{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 "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 24 0 0 0 0 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 1 } 1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE " " -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Out put" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helve tica" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 11 0 0 0 0 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 268 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 275 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 311 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 330 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 332 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 346 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 361 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 391 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 393 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 394 1 {CSTYLE " " -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 406 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 410 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 413 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 414 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 29 "MATEMATICKA ANALYZA V MAP LU \n" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "Symbolicke derivovani" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Pomoci procedury diff muzeme derivovat formule \+ (vyrazy):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "'diff(exp(-x^2 ),x)';\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%%diffG6$-%$expG6#,$*$)% \"xG\"\"#\"\"\"!\"\"F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Apostro fy kolem predchazejiciho vyrazu zamezi vyhodnoceni." }}{PARA 0 "" 0 " " {TEXT -1 82 "Stejneho efektu dosahneme i procedurou Diff. Diff se po uziva pro vetsi prehlednost" }}{PARA 0 "" 0 "" {TEXT -1 38 "a z duvodu kontroly spravnosti zadani." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "%;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"#\"\"\"%\"xGF&-%$ex pG6#,$*$)F'F%F&!\"\"F&F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Diff(ln(x/(x^2+1)),x)=diff(ln(x/(x^2+1)),x);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$-%#lnG6#*&%\"xG\"\"\",&*$)F+\"\"#F,F,F,F,!\" \"F+*(,&*&F,F,F-F1F,*(F0F,F+F0F-!\"#F1F,F+F1F-F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Diff(ln(x/(x^2+1)),x):%=value(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$-%#lnG6#*&%\"xG\"\"\",&*$)F+\"\"# F,F,F,F,!\"\"F+*(,&*&F,F,F-F1F,*(F0F,F+F0F-!\"#F1F,F+F1F-F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "normal(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$-%#lnG6#*&%\"xG\"\"\",&*$)F+\"\"#F,F,F, F,!\"\"F+,$*(,&F.F,F,F1F,F+F1F-F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Diff(x^(x^x),x):%=value(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$)%\"xG)F(F(F(*&F'\"\"\",&*(F)F+,&-%#lnG6#F(F +F+F+F+F/F+F+*&F)F+F(!\"\"F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "collect(%,ln(x), simplify); #diva se na vyraz jako na polynom \+ v promenne ln(x)\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$)%\"x G)F(F(F(,(*&)F(,&F)\"\"\"F(F.F.)-%#lnG6#F(\"\"#F.F.*&F,F.F0F.F.)F(,(F) F.F(F.F.!\"\"F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Derivace vyssi ch radu:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Diff(exp(-x^2), x,x):%=value(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$-%$ex pG6#,$*$)%\"xG\"\"#\"\"\"!\"\"-%\"$G6$F-F.,&*&F.F/F'F/F0*(\"\"%F/F,F/F 'F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Diff(exp(-x^2), x$ 5):%=value(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$-%$expG 6#,$*$)%\"xG\"\"#\"\"\"!\"\"-%\"$G6$F-\"\"&,(*(\"$?\"F/F-F/F'F/F0*(\"$ g\"F/)F-\"\"$F/F'F/F/*(\"#KF/)F-F4F/F'F/F0" }}}{EXCHG {PARA 330 "" 0 " " {TEXT -1 31 "Derivace funkce dane implicitne" }}}{EXCHG {PARA 413 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 268 "> " 0 "" {MPLTEXT 1 0 40 "alias(y=y(x)): #y povazujeme za funkci x" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eq:=x^2+y^2=c;\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#eqG/,&*$)%\"xG\"\"#\"\"\"F+*$)%\"yGF*F+F+%\"cG" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "diff(eq,x);\n" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/,&*&\"\"#\"\"\"%\"xGF'F'*(F&F'%\"yGF'-%%diffG6$ F*F(F'F'\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "dydx:=solv e(%, diff(y,x)); # 1. derivace\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% %dydxG,$*&%\"xG\"\"\"%\"yG!