 MVR4
I,vec_calc/ss:6#%%exprG6"6#%aoCopyright~1995,96~by~Arthur~Belmonte~and~Philip~B
.~Yasskin,~Math,~TAMUGF&-%)simplifyG6$9$.%)symbolicGF&F&F&
MVR4
I/vec_calc/evall:6#%"mG6"6#%aoCopyright~1995,96~by~Arthur~Belmonte~and~Philip~B
.~Yasskin,~Math,~TAMUGF&-%(convertG6$-%&evalmG6#9$%)listlistGF&F&F&
MVR4
I-vec_calc/dot:6$'%"vG<$%%listG%'vectorG'%"wGF'6#%"nG6#%`oCopyright~1995-7~by~A
rthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUG6"C%>8$-%(vectdimG6#9$@$0F3-F5
6#9%-%&ERRORG6#%YThe~two~vectors~must~have~the~same~number~of~components.G-%)si
mplifyG6#-%$addG6$*&&F76#%"iG"""&F<FIFK/FJ;FKF3F0F0F0
MVR4
I,vec_calc/&.:6$'%"vG<$%%listG%'vectorG'%"wGF'6"6#%aoCopyright~1995,96~by~Arthu
r~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF,-%$dotG6$9$9%F,F,F,
MVR4
I-vec_calc/len:6#'%"vG<$%%listG%'vectorG6"6#%`oCopyright~1995-7~by~Arthur~Belmo
nte~and~Philip~B.~Yasskin,~Math,~TAMUGF*-%%sqrtG6$-%$addG6$*$&9$6#%"iG""#/F7;""
"-%(vectdimG6#F5%)symbolicGF*F*F*
MVR4
I/vec_calc/cross:6$'%"vG<$%%listG%'vectorG'%"wGF'6"6#%`oCopyright~1995-7~by~Art
hur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF,C$@$50-%(vectdimG6#9$""$0-F46#
9%F7-%&ERRORG6#%ZEach~argument~must~be~a~list~or~vector~with~3~components.G7%,&
*&&F66#""#"""&F;6#F7FFFF*&&F6FHFF&F;FDFF!"",&*&FJFF&F;6#FFFFFF*&&F6FPFFFGFFFL,&
*&FRFFFKFFFF*&FCFFFOFFFLF,F,F,
MVR4
I,vec_calc/&x:6$'%"vG<$%%listG%'vectorG'%"wGF'6"6#%aoCopyright~1995,96~by~Arthu
r~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF,-%&crossG6$9$9%F,F,F,
MVR4
I5vec_calc/map_unapply:6#%&exprsG6#%"CG6#%aoCopyright~1995,96~by~Arthur~Belmont
e~and~Philip~B.~Yasskin,~Math,~TAMUG6"@%-%%typeG6$9$<$%&arrayG%%listG-%$mapG6%%
,map_unapplyGF/&9"6#;""#9#C$-%(unapplyG6$,&F/"""8$FBF7-%%subsG6$/FC""!%""GF*F*F
*
MVR4
I6vec_calc/makefunction:6$'%%varsG<$-%%listG6#%%nameGF+'%&exprsG%)alg_listG6"6#
%aoCopyright~1995,96~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF/-%,
map_unapplyG6$9%-%#opG6#9$F/F/F/
MVR4
I8vec_calc/curve_velocity:6#'%"rG<$%%listG%'vectorG6"6$%)rememberG%aoCopyright~
1995,96~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF*-%"DG6#9$F*F*F*
MVR4
I<vec_calc/curve_acceleration:6#'%"rG<$%%listG%'vectorG6"6$%)rememberG%aoCopyri
ght~1995,96~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF*-%"DG6#-%/cu
rve_velocityG6#9$F*F*F*
MVR4
I4vec_calc/curve_jerk:6#'%"rG<$%%listG%'vectorG6"6$%)rememberG%aoCopyright~1995
,96~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF*-%"DG6#-%3curve_acce
lerationG6#9$F*F*F*
MVR4
I7vec_calc/curve_tangent:6#'%"rG<$%%listG%'vectorG6$%"tG%"vG6$%)rememberG%aoCop
yright~1995,96~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUG6"C%@%/9#""
#C$>8$&9"6#F5@$4-%%typeG6$F8%%nameG-%&ERRORG6#%MThe~second~argument~must~be~a~v
ariable~name.GC$>F8-%&minusG6$<#-%$seqG6$-%)Get_VarsG6#%"fG/FR9$<#""!@%0-%%nops
G6#F8"""C$-%'printfG6%%'%s|+%s|+G%MCould~not~determine~the~parameter.~~Using~t.
