restart:
Neil Matula
Julia White
Math 253-202
Project 3 Divergence and Curl
Corrections by Yasskin:
Toodles!<3 >>>>> Quit
authors and copyright
reorganized layout and captions
Added div combine.
Combined curl combines
renamed several variables
new_function must clear boxes
with(Maplets[Tools]): with(Maplets[Elements]): with(plots):
StartEngine();
randomize():
great:=
["Good.",
"Cool.",
"Woohoo.",
"Teehee.",
"You da man(or woman).",
"Drinks are on you tonight.",
NULL
]:
randgreat:=rand(1..nops(great)):
bad:=
["Too bad.",
"Darn.",
"Game over. Please try again.",
NULL
]:
randbad:=rand(1..nops(bad)):
ps:=[x*y*z, y^2*z*x, exp(x*z^2), y^2*z^3*cos(x)]:
randps:=rand(1..nops(ps)):
qs:=[cos(y*z)^4, sin(2*x+y^3), exp(x^3+2*z^2), x*y^3+y*z^2+x*z^10]:
randqs:=rand(1..nops(qs)):
rs:=[sin(x)+y^2*z^3, x^2+y, y*exp(x)+z^2]:
randrs:=rand(1..nops(rs)):
new_function:=proc()
global ps, qs, rs, randps, randqs, randrs, p, q, r:
p:=ps[randps()]:
q:=qs[randqs()]:
r:=rs[randrs()]:
Set('nfMML'=MathML[Export]([p,q,r]));
Set(dpdxANS="");
Set(dqdyANS="");
Set(drdzANS="");
Set(divANS="");
Set(drdyANS="");
Set(dqdzANS="");
Set(drdxANS="");
Set(dpdzANS="");
Set(dqdxANS="");
Set(dpdyANS="");
Set(fini=""):
Set(finj=""):
Set(fink=""):
Set(dpdxCK="");
Set(dqdyCK="");
Set(drdzCK="");
Set(drdyCK="");
Set(dqdzCK="");
Set(drdxCK="");
Set(dpdzCK="");
Set(dqdxCK="");
Set(dpdyCK="");
Set(reply="")
end proc:
divx:=proc()
global dpdx,dpdxCK,dpdxANSW,dpdxANS;
dpdx:=diff(p,x);
dpdxANSW:=Get(dpdxANS::anything);
if simplify(normal(dpdxANSW-dpdx))=0 then
Set(dpdxCK="correct");
Set(reply=great[randgreat()])
else
Set(dpdxCK="incorrect");
Set(reply=bad[randbad()])
end if;
end proc:
divxs:=proc()
Set(dpdxANS=diff(p,x));
end proc:
divy:=proc()
global dqdy, dqdyCK, dqdyANSW, dqdyANS;
dqdy:=diff(q,y);
dqdyANSW:=Get(dqdyANS::anything);
if simplify(normal(dqdyANSW-dqdy))=0 then
Set(dqdyCK="correct"),
Set(reply=great[randgreat()])
else
Set(dqdyCK="incorrect"),
Set(reply=bad[randbad()])
end if:
end proc:
divys:=proc()
Set(dqdyANS=diff(q,y)):
end proc:
divz:=proc()
global drdz, drdzCK, drdzANSW, drdzANS:
drdz:=diff(r,z):
drdzANSW:=Get(drdzANS::anything):
if simplify(normal(drdzANSW-drdz))=0 then
Set(drdzCK="correct"),
Set(reply=great[randgreat()])
else
Set(drdzCK="incorrect"),
Set(reply=bad[randbad()])
end if:
end proc:
divzs:=proc()
Set(drdzANS=diff(r,z)):
end proc:
comdiv:=proc()
local dpdxANSW, dqdyANSW, drdzANSW:
dpdxANSW:=Get(dpdxANS::anything);
dqdyANSW:=Get(dqdyANS::anything);
drdzANSW:=Get(drdzANS::anything);
Set(divANS=simplify(dpdxANSW + dqdyANSW + drdzANSW)):
end proc:
curlyr:=proc()
global drdy, drdyANS, drdyANSW, drdyCK:
drdy:=diff(r,y):
drdyANSW:=Get(drdyANS::anything):
if simplify(normal(drdyANSW-drdy))=0 then
Set(drdyCK="correct"),
Set(reply=great[randgreat()])
else
Set(drdyCK="incorrect"),
Set(reply=bad[randbad()])
end if:
end proc:
curlyrs:=proc()