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "diff(eq,x$2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/, (\"\"#\"\"\"*&F%F&)-%%diffG6$%\"yG%\"xGF%F&F&*(F%F&F,F&-F*6$F,-%\"$G6$ F-F%F&F&\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "solve(%,di ff(y,x$2));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&\"\"\"F&*$)-%%d iffG6$%\"yG%\"xG\"\"#F&F&F&F,!\"\"F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "d2ydx2:=normal(subs(diff(y,x)=dydx,%));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'d2ydx2G,$*&,&*$)%\"xG\"\"#\"\"\"F,*$)%\"y GF+F,F,F,F/!\"$!\"\"" }}}{EXCHG {PARA 275 "> " 0 "" {MPLTEXT 1 0 11 "a lias(y=y):" }}}{EXCHG {PARA 332 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "implicitdiff(x^2+y^2,y,x,x) ;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&*$)%\"xG\"\"#\"\"\"F**$)% \"yGF)F*F*F*F-!\"$!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Parcia lni derivace:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Diff(exp(a *x*y^2),x,y$2):%=value(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%Di ffG6%-%$expG6#*(%\"aG\"\"\"%\"xGF,)%\"yG\"\"#F,F--%\"$G6$F/F0,(*(F0F,F +F,F'F,F,*,\"#5F,)F+F0F,F.F,F-F,F'F,F,*,\"\"%F,)F+\"\"$F,)F/F:F,)F-F0F ,F'F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(%);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6%-%$expG6#*(%\"aG\"\"\"%\"xG F,)%\"yG\"\"#F,F--%\"$G6$F/F0,$**F0F,F+F,F'F,,(F,F,**\"\"&F,F+F,F-F,F. F,F,**F0F,)F+F0F,)F/\"\"%F,)F-F0F,F,F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Diff(sin(x+y)/y^4, x$5, y$2):%=value(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6%*&-%$sinG6#,&%\"xG\"\"\"%\"yGF-F- F.!\"%-%\"$G6$F,\"\"&-F16$F.\"\"#,(*&-%$cosGF*F-F.F/!\"\"*(\"\")F-F(F- F.!\"&F-*(\"#?F-F9F-F.!\"'F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "collect(%,cos(x+y),normal);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #/-%%DiffG6%*&-%$sinG6#,&%\"xG\"\"\"%\"yGF-F-F.!\"%-%\"$G6$F,\"\"&-F16 $F.\"\"#,&*(,&*$)F.F6F-F-\"#?!\"\"F-F.!\"'-%$cosGF*F-F=*(\"\")F-F(F-F. !\"&F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "Pokud derivuje funkci ( ve smyslu datove struktury Maplu), musime pouzit funkcniho operatoru D ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "g:=x->x^n*exp(sin(x)); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGj+6#%\"xG6\"6$%)operatorG% &arrowGF(*&)9$%\"nG\"\"\"-%$expG6#-%$sinG6#F.F0F(F(F(6#\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "D(g);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#j+6#%\"xG6\"6$%)operatorG%&arrowGF&,&**)9$%\"nG\"\"\"F. F/F-!\"\"-%$expG6#-%$sinG6#F-F/F/*(F,F/-%$cosGF6F/F1F/F/F&F&F&6#\"+@fE 8?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "D(g)(Pi/6);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*,\"\"'\"\"\"),$*&F%!\"\"%#PiGF&F&% \"nGF&F,F&F+F*-%$expG6##F&\"\"#F&F&*&F0F&*(F'F&\"\"$F0F-F&F&F&" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "diff derivuje vzorec a na vystupu \+ vraci vzorec, D derivuje funkci a na vystupu vraci funkci." }}{PARA 0 "" 0 "" {TEXT -1 9 "Priklady:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "diff(cos(t),t); #derivace vzorce\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$sinG6#%\"tG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "D(cos); #derivace funkce\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%$ sinG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "(D@@2)(cos); # pro druhou derivaci funkce musime pouzit operatoru skladani funkci\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%$cosG!\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 42 "D(cos)(t); # derivace funkce v danem bode\n" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$sinG6#%\"tG!