Bryan Layton & Oscar Carrasco-ZevallosPower Series: Interval of ConvergenceTA: Yang QiProfessor: Dr. Philip Yasskin152-202restart:with(Maplets[Tools]): with(Maplets[Elements]):
StartEngine();randomize():lightorange:="#FFB300":
lightcyan:="#DDFFFF":ColorFooter:=lightcyan:
FontFooter:=Font("helvetica",10):coeffic:=[n^a/n!,p^n/n!, p^n/n^a, 1/n^a, 1/n!, n!/p^n]:#I wanted to replace the coeffic list by the following to reduce the nummber
#of factorials, but it messed up several other computations.
#coeffic:=[n^a/n!, n!/n^a, p^n/n!, n!/p^n, p^n/n^a, n^a/p^n,
# n^a, 1/n^a, p^n, 1/p^n, p^n*n^a, 1/p^n*n^a]:rcoeffic:=rand(1..nops(coeffic)):randa:=rand(-3..3):ps:=[-3,-2,-1,1,2,3,-1/3,-1/2,1/2,1/3,1/4]:rps:=rand(1..nops(ps)):randc:=rand(-5..5):ask:=proc()
global start, p, a, c, ser, R, ps, rps, cif, i1, i2, cn, leftser, rightser, a1;
local whichp, p1, whichcoeffic;
c:=randc();
whichp:=rps();
p1:=ps[whichp];
a1:=randa();
whichcoeffic:=rcoeffic();
cn:=eval(coeffic[whichcoeffic],[a=a1,p=p1]);
cif:=coeffic[whichcoeffic];
while cif=coeffic[6] and p1=0 do
p1:=ps[rps];
end do;
if cif=coeffic[3] or cif=coeffic[4] or (cif=coeffic[1] and a1 < 0) then
start:=1;
else
start:=0;
end if;
ser:=Sum(cn*(x-c)^n,n=start..infinity);
Set(question=ser);
R:=limit(cn/subs(n=n+1,cn),n=infinity);
i1:=c - R;
i2:=c + R;
leftser:=Sum(cn*(-R)^n,n=start..infinity);
rightser:=Sum(cn*(R)^n,n=start..infinity);
Set(answer1="");
Set(answer2="");
Set(leftseries="Sum(a[n]*(x-c)^n,n=0..infinity)");
Set(rightseries="Sum(a[n]*(x-c)^n,n=0..infinity)");
Set(intervalleft="");
Set(intervalright="");
Set(RBleftparen=false);
Set(RBleftbrack=false);
Set(RBrightparen=false);
Set(RBrightbrack=false);
end proc:checkradius:=proc()
global R;
local userR;
userR:=Get(answer2::realcons):
if userR=abs(R)
then Set(reply="Correct! Try another question.")
else Set(reply="Incorrect. Try again.")
end if;
end proc:showradius:=proc()
global R;
Set(answer2=abs(R)):
Set(reply="Try another it yourself next time!")
end proc:checkcenter:=proc()
global c;
local userc;
userc:=Get(answer1::realcons):
if userc=c
then Set(reply="Correct! Try another question.")
else Set(reply="Incorrect. Try again.")
end if;
end proc:showcenter:=proc()
global c;
Set(answer1=c):
Set(reply="Try another it yourself next time!")
end proc:checkleft:=proc()
global leftser;
local userleft;
userleft:=Get(leftseries::function):
if userleft=leftser
then Set(reply="Correct! Try another question.")
else Set(reply="Incorrect. Try again.")
end if;
end proc:showleft:=proc()
global leftser;
Set(leftseries=leftser):
Set(reply="Try another it yourself next time!")
end proc:checkright:=proc()
global rightser;
local userright;
userright:=Get(rightseries::function):
if userright=rightser
then Set(reply="Correct! Try another question.")
else Set(reply="Incorrect. Try again.")
end if;
end proc:showright:=proc()
global rightser;
Set(rightseries=rightser):
Set(reply="Try another it yourself next time!")
