,y=-10..10,axes=boxed,title="Ruimtefiguur",orientation=[30,75]);

restart; with(plots):f:=x^2-2*x^2*y+3*y^2; contourplot3d(f,x=-4..4,y=-4..4,axes=boxed,filled=true,coloring=[blue,white],contours=25,orientation=[21,60],labels=[X,Y,Z]); C:=seq(f=10*k,k=1..3); implicitplot({C},x=-4..4,y=-4..4); plot3d(f,x=-4..4,y=-4..4,axes=boxed,style=patchcontour,contours=25, orientation=[21,60],labels=[X,Y,Z]);

Student:-MultivariateCalculus:-CrossSectionTutor();

restart;with(plots): C:=x^3-3*x*y^2=1; r:=6-5*cos(phi); p1:=implicitplot(C,x=-5..5,y=-5..5,thickness=3,color=black,legend="impliciete functie"): p2:=polarplot([r,phi,phi=0..2*Pi],linestyle=4,color=black,legend="functie in poolco\303\266rdinaten"): display({p1,p2},title="Twee verschillende soorten grafieken");

restart; with(plots): f:=5*x-2*y; y1:=solve(f=0,y); p1:=plot3d(f,x=0..1,y=0..1): p2:=plot3d(0,x=0..1,y=0..1,color=gray,style=patchnogrid): p3:=spacecurve([x,y1,0],x=0..1,thickness=5,color=black, view=[0..1,0..1,-5..5],orientation=[-107,45]): p4:=textplot3d({[0.25,1,0.5,"snijlijn"]},color=black,font=[TIMES,ITALIC,14]): display({p1,p2,p3,p4},axes=boxed,labels=[X,Y,Z]);

restart; interface(warnlevel=0): with(plots): f:=(1-2*x)/(x+1); plot(f,x=-3..4,view=[-3..4,-15..15]); plot(f,x=-3..4,y=-15..15,discont=true,title="discontinue functie"); p1:=plot(f,x=-3..4,y=-15..15,linestyle=2): p2:=plot(f,x=-3..4,y=-15..15,discont=true,color=black,discont=true, thickness=2): display({p1,p2},title="discontinue functie met verticale asymptoot");

restart; interface(warnlevel=0):with(Student): with(Precalculus): with(Calculus1): f:=(3*x^2+2*x-1)/(x+2); RationalFunctionPlot(f,view=[-6..6, -30..30]); with(Calculus1): Asymptotes(f, x);

restart; f:=y/(x^2+y^3); plot3d(f,x=0..2,y=0..2,view=[0..2,0..2,0..15],axes=boxed, orientation=[-125,65] );

restart; with(plots): animatecurve((x^2+1)/(x-1),x=-10..10,view=[-10..10,-10..10],style=point);

with(plots): animatecurve({x-x^3,sin(x)},x=0..Pi/2);

restart; with(plots):animatecurve({x-x^3,sin(x)},x=0..Pi/2,color=black); p1:=animatecurve( x-x^3, x=0..Pi/2,color=blue,thickness=3 ): p2:=animatecurve(sin(x),x=0..Pi/2,color=red, thickness=1,labels=["X","Y"]): display({p1,p2},title="twee grafieken die worden doorlopen als x toeneemt");

with(plots):animatecurve([t-t^3,sin(t),t=0..Pi/2],color=black, thickness=2,frames=50);

with(plots): r:=1-cos(phi); animatecurve([r,phi,phi=0..2*Pi],coords=polar);

restart;with(plots): f:=A*sin(x); animate(plot,[f,x=0..2*Pi],A=1..3);

restart;with(plots): f:=A*sin(x); animate(plot,[f,x=0..2*Pi],A=1..3); OptiesGrafiek:=color=black,thickness=2,labels=[X,Amplitude], labeldirections=[horizontal,vertical], title="Amplitude A van de sinus wordt groter"; achtergrond:=plot(sin(x),x=0..2*Pi,linestyle=2,color=red): animate(plot,[A*sin(x),x=0..2*Pi,OptiesGrafiek],A=1..3,background=achtergrond,frames=30);

restart; interface(warnlevel=0):with(plots): f:=1/((x-t)^2+(y-t)^2+1); PlotOpties:=axes=boxed,orientation=[110,50],style=patchnogrid, title="Muis onder het kleed"; animate(plot3d,[f,x=-5..5,y=-5..5,PlotOpties],t=-5..5);

restart; with(plots): f:=(x^2+1)/(x-1); achtergrond:=plot([1,t,t=-10..10],linestyle=2,color=red): animate(plot,[f,x=-10..A,-10..10,discont=true,thickness=2,color=blue] ,A=-10..10,background=achtergrond);

restart; interface(warnlevel=0): with(plots): v:=[2*cos(t),3*sin(2*t),2*t]; N:=20; P:=seq(spacecurve(v,t=0..2*Pi/N*k,thickness=2,title=cat("Het punt is ",convert(evalf[4](subs(t=2*Pi/N*k,v)),string))),k=1..N): display([P],insequence=true,orientation=[-55,75],axes=boxed,labels=[X ,Y,Z]);

restart; with(Student); with(Calculus1): TangentTutor();

with(Student[VectorCalculus]): SpaceCurveTutor(); ?TangentVector

restart; interface(warnlevel=0): with(plots): a,b,c:=<-2, 1>,<5, 2>,<3, 3>; plaat1:=arrow({a,b,c},shape=arrow,thickness=2,color=green): plaat2:=textplot({[-2,1,A]},align={ABOVE,LEFT},font=[TIMES,BOLDITALIC,14]): plaat3:=textplot({[5,2,B],[3,3,C]},align={ABOVE,RIGHT},font=[TIMES,BOLDITALIC,14]): plaat4:=arrow(a,b,shape=double_arrow,color=blue): display({plaat1,plaat2,plaat3,plaat4},scaling=constrained,title="pijlen"); Hier even onderscheid maken tussen A en de andere letters. Let ook op dubbele pijl, en font.

restart; Digits:=4; interface(warnlevel=0):with(plots): punten:=[seq([i/5,evalf(sin(2*Pi*i/5))],i=0..5)]; p1:=plot(sin(2*Pi*t),t=0..1,thickness=2): p2:=plot(punten,style=point,symbol=circle,color=black,symbolsize=12): p3:=plot(punten,color=black,linestyle=2): display({p1,p2,p3});