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Vsimnete si rozdilu mezi nasledujicimi dv ema prikazy:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "D(cos(t)); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"DG6#-%$cosG6#%\"tG" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Maple povazuje cos(t) za slozeni f unkci cos a t, spravny zapis je tedy:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "D(cos @ t);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-% \"@G6$,$%$sinG!\"\"%\"tG\"\"\"-%\"DG6#F*F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Derivace implicitni funkce pomoci operatoru D:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eq:=x^2+y^2=c:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "D(eq);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*(\"\"#\"\"\"-%\"DG6#%\"xGF'F+F'F'*(F&F'-F)6#%\"yGF' F/F'F'-F)6#%\"cG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "solve(% ,D(y));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"#F&*&,&*(F 'F&-%\"DG6#%\"xGF&F.F&F&-F,6#%\"cG!\"\"F&%\"yGF2F&F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "dydx:=subs(D(x)=1, D(c)=0, %);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dydxG,$*&%\"xG\"\"\"%\"yG!\"\"F*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "(D@@2)(eq);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,**(\"\"#\"\"\"--%#@@G6$%\"DGF&6#%\"xGF'F.F'F' *&F&F')-F,F-F&F'F'*(F&F'-F)6#%\"yGF'F5F'F'*&F&F')-F,F4F&F'F'-F)6#%\"cG " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "solve(%,(D@@2)(y));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"#F&*&,**(F'F&--%#@@G6 $%\"DGF'6#%\"xGF&F1F&F&*&F'F&)-F/F0F'F&F&*&F'F&)-F/6#%\"yGF'F&F&-F,6#% \"cG!\"\"F&F9F=F&F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "d2yd x2:=normal(subs(D(x)=1, (D@@2)(x)=0, (D@@2)(c)=0, D(y)=dydx, %));\n" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'d2ydx2G,$*&,&*$)%\"xG\"\"#\"\"\"F, *$)%\"yGF+F,F,F,F/!\"$!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Op eratoru D je mozno pouzit i pro vypocet parcialnich derivaci:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "h:=(x,y,z)->1/(x^2+y^2+z^2)^ (1/2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGj+6%%\"xG%\"yG%\"zG6 \"6$%)operatorG%&arrowGF**&\"\"\"F/*$,(*$)9$\"\"#F/F/*$)9%F5F/F/*$)9&F 5F/F/#F/F5!\"\"F*F*F*6%\"\"!F?F?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "'D[1](h)'=D[1](h);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-&%\"DG6#\"\"\"6#%\"hGj+6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF 0,$*&,(*$)9$\"\"#F(F(*$)9%F:F(F(*$)9&F:F(F(#!\"$F:F9F(!\"\"F0F0F06%\"* <4(o`\"\"!\"*S],S\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Zde D[1](h ) je parcialni derivace vzhledem k x." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "'D[1,2](h)'=D[1,2](h);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-&%\"DG6$\"\"\"\"\"#6#%\"hGj+6%%\"xG%\"yG%\"zG6\"6$%)o peratorG%&arrowGF1,$**\"\"$F(,(*$)9$F)F(F(*$)9%F)F(F(*$)9&F)F(F(#!\"&F )F>F(F;F(F(F1F1F16%\"*<4(o`\"\"!\"*O(e'R\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "D[1,2](h) je vlastne D[1](D[2](h)) - smisena parcialni de rivace vzhledem k x a y." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "'D[1,1](h)'=D[1,1](h);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-&%\"DG6 $\"\"\"F(6#%\"hGj+6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF0,&*(\"\"$ F(,(*$)9$\"\"#F(F(*$)9%F;F(F(*$)9&F;F(F(#!\"&F;F:F;F(*&F(F(*$)F7#F6F;F (!\"\"FHF0F0F06%\"*<4(o`\"\"!\"*7TwR\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Druha parcialni derivace vzhledem k x." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "L[h]:=(D[1,1]+D[2,2]+D[3,3])(h);\n" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>&%\"LG6#%\"hG,(j+6%%\"xG%\"yG%\"zG6\" 6$%)operatorG%&arrowGF.,&*(\"\"$\"\"\",(*$)9$\"\"#F5F5*$)9%F:F5F5*$)9& F:F5F5#!\"&F:F9F:F5*&F5F5*$)F6#F4F:F5!\"\"FGF.F.F.6%\"\"!\"#lFIF5j+6%% \"xG%\"yG%\"zGF.F/F.,&*(F4F5F6FAF=F:F5FCFGF.F.F.6%FIFJFIF5j+6%%\"xG%\" yG%\"zGF.F/F.,&*(F4F5F6FAF@F:F5FCFGF.F.F.6%FIFJFIF5" }}}{EXCHG {PARA 311 "" 0 "" {TEXT -1 53 "Maple muze derivovat i po castech definovane \+ funkce:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "F:=x->piecewis e(x>0, sin(x), arctan(x));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 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"int(exp(arcsin(x)), x=0..1); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$-%$expG6#-%'arcsinG6#% \"xG/F,;\"\"!