Set(drdyANS=diff(r,y)):
end proc:
curlzq:=proc()
global dqdz, dqdzANS, dqdzANSW, dqdzCK:
dqdz:=diff(q,z):
dqdzANSW:=Get(dqdzANS::anything):
if simplify(normal(dqdzANSW-dqdz))=0 then
Set(dqdzCK="correct"),
Set(reply=great[randgreat()])
else
Set(dqdzCK="incorrect"),
Set(reply=bad[randbad()])
end if:
end proc:
curlzqs:=proc():
Set(dqdzANS=diff(q,z)):
end proc:
curlzp:=proc()
global dpdz, dpdzANS, dpdzANSW, dpdzCK:
dpdz:=diff(p,z):
dpdzANSW:=Get(dpdzANS::anything):
if simplify(normal(dpdzANSW-dpdz))=0 then
Set(dpdzCK="correct"),
Set(reply=great[randgreat()])
else
Set(dpdzCK="incorrect"),
Set(reply=bad[randbad()])
end if:
end proc:
curlzps:=proc()
Set(dpdzANS=diff(p,z)):
end proc:
curlxr:=proc()
global drdx, drdxANS, drdxANSW, drdxCK:
drdx:=diff(r,x):
drdxANSW:=Get(drdxANS::anything):
if simplify(normal(drdxANSW-drdx))=0 then
Set(drdxCK="correct"),
Set(reply=great[randgreat()])
else
Set(drdxCK="incorrect"),
Set(reply=bad[randbad()])
end if:
end proc:
curlxrs:=proc()
Set(drdxANS=diff(r,x)):
end proc:
curlxq:=proc()
global dqdx, dqdxANS, dqdxANSW, dqdxCK:
dqdx:=diff(q,x):
dqdxANSW:=Get(dqdxANS::anything):
if simplify(normal(dqdxANSW-dqdx))=0 then
Set(dqdxCK="correct"),
Set(reply=great[randgreat()])
else
Set(dqdxCK="incorrect"),
Set(reply=bad[randbad()])
end if:
end proc:
curlxqs:=proc()
Set(dqdxANS=diff(q,x)):
end proc:
curlyp:=proc()
global dpdy, dpdyANS, dpdyANSW, dpdyCK:
dpdy:=diff(p,y):
dpdyANSW:=Get(dpdyANS::anything):
if simplify(normal(dpdyANSW-dpdy))=0 then
Set(dpdyCK="correct"),
Set(reply=great[randgreat()])
else
Set(dpdyCK="incorrect"),
Set(reply=bad[randbad()])
end if:
end proc:
curlyps:=proc()
Set(dpdyANS=diff(p,y)):
end proc:
comcurl:=proc()
local yrANS, zqANS, zpANS, xrANS, ypANS, xqANS:
yrANS:=Get(drdyANS::anything):
zqANS:=Get(dqdzANS::anything):
xrANS:=Get(drdxANS::anything):
zpANS:=Get(dpdzANS::anything):
xqANS:=Get(dqdxANS::anything):
ypANS:=Get(dpdyANS::anything):
Set(fini=simplify(yrANS-zqANS)):
Set(finj=simplify(xrANS-zpANS)):
Set(fink=simplify(xqANS-ypANS)):
end proc:
DivCurl:=Maplet(onstartup = RunWindow(MAIN),
Window[MAIN]('title'="Divergence and Curl",
[ halign=none,
[ halign=none,
Button("New function", Evaluate(function = "new_function")),
HorizontalGlue(),
Button("Quit", Shutdown())],
[ halign=none, border=true,
caption="Find the Divergence and Curl of the vector field:",
"F = [P,Q,R] =",
MathMLViewer[nfMML](width=400, height=30),
HorizontalGlue()
],
[ halign=none, inset=0,
[ halign=none, valign=none, border=true,
caption="Divergence",
"Div F = dP/dx + dQ/dy + dR/dz",
BoxColumn( halign=none, valign=none, border=true, spacing=0,
[ "dP/dx =",
TextField['dpdxANS']('width'=15)
],
[ Button("Check",Evaluate(function="divx")),
TextField['dpdxCK']('width'=5),
Button("Show",Evaluate(function="divxs"))
]
),
BoxColumn( halign=none, valign=none, border=true, spacing=0,
[ "dQ/dy =",
TextField['dqdyANS']('width'=15)
],