G%RYou~may~specify~a~parameter~as~a~second~argument.G>F8.F8>F8-%#opG6#-FboFen>8
%--%/curve_velocityG6#FTFen-%,map_unapplyG6$-%)simplifyG6#-%&evallG6#*&FfoFfn-%
$lenG6#Ffo!""F8F0F0F0
MVR4
I6vec_calc/curve_normal:6#'%"rG<$%%listG%'vectorG6&%"tG%"vG%"aG%"nG6$%)remember
G%aoCopyright~1995,96~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUG6"C'
@%/9#""#C$>8$&9"6#F7@$4-%%typeG6$F:%%nameG-%&ERRORG6#%MThe~second~argument~must
~be~a~variable~name.GC$>F:-%&minusG6$<#-%$seqG6$-%)Get_VarsG6#%"fG/FT9$<#""!@%0
-%%nopsG6#F:"""C$-%'printfG6%%'%s|+%s|+G%MCould~not~determine~the~parameter.~~U
sing~t.G%RYou~may~specify~a~parameter~as~a~second~argument.G>F:.F:>F:-%#opG6#-F
doFgn>8%--%/curve_velocityG6#FVFgn>8&--%3curve_accelerationGF\pFgn>8'-%&evallG6
#,&F^pFhn*(-%$dotG6$F^pFhoFhn-Fjp6$FhoFho!""FhoFhnF^q-%,map_unapplyG6$-%)simpli
fyG6#-Fep6#*&FcpFhn-%$lenG6#FcpF^qF:F2F2F2
MVR4
I8vec_calc/curve_binormal:6#'%"rG<$%%listG%'vectorG6$%"tG%#cpG6$%)rememberG%`oC
opyright~1995-7~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUG6"C&@%/9#"
"#C$>8$&9"6#F5@$4-%%typeG6$F8%%nameG-%&ERRORG6#%MThe~second~argument~must~be~a~
variable~name.GC$>F8-%&minusG6$<#-%$seqG6$-%)Get_VarsG6#%"fG/FR9$<#""!@%0-%%nop
sG6#F8"""C$-%'printfG6%%'%s|+%s|+G%MCould~not~determine~the~parameter.~~Using~t
.G%RYou~may~specify~a~parameter~as~a~second~argument.G>F8.F8>F8-%#opG6#-FboFen@
$0-%(vectdimG6#FT""$-FC6#%NThe~binormal~is~only~defined~in~3~dimensions.G>8%-%&
crossG6$--%/curve_velocityGFioFen--%3curve_accelerationGFioFen-%,map_unapplyG6$
-%)simplifyG6#-%&evallG6#*&F_pFfn-%$lenG6#F_p!""F8F0F0F0
MVR4
I9vec_calc/curve_curvature:6#'%"rG<$%%listG%'vectorG6&%"tG%"vG%"aG%"nG6$%)remem
berG%aoCopyright~1995,96~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUG6
"C'@%/9#""#C$>8$&9"6#F7@$4-%%typeG6$F:%%nameG-%&ERRORG6#%MThe~second~argument~m
ust~be~a~variable~name.GC$>F:-%&minusG6$<#-%$seqG6$-%)Get_VarsG6#%"fG/FT9$<#""!
