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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "File: depart\\math\\mat250
0\\examples\\stewart\\s12-6.mws
Date: 26-mar-1999
By: bob jantzen" }
}{PARA 18 "" 0 "" {TEXT -1 12 "Surface area" }}}{EXCHG {PARA 0 "> " 0
"" {MPLTEXT 1 0 94 "restart: \nlibname := libname, `F:\\\\depart\\\\ma
th\\\\maple\\\\vec_calc`:\nwith(vec_calc):\nvc_aliases:" }}{PARA 7 ""
1 "" {TEXT -1 32 "Warning, new definition for norm" }}{PARA 7 "" 1 ""
{TEXT -1 33 "Warning, new definition for trace" }}{PARA 6 "" 1 ""
{TEXT -1 33 "Package:
Version 4.3" }}{PARA 6 "" 1 ""
{TEXT -1 32 "For all HELP, execute: ?vec_calc" }}{PARA 6 "" 1 ""
{TEXT -1 38 "To use aliases, execute:
vc_" }}}{SECT 1 {PARA
3 "" 0 "" {TEXT -1 44 "example 1. area of sphere (spherical coords)" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "r:=makefunction([theta,phi
],\n[a*sin(phi)*cos(theta),a*sin(phi)*sin(theta),a*cos(phi)]): r(theta
,phi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%*(%\"aG\"\"\"-%$sinG6#%$ph
iGF&-%$cosG6#%&thetaGF&*(F%\"\"\"F'F0-F(F-F&*&F%F0-F,F)F&" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "a:=1:\nplot3d(r(theta,phi),theta=0.
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6CBBFD87DE2A6AEA9403FEBB67AE8584CB4BCF9CE3BFDFFFFFFFFFFFE03FE
49EBCF716C98BF01120BFE37AF93FA09E667F3BDCBCF494379
F9F70D7BFE6A09E667F3BBE3FE37AF93F9513FBBCF1B781B12087D5BFE48
53FE4BCED1ABFEBB67AEFD87DE2A6AEA991BCE64
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8BF0E3FC0BEBCCE63C32AE4AE3FBFEFB9EA92EC68983CED1AB
9FA77E814D8FF3FBFF0-%(SCALINGG6#%,CONSTRAINEDG" 1 2 0 1 0
2 1 1 2 1 1... }}}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 113 "r1:=D[1](r)(theta,phi);\nr2:=D[2](r)(theta,phi);\nn:
=crossprod(r1,r2);\nn2:=simplify(len(n)^2);\nlen_n:=a^2*sin(phi);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r1G7%,$*(%\"aG\"\"\"-%$sinG6#%$phiG
F)-F+6#%&thetaGF)!\"\"*(F(\"\"\"F*F3-%$cosGF/F)\"\"!" }}{PARA 11 "" 1
"" {XPPMATH 20 "6#>%#r2G7%*(%\"aG\"\"\"-%$cosG6#%$phiGF(-F*6#%&thetaGF
(*(F'\"\"\"F)F1-%$sinGF.F(,$*&F'F1-F3F+F(!\"\"" }}{PARA 12 "" 1 ""
{XPPMATH 20 "6#>%\"nG-%'vectorG6#7%,$*()%\"aG\"\"#\"\"\")-%$sinG6#%$ph
iGF-F.-%$cosG6#%&thetaG\"\"\"!\"\",$*(F+F.F/F.-F1F6F8F9,&**F+F.F0F8)F%#n2G,&*$)%\"aG\"\"%\"\"\"\"\"\"*&F'F*)-%$cosG6#%$phiG\"\"#F*!\"\"
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&len_nG*&)%\"aG\"\"#\"\"\"-%$sin
G6#%$phiG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "Int(Int(
len_n,phi=0..Pi),theta=0..2*Pi)\n=int(int(len_n,phi=0..Pi),theta=0..2*
Pi);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$-F%6$*&)%\"aG\"\"#
\"\"\"-%$sinG6#%$phiG\"\"\"/F1;\"\"!%#PiG/%&thetaG;F5,$F6F,,$*&F*F-F6F
2\"\"%" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 45 "example 1b. area of s
phere (cartesian coords)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "
f:=makefunction([x,y],sqrt(a^2-x^2-y^2));" }}{PARA 11 "" 1 ""
{XPPMATH 20 "6#>%\"fGR6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF)*$-%%sqrtG
6#,(*$)%\"aG\"\"#\"\"\"\"\"\"*$)9$F5F6!\"\"*$)9%F5F6F;F6F)F)F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "r:=makefunction([x,y],[x,y,f
(x,y)]): r(x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%%\"xG%\"yG*$-%%s
qrtG6#,(*$)%\"aG\"\"#\"\"\"\"\"\"*$)F$F.F/!\"\"*$)F%F.F/F3F/" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "a:=1:\nplot3d(r(x,y),y=-sqr
t(a^2-x^2)..sqrt(a^2-x^2),x=-a..a,scaling=constrained,grid=[100,25]);
\na:='a':" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6%-%%
MESHG6#7`q7;7%$!\"\"\"\"!F+F+7%$!1mmmmmmm\"*!#;$!1:Fmoi_'*RF/F+7%$!1LL
LLLLL$)F/$!1G1#H)zqFbF/F+7%$!1*************\\(F/$!1$eFlFyVh'F/$\"1GQ#p
f!e]u!#C7%$!1lmmmmmmmF/$!1In!Q#*fNX(F/F+7%$!1JLLLLLLeF/$!1grZ>'GB7)F/$
\"1^Bx77n`5!#B7%$!1)*************\\F/$!1'o*oOSDg')F/%%FAILG7%$!1lmmmmm
mTF/$!19OzFMf!4*F/F+7%$!1KLLLLLLLF/$!1Cy([T!4G%*F/F+7%$!1*************
\\#F/$!1YRuk$eCo*F/F+7%$!1F/$!1e#p7(H8g)*F/F+7%$!1DLLLLLL$)!#<
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