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M\366glichkeit" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 258 22 "Ausdr\374cke manipulieren" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 "simplify((x^2-1)/(x^3-1));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#*&,&%\"xG\"\"\"F&F&F&,(*$)F%\"\"#F&F&F%F&F&F&!\"\"" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "convert((x^2+1)/(x^3-1), p arfrac, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(\"\"#\"\"\"\"\"$!\" \",&%\"xGF&F&F(F(F&*(F'F(F)F&,(*$)F*F%F&F&F*F&F&F&F(F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "expand((x^2-1)/(x^3-1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&,&*$)%\"xG\"\"$\"\"\"F*F*!\"\"F+F(\"\"#F **&F*F*F%F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "factor((x^ 2-1)/(x^3-1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"F&F&F &,(*$)F%\"\"#F&F&F%F&F&F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "combine(sin(x+y)*cos(x-y), trig);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&#\"\"\"\"\"#F&-%$sinG6#,$*&F'F&%\"xGF&F&F&F&*&F%F&- F)6#,$*&F'F&%\"yGF&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(sin(x+y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$sinG6# %\"xG\"\"\"-%$cosG6#%\"yGF)F)*&-F+F'F)-F&F,F)F)" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "convert(sin(2*x), tan);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"#\"\"\"-%$tanG6#%\"xGF&,&F&F&*$)F'F%F&F&!\"\"F& " }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 259 17 "Summe und Produkt" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Sum(i, i=1..100);sum(i, i=1. .100);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$%\"iG/F&;\"\"\"\"$+ \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%]]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Product(i, i=1..10);product(i, i=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%(ProductG6$%\"iG/F&;\"\"\"\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(+)GO" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 260 8 "Integral" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Int(1/x, \+ x);int(1/x, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*&\"\"\"F' %\"xG!\"\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#%\"xG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Int(1/x, x=1..2);int(1/x, x= 1..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*&\"\"\"F'%\"xG!\" \"/F(;F'\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "int(1/x, x=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)infinityG" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 261 11 "Ableitungen" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "f:=x->3*x^2-5*x+2;\ng:=x->x/(1+x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,(*&\"\"$\"\"\")9$\"\"#F/F/* &\"\"&F/F1F/!\"\"F2F/F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf *6#%\"xG6\"6$%)operatorG%&arrowGF(*&9$\"\"\",&F-F.F.F.!\"\"F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "diff(f(x), x);\ndiff(f(x), x , x);\ndiff(f(x), x, x, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\" \"'\"\"\"%\"xGF&F&\"\"&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"' " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 89 "diff(g(x), x); simplify(\");\ndiff(g(x), x$2); si mplify(\");\ndiff(g(x), x$3); simplify(\");" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 53 "Warning, incomplete s tring; use \" to end the string\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f1:=D(f); f1(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#f1Gf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&*&\"\"'\"\"\"9$F/F/\"\"&!\" \"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 29 "g2:=(D@@2)(g);\ngn:=(D@@n)(g);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#g2Gf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&*&\" \"#\"\"\",&9$F/F/F/!\"#!\"\"*(F.F/F1F/F0!\"$F/F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#gnG--%#@@G6$%\"DG%\"nG6#%\"gG" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 262 21 "Partielle Ableitungen" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "f:=(x,y,z)->(x+y)*sin(z)+(x-y)*exp(z)-x*z^3/y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6%%\"xG%\"yG%\"zG6\"6$%)oper atorG%&arrowGF*,(*&,&9$\"\"\"9%F2F2-%$sinG6#9&F2F2*&,&F1F2F3!\"\"F2-%$ expGF6F2F2*(F1F2F7\"\"$F3F:F:F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "D[1](f);\nD[2](f);\nD[3](f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF(,(-%$sinG6 #9&\"\"\"-%$expGF/F1*&F0\"\"$9%!