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{SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "Vector Fields" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 261 12 "Description:" }{TEXT -1 
53 " Examples of two and three-dimensional vector fields " }{TEXT -1 
2 " (" }{TEXT 263 9 "animation" }{TEXT -1 3 "). " }}}{SECT 1 {PARA 3 "
" 0 "" {TEXT -1 4 "Code" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "w
ith(plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(plottools):" }}
{PARA 7 "" 1 "" {TEXT -1 43 "Warning, the name arrow has been redefine
d\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 
"" 0 "" {TEXT -1 27 "2-Dimensional Vector Fields" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 144 "two_dim_vf1 := fieldplot([x,y], x=-6..6, y=-6
..6, color=sqrt(x^2+y^2), grid=[15,15], arrows=THICK, title=`The vecto
r field F(x,y) = x*i + y*j`):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "t
wo_dim_vf2 := fieldplot([-y,x], x=-6..6, y=-6..6, color=sqrt(x^2+y^2),
 grid=[15,15], arrows=THICK, title=`The vector field F(x,y) = -y*i + x
*j`):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "two_dim_vf3 := fieldplot(
[y,sin(x)], x=-2*Pi..2*Pi, y=-2*Pi..2*Pi, color=sin(x), grid=[15,15], \+
arrows=THICK, title=`The vector field F(x,y) = y*i + sin(x)*j`):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "two_dim_vf4 := fieldplot([x-y,x+y]
, x=-6..6, y=-6..6, color=sqrt(x^2+y^2), grid=[15,15], arrows=THICK, t
itle=`The vector field F(x,y) = (x-y)*i + (x+y)*j`):" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 176 "two_dim_vf5 := fieldplot([cos(x),sin(y)], x=-2*
Pi..2*Pi, y=-2*Pi..2*Pi, color=cos(x)*sin(y), grid=[15,15], arrows=THI
CK, title=`The vector gield F(x,y) = cos(x)*i + sin(y)*j`):" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 176 "two_dim_vf6 := fieldplot([cos(y),sin(x)]
, x=-2*Pi..2*Pi, y=-2*Pi..2*Pi, color=cos(x)*sin(y), grid=[15,15], arr
ows=THICK, title=`The vector field F(x,y) = cos(y)*i + sin(x)*j`):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "two_dim_vect_fields := [two_dim_vf
1, two_dim_vf2, two_dim_vf3, two_dim_vf4, two_dim_vf5, two_dim_vf6]:" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 
0 "" {TEXT -1 27 "3-Dimensional Vector Fields" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 146 "three_dim_vf1 := fieldplot3d([x,y,z], x=-2..2, \+
y=-2..2, z=-2..2, arrows=THICK, grid=[5,5,5], title=`The vector field \+
F(x,y,z) = x*i + y*j + z*k`):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "t
hree_dim_vf2 := fieldplot3d([y,z,x], x=-2..2, y=-2..2, z=-2..2, arrows
=THICK, grid=[5,5,5], title=`The vector field F(x,y,z) = y*i + z*j + x
*k`):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 160 "three_dim_vf3 := fieldplo
t3d([x,y,1], x=-2..2, y=-2..2, z=-2..2, arrows=THICK, grid=[5,5,5], sh
ading=ZHUE, title = `The vector field F(x,y,z) = x*i + y*j + k`):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 164 "three_dim_vf4 := fieldplot3d([y*z,
x*z,x*y], x=-2..2, y=-2..2, z=-2..2, arrows=THICK, grid=[5,5,5], title
=`The vector field F(x,y,z) = (y*z)*i + (x*z)*j + (x*y)*k`):" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 198 "three_dim_vf5 := fieldplot3d([sin(x*y*z)
,x^2*y,z^2*exp(x/5)], x=-2..2, y=-2..2, z=-2..2, arrows=THICK, grid=[5
,5,5], title=`The vector field F(x,y,z) = sin(x*y*z)*i + (y*x^2)*k + (
exp(x/5)*z^2)*k`):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "three_dim_ve
ct_fields := [three_dim_vf1, three_dim_vf2, three_dim_vf3, three_dim_v
f4, three_dim_vf5]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 "Gravitational Fields" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "rho:=sqrt(x^2+y^2+z^2):" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 69 "grav_field_func := (X,Y,Z) -> -[(x-X)/rho^3
,(y-Y)/rho^3,(z-Z)/rho^3]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "grav
_field := fieldplot3d(grav_field_func(0,0,0), x=-2..2, y=-2..2, z=-2..
2, color=red, grid=[6,6,6], arrows=THICK):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 79 "earth := (X,Y,Z) -> display3d([sphere([X,Y,Z], 0.5, c
olor=blue, style=patch)]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "moon \+
:= (X,Y,Z) -> display3d([sphere([X,Y,Z], 0.2, color=grey, style=patch)
]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 179 "grav_field_earth_moon := (X
e,Ye,Ze,Xm,Ym,Zm) -> fieldplot3d(grav_field_func(Xe,Ye,Ze)+grav_field_
func(Xm,Ym,Zm), x=-2..2, y=-2..2, z=-2..2, color=red, grid=[6,6,6], ar
rows=THICK):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "U := -1/rho
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG,$*&\"\"\"F'*$-%%sqrtG6#,(*
$)%\"xG\"\"#F'F'*$)%\"yGF0F'F'*$)%\"zGF0F'F'F'!\"\"F7" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "F := grad(U,[x,y,z]);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"FG-%'vectorG6#7%*&,(*$)%\"xG\"\"#\"\"\"F/*$)
%\"yGF.F/F/*$)%\"zGF.F/F/#!\"$F.F-F/*&F*F6F2F/*&F*F6F5F/" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 216 "grav_field_x := display(\{\nfieldp
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),\nseq(implicitplot3d(U=-2*k/7,x=-2..2,y=-2..2,z=-2..2,style=wirefram
e),k=0..3)\}\n,scaling=constrained,axes=boxed);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 97 "frame1 := display3d([grav_field], scaling=cons
trained, title=`Gravitational force vector field`):" }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 86 "frame2 := display3d([earth(0,0,0), moon(0,1.5,1.5)
], scaling=constrained, axes=boxed):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 126 "frame3 := display3d([earth(0,0,0), moon(0,1.5,1.5), grav_field_
earth_moon(0,0,0,0,1.5,1.5)], scaling=constrained, axes=boxed):" }}}
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{PARA 4 "" 0 "" {TEXT -1 27 "2-Dimensional Vector Fields" }}{EXCHG 
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