{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 } {CSTYLE "" -1 256 "" 1 24 0 0 0 0 0 0 2 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 "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 6 6 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{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 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 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 "Title" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }2 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "" 258 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 259 "" 0 "" {TEXT 256 54 "Vyuziti systemu pocitacove alg ebry ve vyuce matematiky" }}{PARA 19 "" 0 "" {TEXT -1 21 "Roman Plch, \+ KM PrF MU" }}{SECT 1 {PARA 3 "" 0 "Advantages" {TEXT -1 34 "Vyhody sys temu pocitacove algebry " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r estart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Mame overit, ze funkce " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "f := sin( n*z*sqrt(x^2 +y^2+z^2) / sqrt(y^2+z^2) ) / \n sqrt(x^2+y^2+z^2);" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*&-%$sinG6#**% \"nG\"\"\"%\"zGF+,(*$)%\"xG\"\"#F+F+*$)%\"yGF1F+F+*$)F,F1F+F+#F+F1,&F2 F+F5F+#!\"\"F1F+F-F9" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "je reseni m parcialni diferencialni rovnice ctvrteho radu" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 106 "'diff(diff(f(x),x$2) + diff(f(x),y$2) + diff( f(x),z$2),\n x$2) + n^2*(diff(f(x),x$2) + diff(f(x),y$2))'=0;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/,&-%%diffG6$,(-F&6$-%\"fG6#%\"xG-%\"$ G6$F.\"\"#\"\"\"-F&6$F+-F06$%\"yGF2F3-F&6$F+-F06$%\"zGF2F3F/F3*&)%\"nG F2F3,&F)F3F4F3F3F3\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " settime := time(): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "(di ff(diff(f,x$2) + diff(f,y$2) + diff(f,z$2),\n x$2) + n^2*(diff(f,x$2) + diff(f,y$2))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "radnor mal(diff(diff(f,x$2) + diff(f,y$2) + diff(f,z$2),\n x$2) + n^2*(diff( f,x$2) + diff(f,y$2)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "cpu_time = (time()-settime)* second; # computing time" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%)cpu_tim eG,$*&$\"$$Q!\"$\"\"\"%'secondGF*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Oprava v tabulkach integralu:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Integrate(1/(x*sqrt((b*x+c*x^2)^3)), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*&\"\"\"F'*&%\"xGF'*$),&*&%\"bGF'F)F'F '*&%\"cGF')F)\"\"#F'F'\"\"$F'#F'F2!\"\"F)" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 9 "value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*.\" \"#\"\"\"\"\"$!\"\",&%\"bGF&*&%\"xGF&%\"cGF&F&F&,(*$)F*F%F&F(**\"\"%F& F*F&F,F&F-F&F&*(\"\")F&)F,F%F&)F-F%F&F&F&F*!\"$*&)F,F'F&)F)F'F&#F(F%F& " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "simplify(%) assuming po sitive;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*.\"\"#\"\"\"\"\"$!\"\",( *$)%\"bGF%F&F(**\"\"%F&F,F&%\"xGF&%\"cGF&F&*(\"\")F&)F/F%F&)F0F%F&F&F& F,!\"$F/#F5F%,&F,F&*&F/F&F0F&F&#F(F%F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Prevod na tvar uvedeny v tabulkach:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "subs(b+c*x=y/x, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*.\"\"#\"\"\"\"\"$!\"\",(*$)%\"bGF%F&F(**\"\"%F&F,F&% \"xGF&%\"cGF&F&*(\"\")F&)F/F%F&)F0F%F&F&F&F,!\"$F/#F5F%*&%\"yGF&F/F(#F (F%F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "simplify(%) assumi ng positive;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*.\"\"#\"\"\"\"\"$! \"\",(*$)%\"bGF%F&F(**\"\"%F&F,F&%\"xGF&%\"cGF&F&*(\"\")F&)F/F%F&)F0F% F&F&F&F,!\"$F/F(%\"yG#F(F%F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*,\"\"#\"\"\"\" \"$!\"\"%\"bGF(%\"xGF(%\"yG#F(F%F(*,\"\")F&F'F(F)!\"#F+F,%\"cGF&F&*.\" #;F&F'F(F)!\"$F*F&F+F,F0F%F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "collect(3/2*%, sqrt(y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,( *&\"\"\"F&*&%\"bGF&%\"xGF&!\"\"F**(\"\"%F&F(!\"#%\"cGF&F&**\"\")F&F(! \"$F)F&F.\"\"#F&F&%\"yG#F*F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "subs(y=b*x+c*x^2, 2/3*%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$* *\"\"#\"\"\"\"\"$!\"\",(*&F&F&*&%\"bGF&%\"xGF&F(F(*(\"\"%F&F,!\"#%\"cG F&F&**\"\")F&F,!\"$F-F&F1F%F&F&,&*&F,F&F-F&F&*&F1F&)F-F%F&F&#F(F%F&" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Kontrola spravnosti vypoctu:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "simplify(diff(%,x) - 1/(x*s qrt((b*x+c*x^2)^3))) assuming positive;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "Properties" {TEXT -1 45 "Nektere vlastnosti systemu pocitacove algebr y" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "f := arctan((2*x^2-1)/(2*x^2+1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%'arctanG6#*&,&*&\"\"#\"\"\") %\"xGF+F,F,F,!\"\"F,,&*&F+F,F-F,F,F,F,F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "derivative := diff(f, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 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