{VERSION 4 0 "IBM INTEL NT" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 
{CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 
0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 
-1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 
0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra
ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 62 "f:=[r*cos(phi)*cos(theta),r*sin(phi)*cos(theta),r*sin
(theta)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG7%*(%\"rG\"\"\"-%$c
osG6#%$phiGF(-F*6#%&thetaGF(*(F'F(-%$sinGF+F(F-F(*&F'F(-F2F.F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "Jacobimatrix:=proc(f,variab
len)\nlocal j;\nreturn(transpose(matrix([seq(diff(f,variablen[j]),j=1.
.nops(variablen))])));\nend proc:\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "Jacobimatrix(f,[r,theta,phi]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'matrixG6#7%7%*&-%$cosG6#%$phiG\"\"\"-F*6#%&thetaGF-,
$*(%\"rGF-F)F--%$sinGF/F-!\"\",$*(F3F--F5F+F-F.F-F67%*&F9F-F.F-,$*(F3F
-F9F-F4F-F6*(F3F-F)F-F.F-7%F4*&F3F-F.F-\"\"!" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 7 "det(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**()-
%$cosG6#%$phiG\"\"#\"\"\")-F'6#%&thetaG\"\"$F+)%\"rGF*F+!\"\"*()-%$sin
GF(F*F+F,F+F1F+F3**F1F+F%F+)-F7F.F*F+F-F+F3**F1F+F5F+F-F+F9F+F3" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,$*&-%$cosG6#%&thetaG\"\"\")%\"rG\"\"#F)!\"\"" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "also ist f lokal umkehrbar in R^3 \+
\\ \{z-Achse\}" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Mit der eingeba
uten Maplefunktion:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "jaco
bian(f,[r,theta,phi]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#
7%7%*&-%$cosG6#%$phiG\"\"\"-F*6#%&thetaGF-,$*(%\"rGF-F)F--%$sinGF/F-!
\"\",$*(F3F--F5F+F-F.F-F67%*&F9F-F.F-,$*(F3F-F9F-F4F-F6*(F3F-F)F-F.F-7
%F4*&F3F-F.F-\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{MARK "9 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 
33 1 1 }