\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "eval f(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+!pQ_!>!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Nekdy je vyhodne Maplu pri reseni asistov at:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(student):\n" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Int(sqrt(9-x^2), x);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*$,&\"\"*\"\"\"*$)%\"xG\"\"#F )!\"\"#F)F-F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "changevar( x=3*sin(t), Int(sqrt(9-x^2), x),t);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*(\"\"$\"\"\",&\"\"*F)*&F+F))-%$sinG6#%\"tG\"\"#F)!\"\"# F)F2-%$cosGF0F)F)F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "valu e(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&#\"\"*\"\"#\"\"\"*&,&F( F(*$)-%$sinG6#%\"tGF'F(!\"\"#F(F'F-F(F(F(*(F&F(F'F1F0F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "simplify(subs(t=arcsin(x/3), %));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(\"\"#!\"\"%\"xG\"\"\",&\"\"*F(*$ )F'F%F(F&#F(F%F(*&#F*F%F(-%'arcsinG6#,$*&\"\"$F&F'F(F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Pro metodu per - partes:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "i:=Int((x^2+1)*ln(x), x=1..2);\n" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG-%$IntG6$*&,&*$)%\"xG\"\"#\"\" \"F.F.F.F.-%#lnG6#F,F./F,;F.F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "i=intparts(i, ln(x));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-% $IntG6$*&,&*$)%\"xG\"\"#\"\"\"F-F-F-F--%#lnG6#F+F-/F+;F-F,,&*&#\"#9\" \"$F--F/6#F,F-F--F%6$*&F+!\"\",&F+F-*&#F-F7F-*$)F+F7F-F-F-F-F1F=" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "i=value(lhs(%));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&,&*$)%\"xG\"\"#\"\"\"F-F-F-F--%# lnG6#F+F-/F+;F-F,,&*&#\"#9\"\"$F--F/6#F,F-F-#\"#;\"\"*!\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Zobrazeni postupu vypoctu:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "read \"VypocetIntegralu.txt \":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "VypocetIntegralu(exp (x)*sin(x), czech);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&-%$ expG6#%\"xG\"\"\"-%$sinGF*F,F+%!G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7 %%:u|itijeme~metodu~per~partesG/%\"uG-%$expG6#%\"xG/%\"vG,$-%$cosGF)! \"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%!G,&*&-%$expG6#%\"xG\"\"\"-% $cosGF)F+!\"\"-%$IntG6$,$F&F.F*F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7 %%:u|itijeme~metodu~per~partesG/%\"uG-%$expG6#%\"xG/%\"vG-%$sinGF)" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/%!G,(*&-%$expG6#%\"xG\"\"\"-%$cosGF)F +!\"\"*&F'F+-%$sinGF)F+F+-%$IntG6$F/F*F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#%?integr|\\yl~spo|cy|hyt|\\yme~algebraickyG" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#/%!G,&*&#\"\"\"\"\"#F(*&-%$expG6#%\"xGF(-%$cosGF-F(F( !\"\"*&#F(F)F(*&F+F(-%$sinGF-F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #7#%/uprav|hyme~v|hzrazG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%!G,$*&# \"\"\"\"\"#F(*&-%$expG6#%\"xGF(,&-%$cosGF-F(-%$sinGF-!\"\"F(F(F4" }}} {EXCHG {PARA 361 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Konecne a nekonecne soucty:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Sum(k^7, k=1..20): %=value(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$*$)%\"kG\"\"(\"\"\"/F);F+\"#?\"++n GxQ" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Sum(k^7, k=1..n): %= value(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$*$)%\"kG\"\"( \"\"\"/F);F+%\"nG,,*&\"\")!\"\",&F.F+F+F+F1F+*&\"\"#F2F3F*F2*(F*F+\"#7 F2F3\"\"'F+*(F*F+\"#CF2F3\"\"%F2*&F7F2F3F5F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# /-%$SumG6$*$)%\"kG\"\"(\"\"\"/F);F+%\"nG,$**\"#C!\"\"F.\"\"#,,*&\"\"$F +)F.\"\"%F+F+*&\"\"'F+)F.F6F+F+*$)F.F3F+F2*&F8F+F.F+F2F3F+F+,&F.F+F+F+ F3F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "Sum(1/(k^2-4), k=3. .infinity): %=value(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6 $*&\"\"\"F(,&*$)%\"kG\"\"#F(F(\"\"%!