end proc:checkinterval:=proc()
global i1, i2, cif, R, c, a1;
local useri1, useri2, rightans1, rightans2, userleftparen, userrightparen, userleftbrack, userrightbrack;
useri1:=Get(intervalleft::realcons):
useri2:=Get(intervalright::realcons):
if ((cif=coeffic[3]) or (cif=coeffic[4])) and (a1 > 1) then
userleftbrack:=Get(RBleftbrack::truefalse):
userrightbrack:=Get(RBrightbrack::truefalse):
if (useri1=i1) and (userleftbrack=true)
then rightans1:=true
else rightans1:=false
end if;
if (useri2=i2) and (userrightbrack=true)
then rightans2:=true
else rightans2:=false
end if;
end if;
if ((cif=coeffic[3]) or (cif=coeffic[4])) and ((a1=0) or (a1 < 0)) then
userleftparen:=Get(RBleftparen::truefalse):
userrightparen:=Get(RBrightparen::truefalse):
if (useri1=i1) and (userleftparen=true)
then rightans1:=true
else rightans1:=false
end if;
if (useri2=i2) and (userrightparen=true)
then rightans2:=true
else rightans2:=false
end if;
end if;
if ((cif=coeffic[3]) or (cif=coeffic[4])) and ((0 < a1) and ((a1 < 1) or (a1=1))) then
userleftbrack:=Get(RBleftbrack::truefalse):
userrightparen:=Get(RBrightparen::truefalse):
if (useri1=i1) and (userleftbrack=true)
then rightans1:=true
else rightans1:=false
end if;
if (useri2=i2) and (userrightparen=true)
then rightans2:=true
else rightans2:=false
end if;
end if;
if (cif=coeffic[3] or cif=coeffic[4]) and R < 0 then
if useri1=i2
then rightans1:=true
else rightans1:=false
end if;
if useri2=i1
then rightans2:=true
else rightans2:=false
end if;
end if;
if cif=coeffic[1] or cif=coeffic[2] or cif=coeffic[5] then
userleftparen:=Get(RBleftparen::truefalse):
userrightparen:=Get(RBrightparen::truefalse):
if (useri1=-1*R) and (userleftparen=true)
then rightans1:=true
else rightans1:=false
end if;
if (useri2=R) and (userrightparen=true)
then rightans2:=true
else rightans2:=false
end if;
end if;
if cif=coeffic[6] then
userleftbrack:=Get(RBleftbrack::truefalse):
userrightbrack:=Get(RBrightbrack::truefalse):
if (useri1=c) and (userleftbrack=true)
then rightans1:=true
else rightans1:=false
end if;
if (useri2=c) and (userrightbrack=true)
then rightans2:=true
else rightans2:=false
end if;
end if;
if rightans1=true and rightans2=true
then Set(reply="Correct! Try another question.")
else Set(reply="Incorrect. Try again.")
end if;
end proc:showinterval:=proc()
global i1, i2, cif, R, c, a1;
if ((cif=coeffic[3]) or (cif=coeffic[4])) and (a1 > 1) then
Set(intervalleft=i1):
Set(intervalright=i2):
Set(RBleftbrack=true):
Set(RBrightbrack=true):
end if;
if ((cif=coeffic[3]) or (cif=coeffic[4])) and ((0 < a1) and ((a1 < 1) or (a1=1))) then
Set(intervalleft=i1):
Set(intervalright=i2):
Set(RBleftbrack=true):
Set(RBrightparen=true):
end if;
if ((cif=coeffic[3]) or (cif=coeffic[4])) and ((a1=0) or (a1 < 0)) then
Set(intervalleft=i1):
Set(intervalright=i2):
Set(RBleftparen=true):
Set(RBrightparen=true):
end if;
if (cif=coeffic[3] or cif=coeffic[4]) and R < 0 then
Set(intervalleft=i2):
Set(intervalright=i1):
end if;
if cif=coeffic[1] or cif=coeffic[2] or cif=coeffic[5] then
Set(intervalleft=-R):
Set(intervalright=R):
Set(RBleftparen=true):
Set(RBrightparen=true):
end if;
if cif=coeffic[6] then
Set(intervalleft=c):
Set(intervalright=c):
Set(RBleftbrack=true):
Set(RBrightbrack=true):
end if;
Set(reply="Try another it yourself next time!"):
end proc:Preview:=proc(TFname)
global CurrentTFname;
local expr;
options `Copyright 2004-07, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
if Get(TFname)="" then
Set(reply="Please enter an expression to preview.");
return;
end if;
CurrentTFname:=TFname;
