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{SECT 0 {PARA 208 "" 0 "" {TEXT 200 0 "" }{TEXT 200 0 "" }{TEXT 200 9 
"Maple Lab" }}{PARA 209 "" 0 "" {TEXT 200 6 "Week 9" }}{PARA 210 "" 0 
"" {TEXT 200 13 "Vector fields" }}{PARA 211 "" 0 "" {TEXT 200 0 "" }}
{PARA 0 "" 0 "" {TEXT 200 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 217 33 "
We will need these two libraries:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "with(VectorCalculus):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 0 "
" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 218 23 "2D and 3D vector fields" }}
{EXCHG {PARA 0 "" 0 "" {TEXT 200 105 "The fieldplot command allows you
 to plot two-dimensional vector fields.  Here's what you need to speci
fy:" }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}{PARA 212 "" 0 "" {TEXT 200 
13 "fieldplot( [ " }{TEXT 215 6 "P(x,y)" }{TEXT 200 3 " , " }{TEXT 
216 6 "Q(x,y)" }{TEXT 200 33 " ], x = a..b, y = c..d , options)" }}
{PARA 213 "" 0 "" {TEXT 200 0 "" }}{PARA 0 "" 0 "" {TEXT 200 35 "Consi
der the vector field given by " }{XPPEDIT 2 0 "Typesetting:-mrow(Types
etting:-mi(\"P\", italic = \"true\", mathvariant = \"italic\"), Typese
tting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x\", italic = \"tru
e\", mathvariant = \"italic\"), Typesetting:-mo(\",\", mathvariant = \+
\"normal\", fence = \"false\", separator = \"true\", stretchy = \"fals
e\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fal
se\", accent = \"false\", form = \"infix\", lspace = \"0em\", rspace =
 \"verythickmathspace\", minsize = \"1\", maxsize = \"infinity\"), Typ
esetting:-mi(\"y\", italic = \"true\", mathvariant = \"italic\")), mat
hvariant = \"normal\"), Typesetting:-mo(\"=\", mathvariant = \"normal
\", fence = \"false\", separator = \"false\", stretchy = \"false\", sy
mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a
ccent = \"false\", form = \"infix\", lspace = \"thickmathspace\", rspa
ce = \"thickmathspace\", minsize = \"1\", maxsize = \"infinity\"), Typ
esetting:-msup(Typesetting:-mi(\"x\", italic = \"true\", mathvariant =
 \"italic\"), Typesetting:-mrow(Typesetting:-mn(\"2\", mathvariant = \+
\"normal\")), superscriptshift = \"0\"), Typesetting:-mo(\"+\", mathva
riant = \"normal\", fence = \"false\", separator = \"false\", stretchy
 = \"false\", symmetric = \"false\", largeop = \"false\", movablelimit
s = \"false\", accent = \"false\", form = \"infix\", lspace = \"medium
mathspace\", rspace = \"mediummathspace\", minsize = \"1\", maxsize = \+
\"infinity\"), Typesetting:-msup(Typesetting:-mi(\"y\", italic = \"tru
e\", mathvariant = \"italic\"), Typesetting:-mrow(Typesetting:-mn(\"2
\", mathvariant = \"normal\")), superscriptshift = \"0\"), Typesetting
:-mo(\";\", mathvariant = \"normal\", fence = \"false\", separator = \+
\"true\", stretchy = \"false\", symmetric = \"false\", largeop = \"fal
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ow(Typesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")
, Typesetting:-mo(\",\", mathvariant = \"normal\", fence = \"false\", \+
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 = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \+
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e = \"1\", maxsize = \"infinity\"), Typesetting:-msup(Typesetting:-mi(
\"x\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mrow
(Typesetting:-mn(\"2\", mathvariant = \"normal\")), superscriptshift =
 \"0\"), Typesetting:-mo(\"&uminus0;\", mathvariant = \"normal\", fenc
e = \"false\", separator = \"false\", stretchy = \"false\", symmetric \+
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mediummathspace\", minsize = \"1\", maxsize = \"infinity\"), Typesetti
ng:-msup(Typesetting:-mi(\"y\", italic = \"true\", mathvariant = \"ita
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alse\", accent = \"false\", form = \"infix\", lspace = \"0em\", rspace
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modulenameG6\"I,TypesettingGI(_syslibGF'61-I#miGF$6%Q\"PF'/%'italicGQ%
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diummathspaceF'/FYFepFenFhn-Ffo6%F[oFhoF^p-F>60Q\";F'FAFCFFFHFJFLFNFPF
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Q\".F'FAFCFaoFHFJFLFNFPFRFUFaqFenFhn" }}{PARA 0 "" 0 "" {TEXT 200 42 "
To plot the field, we enter the following:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 49 "fieldplot([x^2+y^2,x^2-y^2],x=-10..10,y=-10..10);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT 200 229 "Of course, as with many other Maple commands, we have
 many options that we can add to the command in order to make the vect
or field easier to view.  Consider the same example, only this time, w
e shall add the alternative options." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 62 "fieldplot([x^2+y^2,x^2-y^2],x=-10..10,y=-10..10,arrow
s=THICK);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "fieldplot([x^2+y^2,x^2-y^2],x=-10..
