Direction Fields
Sarah Jones & Lindsay Turnerrestart:with(Maplets[Tools]): with(Maplets[Elements]):
with(plots):with(DEtools):with(combinat,randperm):
StartEngine();randomize():lightorange:="#FFB300":Fns:=[
x+y, x-y, y-x, -x-y,
x^2+y, x^2-y, y-x^2, -x^2-y,
x+y^2, x-y^2, y^2-x, -x-y^2,
x^2+y^2, x^2-y^2, y^2-x^2, -x^2-y^2,
x*y, x/y, y/x, 1/x/y,
-x*y, -x/y, -y/x, -1/x/y,
x^2*y, x^2/y, y/x^2, 1/x^2/y,
-x^2*y, -x^2/y, -y/x^2, -1/x^2/y,
x*y^2, x/y^2, y^2/x, 1/x/y^2,
-x*y^2, -x/y^2, -y^2/x, -1/x/y^2,
NULL
];Ask_Question:=proc()
global Fns, ans;
local rand_Fns, rand_ans, RHS, p1, p2, p3, p4, i;
rand_Fns:=randperm(nops(Fns));
RHS[1]:=Fns[rand_Fns[1]];
RHS[2]:=Fns[rand_Fns[2]];
RHS[3]:=Fns[rand_Fns[3]];
RHS[4]:=Fns[rand_Fns[4]];
rand_ans:=randperm(4);
for i from 1 to 4 do
if rand_ans[i]=1 then
ans:=i;
end if;
end do;
Set(MMLequation(value)=MathML[Export](diff(y(x),x)=RHS[1]));
p1:=DEplot(diff(y(x),x)=subs(y=y(x),RHS[rand_ans[1]]),y(x),x=-3..3,y=-3..3);
p2:=DEplot(diff(y(x),x)=subs(y=y(x),RHS[rand_ans[2]]),y(x),x=-3..3,y=-3..3);
p3:=DEplot(diff(y(x),x)=subs(y=y(x),RHS[rand_ans[3]]),y(x),x=-3..3,y=-3..3);
p4:=DEplot(diff(y(x),x)=subs(y=y(x),RHS[rand_ans[4]]),y(x),x=-3..3,y=-3..3);
Set(PL1=p1);
Set(PL2=p2);
Set(PL3=p3);
Set(PL4=p4);
Set(RP1=false);
Set(RP2=false);
Set(RP3=false);
Set(RP4=false);
Set(PlotComment=""):
end proc:Check_Answer:=proc()
global ans;
local plotans;
plotans:=0;
if Get(RP1) then plotans:=1 end if;
if Get(RP2) then plotans:=2 end if;
if Get(RP3) then plotans:=3 end if;
if Get(RP4) then plotans:=4 end if;
if plotans=0 then
Set(PlotComment="Please select a plot.")
elif plotans=ans then
Set(PlotComment="Way to go! You answered correctly!"):
else
Set(PlotComment="Oops! Try again. "):
end if;
end proc:Show_Answer:=proc()
global ans;
if ans=1 then Set(RP1=true) end if;
if ans=2 then Set(RP2=true) end if;
if ans=3 then Set(RP3=true) end if;
if ans=4 then Set(RP4=true) end if;
end proc:DirectionFields:=Maplet(onstartup=RunWindow(MAIN),
Window[MAIN](title="Reflections of Functions",
[ [ Button("New Differential Equation", Evaluate(function="Ask_Question"), background=magenta),
HorizontalGlue(),
Button("Quit", Shutdown(), background=pink)
],
[ "Find the direction field of the differential equation:",
MathMLViewer[MMLequation](width=200,height=50)
],
[ halign=none, inset=0, spacing=0,
[ background=wheat,
Plotter[PL1](plot1, width=200, height=200),
RadioButton[RP1]("Plot # 1", value=false, group=BG1, background=tan)
],
[ background=wheat,
Plotter[PL2](plot2, width=200, height=200),
RadioButton[RP2]("Plot # 2", value=false, group=BG1, background=tan)
],
[ background=wheat,
Plotter[PL3](plot3, width=200, height=200),
RadioButton[RP3]("Plot # 3", value=false, group=BG1, background=tan)
],
[ background=wheat,
Plotter[PL4](plot4, width=200, height=200),
RadioButton[RP4]("Plot # 4", value=false, group=BG1, background=tan)
]
],
[ Button("Check",Evaluate(function="Check_Answer"), background=green),
Button("Show", Evaluate(function="Show_Answer"), background=lightorange),
TextBox[PlotComment]("", width=40)
],
[ "Programmers: Sarah Jones & Lindsay Turner",
HorizontalGlue(),
"@ Copyright P. Yasskin 2007"
]
]
),
ButtonGroup[BG1]()
):Maplets[Display](DirectionFields):