expr:=Get(TFname::anything, corrections=true, update=true);
Set(TFPreview=expr);
Set(MMLPreview=MathML[Export](expr));
Set(ARunPreview(run)=true);
end proc:Update_Preview:=proc()
global CurrentTFname;
local expr;
options `Copyright 2004-07, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
if Get(TFPreview)="" then
Set(reply="Please enter an expression to preview.");
return;
end if;
expr:=Get(TFPreview::anything, corrections=true, update=true);
Set(MMLPreview=MathML[Export](expr));
Set(CurrentTFname=expr);
end proc:PowerSeries:=Maplet(onstartup=RunWindow(MAIN),
Window[MAIN](title="Power Series: Interval of Convergence",
[ halign=none,
[ Button("New Series", Evaluate(function="ask"), background=magenta),
HorizontalGlue(),
Button("Quit", Shutdown(), background=pink)
],
[ inset=0,
[ border=true,
caption="Find the center, radius and inteval of convergence of the series:",
MathMLViewer[question](Sum(a[n]*(x-c)^n,n=0..infinity), width=300, height=60)
],
[ inset=0,
[ border=true,
caption="Enter the center:",
"C =",
TextField[answer1](width=5),
Button("Check", Evaluate(function="checkcenter"), background=green),
Button("Show", Evaluate(function="showcenter"), background=lightorange)
],
[ border=true,
caption="Enter the radius:",
"R =" ,
TextField[answer2](width=5),
Button("Check", Evaluate(function="checkradius"), background=green),
Button("Show", Evaluate(function="showradius"), background=lightorange)
]
]
],
[ border=true,
caption="Enter the series at the left endpoint:",
TextField[leftseries]("Sum(a[n]*(x-c)^n,n=0..infinity)", width=37),
HorizontalGlue(),
Button("Preview", onclick=APreleft, background=yellow),
Button("Check", Evaluate(function="checkleft"), background=green),
Button("Show", Evaluate(function="showleft"), background=lightorange)
],
[ border=true,
caption="Enter the series at the right endpoint:",
TextField[rightseries]("Sum(a[n]*(x-c)^n,n=0..infinity)", width=37),
HorizontalGlue(),
Button("Preview", onclick=APreright, background=yellow),
Button("Check", Evaluate(function="checkright"), background=green),
Button("Show", Evaluate(function="showright"), background=lightorange)
],
[ border=true, halign=none, inset=1,
caption="Enter the interval of convergence:",
HorizontalGlue(),
[ RadioButton[RBleftparen]("(", value=false, group=BGleft),
RadioButton[RBleftbrack]("[", value=false, group=BGleft)
],
TextField[intervalleft](width=8),
",",
TextField[intervalright](width=8),
[ RadioButton[RBrightparen](")", 'value'=false, 'group'='BGright'),
RadioButton[RBrightbrack]("]", 'value'=false, 'group'='BGright')
],
HorizontalGlue(),
Button("Check", Evaluate(function="checkinterval"), background=green),
Button("Show", Evaluate(function="showinterval"), background=lightorange)
],
[TextField[reply](width=40, editable=false) ],
[ halign=none, background=ColorFooter,
Label("Programmers: Bryan Layton & Oscar Carrasco-Zevallos", font=FontFooter),
HorizontalGlue(),
Label("Copyright: P. Yasskin 2008", font=FontFooter)
]
]
),
Window[PREVIEW]( title="Preview", defaultbutton=UpdatePreview,
[ halign=none,
[ TextField[TFPreview](width=50, background=turquoise),
Button[UpdatePreview]("Update", Evaluate(function="Update_Preview"), background=lightorange),
Button[ClosePreview]("Close", CloseWindow(PREVIEW), background=pink)
],
[ MathMLViewer[MMLPreview](value=MathML[Export](""), width=500, height=100)
]
]),
ButtonGroup[BGleft](),
ButtonGroup[BGright](),
Action[APreleft](Evaluate(function="Preview(leftseries)")),
Action[APreright](Evaluate(function="Preview(rightseries)")),
Action[ARunPreview](RunWindow(PREVIEW))
):Maplets[Display]( PowerSeries );