@%0-%%nopsG6#F:"""C$-%'printfG6%%'%s|+%s|+G%MCould~not~determine~the~parameter.
~~Using~t.G%RYou~may~specify~a~parameter~as~a~second~argument.G>F:.F:>F:-%#opG6
#-FdoFgn>8%--%/curve_velocityG6#FVFgn>8&--%3curve_accelerationGF\pFgn>8'-%&eval
lG6#,&F^pFhn*(-%$dotG6$F^pFhoFhn-Fjp6$FhoFho!""FhoFhnF^q-%(unapplyG6$-%)simplif
yG6#*(-Fjp6$F^pFcpFhn-%$lenG6#FcpF^qF\qF^qF:F2F2F2
MVR4
I7vec_calc/curve_torsion:6#'%"rG<$%%listG%'vectorG6$%"tG%#cpG6$%)rememberG%`oCo
pyright~1995-7~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUG6"C&@%/9#""
#C$>8$&9"6#F5@$4-%%typeG6$F8%%nameG-%&ERRORG6#%MThe~second~argument~must~be~a~v
ariable~name.GC$>F8-%&minusG6$<#-%$seqG6$-%)Get_VarsG6#%"fG/FR9$<#""!@%0-%%nops
G6#F8"""C$-%'printfG6%%'%s|+%s|+G%MCould~not~determine~the~parameter.~~Using~t.
G%RYou~may~specify~a~parameter~as~a~second~argument.G>F8.F8>F8-%#opG6#-FboFen@$
0-%(vectdimG6#FT""$-FC6#%MThe~torsion~is~only~defined~in~3~dimensions.G>8%-%&cr
ossG6$--%/curve_velocityGFioFen--%3curve_accelerationGFioFen-%(unapplyG6$-%)sim
plifyG6#*&-%$dotG6$F_p--%+curve_jerkGFioFenFfn-Faq6$F_pF_p!""F8F0F0F0
MVR4
I9vec_calc/curve_arclength:6#'%"rG<$%%listG%'vectorG6%%"tG%"aG%"bG6$%)rememberG
%aoCopyright~1995,96~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUG6"C$@
%/9#""#C$>8$&9"6#F6@$4-%%typeG6$F9%%nameG-%&ERRORG6#%MThe~second~argument~must~
be~a~variable~name.GC$>F9-%&minusG6$<#-%$seqG6$-%)Get_VarsG6#%"fG/FS9$<#""!@%0-
%%nopsG6#F9"""C$-%'printfG6%%'%s|+%s|+G%MCould~not~determine~the~parameter.~~Us
ing~t.G%RYou~may~specify~a~parameter~as~a~second~argument.G>F9.F9>F9-%#opG6#-Fc
oFfn-%(unapplyG6%-%$IntG6$-%)simplifyG6#-%$lenG6#--%/curve_velocityG6#FUFfn/F9;
8%8&FhpFipF1F1F1
MVR4
IGvec_calc/curve_tangential_acceleration:6#'%"rG<$%%listG%'vectorG6#%"tG6$%)rem
emberG%aoCopyright~1995,96~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMU
G6"C$@%/9#""#C$>8$&9"6#F4@$4-%%typeG6$F7%%nameG-%&ERRORG6#%MThe~second~argument
~must~be~a~variable~name.GC$>F7-%&minusG6$<#-%$seqG6$-%)Get_VarsG6#%"fG/FQ9$<#"
"!@%0-%%nopsG6#F7"""C$-%'printfG6%%'%s|+%s|+G%MCould~not~determine~the~paramete
r.~~Using~t.G%RYou~may~specify~a~parameter~as~a~second~argument.G>F7.F7>F7-%#op
G6#-FaoFZ-%(unapplyG6$-%)simplifyG6#-%%diffG6$-%$lenG6#--%/curve_velocityG6#FSF
ZF7F7F/F/F/
MVR4
ICvec_calc/curve_normal_acceleration:6#'%"rG<$%%listG%'vectorG6&%"tG%"vG%"aG%"n