\"\"F7F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF(,(-%$sinG6 #9&\"\"\"-%$expGF/!\"\"*(9$F1F0\"\"$9%!\"#F1F(F(F(" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#f*6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF(,(*&,&9$ \"\"\"9%F0F0-%$cosG6#9&F0F0*&,&F/F0F1!\"\"F0-%$expGF4F0F0**\"\"$F0F/F0 F5\"\"#F1F8F8F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "D[1 ,1](f); # zweimal nach x\nD[1,2](f); # nach y und nach x\nD[1, 3](f); # nach z und nach x" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\" !" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6%%\"xG%\"yG%\"zG6\"6$%)operato rG%&arrowGF(*&9&\"\"$9%!\"#F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f *6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF(,(-%$cosG6#9&\"\"\"-%$expG F/F1*(\"\"$F1F0\"\"#9%!\"\"F8F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "with(linalg):\nhessian(f(x,y,z),[x,y,z]); # M atrix aller partiellen Ableitungen 2. Ordnung\nhessian(f(x,y,z),[x,y,z ])[2,1]; " }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected nam es norm and trace have been redefined and unprotected\n" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"!*&%\"zG\"\"$%\"yG!\"#,(-%$c osG6#F*\"\"\"-%$expGF1F2*(F+F2F*\"\"#F,!\"\"F77%F),$**F6F2%\"xGF2F*F+F ,!\"$F7,(F/F2F3F7**F+F2F;F2F*F6F,F-F27%F.F=,(*&,&F;F2F,F2F2-%$sinGF1F2 F7*&,&F;F2F,F7F2F3F2F2**\"\"'F2F;F2F*F2F,F7F7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"zG\"\"$%\"yG!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "D[1,2,3](f);D[1,3,2](f); # die Reihenfolge spielt keine Rolle\nD[2,1,3](f);D[2,3,1](f);\nD[3,1,2](f);D[3,2,1](f);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#f*6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&a rrowGF(,$*(\"\"$\"\"\"9&\"\"#9%!\"#F/F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF(,$*(\"\"$ \"\"\"9&\"\"#9%!\"#F/F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6%%\" xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF(,$*(\"\"$\"\"\"9&\"\"#9%!\"#F/F( F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6%%\"xG%\"yG%\"zG6\"6$%)oper atorG%&arrowGF(,$*(\"\"$\"\"\"9&\"\"#9%!\"#F/F(F(F(" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#f*6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF(,$*(\"\" $\"\"\"9&\"\"#9%!\"#F/F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6%% \"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF(,$*(\"\"$\"\"\"9&\"\"#9%!\"#F/ F(F(F(" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 256 24 "Eigenwerte und -vekt oren" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A:=([[3, -2],[-4, 1]]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG7$7$\"\"$!\"#7$!\"%\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "eigenvals(A);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6$\"\"&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eigenvects(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$7%! \"\"\"\"\"<#-%'vectorG6#7$F%\"\"#7%\"\"&F%<#-F(6#7$F$F%" }}}{PARA 0 " " 0 "" {TEXT -1 8 " " }{TEXT 257 52 "Legende: [ Eigenwert, Vi elfachheit, \{Eigenvektor\}]" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 263 12 "Potenzreihen" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "taylor(exp( x), x=0);\na:=taylor(exp(x), x=0, 9);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+1%\"xG\"\"\"\"\"!F%F%#F%\"\"#F(#F%\"\"'\"\"$#F%\"#C\"\"%#F%\"$?\" \"\"&-%\"OG6#F%F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG+7%\"xG\"\" \"\"\"!F'F'#F'\"\"#F*#F'\"\"'\"\"$#F'\"#C\"\"%#F'\"$?\"\"\"&#F'\"$?(F, #F'\"%S]\"\"(#F'\"&?.%\"\")-%\"OG6#F'\"\"*" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 117 "nops(a); # Herausgreifen der Entwick lungskoeffizienten\nop(1,a);op(2,a);op(3,a);op(4,a);op(5,a);op(6,a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "tay lor(exp(x)/x, x);\na:=series(exp(x)/x, x,8);" }}{PARA 8 "" 1 "" {TEXT -1 54 "Error, does not have a taylor expansion, try series()\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG+5%\"xG\"\"\"!\"\"F'\"\"!#F'\"\" #F'#F'\"\"'F+#F'\"#C\"\"$#F'\"$?\"\"\"%#F'\"$?(\"\"&#F'\"%S]F--%\"OG6# F'\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "nops(a);\nop(1,a );op(2,a);op(3,a);op(4,a);op(5,a);op(6,a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 " " {XPPMATH 20 "6##\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\" \"" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{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 }