10,y=-10..10,grid=[30,30]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 68 "T
he length of the arrows corresponds to the magnitude of the vector " }
{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow
(Typesetting:-mi(\"P\", italic = \"true\", mathvariant = \"italic\"), \+
Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x\", italic =
 \"true\", mathvariant = \"italic\"), Typesetting:-mo(\",\", mathvaria
nt = \"normal\", fence = \"false\", separator = \"true\", stretchy = \+
\"false\", symmetric = \"false\", largeop = \"false\", movablelimits =
 \"false\", accent = \"false\", form = \"infix\", lspace = \"0em\", rs
pace = \"verythickmathspace\", minsize = \"1\", maxsize = \"infinity\"
), Typesetting:-mi(\"y\", italic = \"true\", mathvariant = \"italic\")
), mathvariant = \"normal\"), Typesetting:-mo(\",\", mathvariant = \"n
ormal\", fence = \"false\", separator = \"true\", stretchy = \"false\"
, symmetric = \"false\", largeop = \"false\", movablelimits = \"false
\", accent = \"false\", form = \"infix\", lspace = \"0em\", rspace = \+
\"verythickmathspace\", minsize = \"1\", maxsize = \"infinity\"), Type
setting:-mi(\"Q\", italic = \"true\", mathvariant = \"italic\"), Types
etting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"x\", italic = \"tr
ue\", mathvariant = \"italic\"), Typesetting:-mo(\",\", mathvariant = \+
\"normal\", fence = \"false\", separator = \"true\", stretchy = \"fals
e\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fal
se\", accent = \"false\", form = \"infix\", lspace = \"0em\", rspace =
 \"verythickmathspace\", minsize = \"1\", maxsize = \"infinity\"), Typ
esetting:-mi(\"y\", italic = \"true\", mathvariant = \"italic\")), mat
hvariant = \"normal\")), mathvariant = \"normal\", open = \"⟨\", \+
close = \"⟩\"), Typesetting:-mo(\".\", mathvariant = \"normal\", \+
fence = \"false\", separator = \"false\", stretchy = \"false\", symmet
ric = \"false\", largeop = \"false\", movablelimits = \"false\", accen
t = \"false\", form = \"infix\", lspace = \"0em\", rspace = \"0em\", m
insize = \"1\", maxsize = \"infinity\"), Typesetting:-mo(\" \", mathva
riant = \"normal\", fence = \"false\", separator = \"false\", stretchy
 = \"false\", symmetric = \"false\", largeop = \"false\", movablelimit
s = \"false\", accent = \"false\", form = \"\", lspace = \"0em\", rspa
ce = \"0em\", minsize = \"1\", maxsize = \"infinity\"));" "-I%mrowG6#/
I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I(mfencedGF$6&-F#6'-I#miG
F$6%Q\"PF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-F,6$-F#6%-F16%Q
\"xF'F4F7-I#moGF$60Q\",F'/F8Q'normalF'/%&fenceGQ&falseF'/%*separatorGF
6/%)stretchyGFI/%*symmetricGFI/%(largeopGFI/%.movablelimitsGFI/%'accen
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F4F7F:FE/%%openGQ'⟨F'/%&closeGQ'⟩F'-FB60Q\".F'FEFG/FKFIFLFNF
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" }{TEXT 200 61 "That's why the arrows are almost invisible around the
 origin." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 0 "" }}{PARA 0 "" 0 "" 
{TEXT 200 35 "For 3D field plots, the command is:" }}{PARA 0 "" 0 "" 
{TEXT 200 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "fieldplot3
d([x,y,z],x=-10..10,y=-10..10,z=-10..10, color=black, axes=boxed,grid=
[10,10,10]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}}
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