G6$%)rememberG%aoCopyright~1995,96~by~Arthur~Belmonte~and~Philip~B.~Yasskin,~Ma
th,~TAMUG6"C'@%/9#""#C$>8$&9"6#F7@$4-%%typeG6$F:%%nameG-%&ERRORG6#%MThe~second~
argument~must~be~a~variable~name.GC$>F:-%&minusG6$<#-%$seqG6$-%)Get_VarsG6#%"fG
/FT9$<#""!@%0-%%nopsG6#F:"""C$-%'printfG6%%'%s|+%s|+G%MCould~not~determine~the~
parameter.~~Using~t.G%RYou~may~specify~a~parameter~as~a~second~argument.G>F:.F:
>F:-%#opG6#-FdoFgn>8%--%/curve_velocityG6#FVFgn>8&--%3curve_accelerationGF\pFgn
>8'-%&evallG6#,&F^pFhn*(-%$dotG6$F^pFhoFhn-Fjp6$FhoFho!""FhoFhnF^q-%(unapplyG6$
-%)simplifyG6#*&-Fjp6$F^pFcpFhn-%$lenG6#FcpF^qF:F2F2F2
MVR4
I6vec_calc/curve_forget:6"F$6#%aoCopyright~1995,96~by~Arthur~Belmonte~and~Phili
p~B.~Yasskin,~Math,~TAMUGF$C.-%(readlibG6#%'forgetG-F+6$%/curve_velocityG9"-F+6
$%3curve_accelerationGF/-F+6$%+curve_jerkGF/-F+6$%.curve_tangentGF/-F+6$%-curve
_normalGF/-F+6$%/curve_binormalGF/-F+6$%0curve_curvatureGF/-F+6$%.curve_torsion
GF/-F+6$%0curve_arclengthGF/-F+6$%>curve_tangential_accelerationGF/-F+6$%:curve
_normal_accelerationGF/F$F$F$
MVR4
I1vec_calc/deg2rad:6#%&thetaG6"6#%aoCopyright~1995,96~by~Arthur~Belmonte~and~Ph
ilip~B.~Yasskin,~Math,~TAMUGF&C$,$*&9$"""%#PiGF-#F-"$!=@%-%(hastypeG6$F,%&float
G-%&evalfG6#%""GF9F&F&F&
MVR4
I1vec_calc/rad2deg:6#%&thetaG6"6#%aoCopyright~1995,96~by~Arthur~Belmonte~and~Ph
ilip~B.~Yasskin,~Math,~TAMUGF&C$,$*&9$"""%#PiG!"""$!=@%-%(hastypeG6$F,%&floatG-
%&evalfG6#%""GF9F&F&F&
MVR4
I4vec_calc/polar2rect:6#'%#pcG<$%%listG%'vectorG6"6#%`oCopyright~1995-7~by~Arth
ur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF*C$@$0-%(vectdimG6#9$""#-%&ERROR
G6#%YThe~argument~must~be~a~list~or~vector~with~2~components.G7$*&&F36#"""F=-%$
cosG6#&F36#F4F=*&F;F=-%$sinGF@F=F*F*F*
MVR4
I4vec_calc/rect2polar:6#'%#rcG<$%%listG%'vectorG6"6#%`oCopyright~1995-7~by~Arth
ur~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF*C$@$0-%(vectdimG6#9$""#-%&ERROR
G6#%YThe~argument~must~be~a~list~or~vector~with~2~components.G7$-%$lenGF2-%)sim
plifyG6#-%'arctanG6$&F36#F4&F36#"""F*F*F*
MVR4
I2vec_calc/cyl2rect:6#'%#ccG<$%%listG%'vectorG6"6#%`oCopyright~1995-7~by~Arthur
~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF*C$@$0-%(vectdimG6#9$""$-%&ERRORG6
#%YThe~argument~must~be~a~list~or~vector~with~3~components.G7%*&&F36#"""F=-%$co