[ Button("Check",Evaluate(function="divy")),
TextField['dqdyCK']('width'=5),
Button("Show",Evaluate(function="divys"))
]
),
BoxColumn( halign=none, valign=none, border=true, spacing=0,
[ "dR/dz =",
TextField['drdzANS']('width'=15)
],
[ Button("Check",Evaluate(function="divz")),
TextField['drdzCK']('width'=5),
Button("Show",Evaluate(function="divzs"))
]
),
BoxColumn( halign=none, valign=none, border=true, spacing=0,
caption="Combine",
[ "Div F =",
TextField['divANS']('width'=15, editable=false)
],
[ Button("Combine",Evaluate(function="comdiv"))
]
)
],
[ halign=none, valign=none, border=true,
caption="Curl",
"Curl F = (dR/dy - dQ/dz) i - (dR/dx - dP/dz) j + (dQ/dx - dP/dy) k",
[ halign=none, valign=none, inset=0, spacing=0,
BoxColumn( halign=none, valign=none, border=true, spacing=0,
[ "dR/dy =",
TextField['drdyANS']('width'=15)
],
[ Button("Check",Evaluate(function="curlyr")),
TextField['drdyCK']('width'=5),
Button("Show",Evaluate(function="curlyrs"))
]
),
BoxColumn( halign=none, valign=none, border=true, spacing=0,
[ "dQ/dz =",
TextField['dqdzANS']('width'=15)
],
[ Button("Check",Evaluate(function="curlzq")),
TextField['dqdzCK']('width'=5),
Button("Show",Evaluate(function="curlzqs"))
]
)
],
[ halign=none, valign=none, inset=0, spacing=0,
BoxColumn( halign=none, valign=none, border=true, spacing=0,
[ "dR/dx =",
TextField['drdxANS']('width'=15)
],
[ Button("Check",Evaluate(function="curlxr")),
TextField['drdxCK']('width'=5),
Button("Show",Evaluate(function="curlxrs"))
]
),
BoxColumn( halign=none, valign=none, border=true, spacing=0,
[ "dP/dz =",
TextField['dpdzANS']('width'=15)
],
[ Button("Check",Evaluate(function="curlzp")),
TextField['dpdzCK']('width'=5),
Button("Show",Evaluate(function="curlzps"))
]
)
],
[ halign=none, valign=none, inset=0, spacing=0,
BoxColumn( halign=none, valign=none, border=true, spacing=0,
[ "dQ/dx =",
TextField['dqdxANS']('width'=15)
],
[ Button("Check",Evaluate(function="curlxq")),
TextField['dqdxCK']('width'=5),
Button("Show",Evaluate(function="curlxqs"))
]
),
BoxColumn( halign=none, valign=none, border=true, spacing=0,
[ "dP/dy =",
TextField['dpdyANS']('width'=15)
],
[ Button("Check",Evaluate(function="curlyp")),
TextField['dpdyCK']('width'=5),
Button("Show",Evaluate(function="curlyps"))
]
)
],
[ halign=none, valign=none, inset=0, spacing=0,
BoxColumn( halign=none, valign=none, border=true, spacing=0,
caption="Combine",
[ "Curl F = (",
TextField['fini']('width'=15, editable=false),
") i - (",
TextField['finj']('width'=15, editable=false),
") j + (",
TextField['fink']('width'=15, editable=false),
") k"
],
[ Button("Combine",Evaluate(function="comcurl"))
]
)
]
]
],
[TextField['reply']('width'=40)
],
[ halign=none, background="#DDFFFF", inset=0, spacing=0,
"Programmers: Neil Matula and Julia White",
HorizontalGlue(),
"\302\251 Copyright: P. Yasskin 2006"
]
]
)
):
Maplets[Display]( DivCurl );