sG6#&F36#""#F=*&F;F=-%$sinGF@F=&F36#F4F*F*F*
MVR4
I2vec_calc/rect2cyl:6#'%#rcG<$%%listG%'vectorG6"6#%`oCopyright~1995-7~by~Arthur
~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF*C$@$0-%(vectdimG6#9$""$-%&ERRORG6
#%YThe~argument~must~be~a~list~or~vector~with~3~components.G7%-%$lenG6#&F36#;""
"""#-%)simplifyG6#-%'arctanG6$&F36#FA&F36#F@&F36#F4F*F*F*
MVR4
I2vec_calc/sph2rect:6#'%#scG<$%%listG%'vectorG6"6#%`oCopyright~1995-7~by~Arthur
~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF*C$@$0-%(vectdimG6#9$""$-%&ERRORG6
#%YThe~argument~must~be~a~list~or~vector~with~3~components.G7%*(&F36#"""F=-%$si
nG6#&F36#F4F=-%$cosG6#&F36#""#F=*(F;F=F>F=-F?FEF=*&F;F=-FDF@F=F*F*F*
MVR4
I2vec_calc/rect2sph:6#'%#rcG<$%%listG%'vectorG6"6#%`oCopyright~1995-7~by~Arthur
~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF*C$@$0-%(vectdimG6#9$""$-%&ERRORG6
#%YThe~argument~must~be~a~list~or~vector~with~3~components.G7%-%$lenGF2-%)simpl
ifyG6#-%'arctanG6$&F36#""#&F36#"""-F=6#-F@6$-F;6#&F36#;FGFD&F36#F4F*F*F*
MVR4
I1vec_calc/sph2cyl:6#'%#scG<$%%listG%'vectorG6"6#%`oCopyright~1995-7~by~Arthur~
Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF*C$@$0-%(vectdimG6#9$""$-%&ERRORG6#
%YThe~argument~must~be~a~list~or~vector~with~3~components.G7%*&&F36#"""F=-%$sin
G6#&F36#F4F=&F36#""#*&F;F=-%$cosGF@F=F*F*F*
MVR4
I1vec_calc/cyl2sph:6#'%#ccG<$%%listG%'vectorG6"6#%`oCopyright~1995-7~by~Arthur~
Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUGF*C$@$0-%(vectdimG6#9$""$-%&ERRORG6#
%YThe~argument~must~be~a~list~or~vector~with~3~components.G7%-%$lenG6#7$&F36#""
"&F36#F4&F36#""#-%)simplifyG6#-%'arctanG6$F>FAF*F*F*
MVR4
I5vec_calc/MuInt_noChk:6"6$%"iG%'my_intG6#%aoCopyright~1995,96~by~Arthur~Belmon
te~and~Philip~B.~Yasskin,~Math,~TAMUGF$C$>8%&9"6#"""?(8$""#F09#%%trueG>F,-%$Int
G6$F,&F.6#F2F$F$F$
MVR4
I5vec_calc/Multipleint:6"F$6#%aoCopyright~1995,96~by~Arthur~Belmonte~and~Philip
~B.~Yasskin,~Math,~TAMUGF$C%@$29#""#-%&ERRORG6#%WAn~integral~needs~at~least~one
~variable~of~integrationG@$4-%%typeG6$7#&9"6#;F+F*-%%listG6#<$%%nameG/F>%&range
G-F-6#%hnEach~variable~of~integration~must~be~a~name~or~a~name~=~rangeG-%,MuInt
_noChkG6#F7F$6#FEF$
MVR4
I5vec_calc/multipleint:6"6+%*integrandG%"iG%*var_rangeG%$varG%%rngeG%(antiderG%
&lowerG%&upperG%,subsantiderG6#%aoCopyright~1995,96~by~Arthur~Belmonte~and~Phil
ip~B.~Yasskin,~Math,~TAMUGF$C3@$29#""#-%&ERRORG6#%WAn~integral~needs~at~least~o
ne~variable~of~integrationG@$0&9"6#!""%%stepG@%-%%typeG6$7#&F=6#;F5F4-%%listG6#
/%%nameG%&rangeG-%'RETURNG6#-%&valueG6#-%,MuInt_noChkG6#F=-F76#%TEach~variable~
of~integration~must~be~a~name~=~rangeG@$4-FC6$7#&F=6#;F5!"#FIFX-%&printG6#-FV6#
&F=6#;"""F]o>8$&F=6#Ffo?(8%F5Ffo,&F4FfoF]oFfo%%trueGC,>8&&F=6#F\p>8'-%$lhsG6#Fa
p>8(-%$rhsGFhp>8*-Fgp6#Fjp>8+-F\qF`q>8)-%$intG6$FhoFep>8,*&-%&arrayG6#7#FeqFfo-
%'matrixG6#7%7#&%!G6#/FepFbq7#Ffr7#&Ffr6#/FepF^qFfo>Fho,&-%%subsG6$FhrFeqFfo-Fa
s6$F]sFeqF?-F_o6#/%"~G-FV6$Fjq&F=6#;,&F\pFfoFfoFfo,&F4FfoF?Ffo-F_o6#/Fhs-FV6$Fh
oF[t>Fap&F=6#F]o>FepFfp>FjpF[q>F^qF_q>FbqFcq>FeqFfq>FjqF[r>FhoF_s-F_o6#/FhsFjq-
F_o6#/FhsFhoFhoF$6#FVF$
MVR4
I2vec_calc/Get_Vars:6#%"fG6"6#%^oCopyright~1996~by~Arthur~Belmonte~and~Philip~B
.~Yasskin,~Math,~TAMUGF&C$@$-%%typeG6$9$%*procedureG-%'RETURNG6#7#-%#opG6$"""-%
%evalG6#F.""!F&F&F&
MVR4
I.vec_calc/GRAD:6#'%"fG%*procedureG6$%%varsG%"iG6#%aoCopyright~1995,96~by~Arthu
r~Belmonte~and~Philip~B.~Yasskin,~Math,~TAMUG6"C$@%/9#""#C$>8$&9"6#F2@$4-%%type
G6$F5-%%listG6#%%nameG-%&ERRORG6#%VThe~second~argument~must~be~a~list~of~variab
le~names.GC$>F5-%&minusG6$<#-%)Get_VarsG6#9$<#""!@%0-%%nopsG6#F5"""-FC6$%CCould
~not~determine~the~variables.G%fn|+~You~may~specify~a~list~of~variables~as~a~se
cond~argument.G>F5-%#opGFV-%-makefunctionG6$F5-%)simplifyG6#-7#-%$seqG6$-&%"DG6
#8%FN/Fho;FWFT6#FgnF-F-F-
MVR4
I-vec_calc/DIV:6#'%"FG<$-%%listG6#<%%)constantG%*procedureG%%nameG-%'vectorGF*6
&%%varsG%%nvarG%'varseqG%"iG6#%aoCopyright~1995,96~by~Arthur~Belmonte~and~Phili
p~B.~Yasskin,~Math,~TAMUG6"C'@%/9#""#C$>8$&9"6#F=@$4-%%typeG6$F@-F)6#F.-%&ERROR
G6#%VThe~second~argument~must~be~a~list~of~variable~names.GC$>F@-%&minusG6$<#-%
$seqG6$-%)Get_VarsG6#%"fG/Fen9$<#""!@'/-%%nopsG6#F@Fin-%'RETURNG6#Fin2"""F\o-FL
6%%VThe~variables~were~different~for~different~componentsG%gn|+~or~Maple's~auto
matic~simplification~changed~the~variables.G%fn|+~You~may~specify~a~list~of~var
iables~as~a~second~argument.G>F@-%#opGF^o>8%F\o@$0-F]o6#FgnF]p-FL6#%gnThe~numbe
r~of~components~must~equal~the~number~of~variables.G>8&Fjo-%(unapplyG6$-%)simpl
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MVR4
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