\"\"F//F,;\"\"$%)infinityG#\"#D\"# [" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 "Tayloruv rozvoj" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "taylor(sin(tan(x))-tan(sin(x)), x=0 , 25);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#+7%\"xG#!\"\"\"#I\"\"(#!#H \"$c(\"\"*#!%8>\"&+c(\"#6#!#&*\"%#R(\"#8#!*p)[6J\",+?V'[a\"#:#!)2K>5\" +gX\"*eV\"#<#!+j$3Tm\"\".+[Ooa!>\"#>#!.,+Ybv4#\"1+?bv(=Gg(\"#@#!0$)[2D Ypu$\"4++w&[A0[!p'\"#B-%\"OG6#\"\"\"\"#D" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "whattype(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'s eriesG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "order(%%);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#D" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "25;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#D" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Order;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Ord er:=3: taylor(f(x), x=a);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++,&%\" xG\"\"\"%\"aG!\"\"-%\"fG6#F'\"\"!--%\"DG6#F*F+F&,$*&#F&\"\"#F&---%#@@G 6$F/F4F0F+F&F&F4-%\"OG6#F&\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "sin_series:=taylor(sin(x), x=0, 6);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+sin_seriesG++%\"xG\"\"\"F'#!\"\"\"\"'\"\"$#F'\"$?\" \"\"&-%\"OG6#F'\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "sin _series := series(1*x-1/6*x^3+1/120*x^5+O(x^7),x,7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+sin_seriesG++%\"xG\"\"\"F'#!\"\"\"\"'\"\"$#F'\"$? \"\"\"&-%\"OG6#F'\"\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "I kdyz \+ struktura rozvoje nam pripomina polynom, interni datova reprezentace j e jina:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "subs(x=2, sin_se ries);\n" }}{PARA 8 "" 1 "" {TEXT -1 38 "Error, invalid substitution i n series\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "op(sin_series );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6*\"\"\"F##!\"\"\"\"'\"\"$#F#\"$ ?\"\"\"&-%\"OG6#F#\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " sin_series*sin_series;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)++%\"xG \"\"\"F'#!\"\"\"\"'\"\"$#F'\"$?\"\"\"&-%\"OG6#F'\"\"(\"\"#F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "expand(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)++%\"xG\"\"\"F'#!\"\"\"\"'\"\"$#F'\"$?\"\"\"&-% \"OG6#F'\"\"(\"\"#F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "tay lor(%,x);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+'%\"xG\"\"\"\"\"#-%\"O G6#F%\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "mtaylor(sin(x ), x=0,6);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"xG\"\"\"*&#F%\"\" 'F%*$)F$\"\"$F%F%!\"\"*&#F%\"$?\"F%*$)F$\"\"&F%F%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 107 "mtaylor pocita Taylorovy rozvoje i pro funkce \+ vice promennych a vysledkem je datova struktura typu polynom." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(x=2, %);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#9\"#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "whattype(%%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% \"+G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "Muzeme urcovat i koeficie nty u danych mocnin x bez nutnosti pocitat cely rozvoj:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "coeftayl(sin(x), x=0, 19);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6##!\"\"\"3+?$)3/5X;7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "sin_series;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"xG\"\"\"F%#!\"\"\"\"'\"\"$#F%\"$?\"\"\"&-%\"OG6#F% \"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "diff(sin_series, x );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"xG\"\"\"\"\"!#!\"\"\"\"#F )#F%\"#C\"\"%-%\"OG6#F%\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "integrate(sin_series, x);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+ +%\"xG#\"\"\"\"\"#F'#!\"\"\"#C\"\"%#F&\"$?(\"\"'-%\"OG6#F&\"\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "convert(sin_series, 'polynom ');\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"xG\"\"\"*&#F%\"\"'F%*$)F $\"\"$F%F%!\"\"*&#F%\"$?\"F%*$)F$\"\"&F%F%F%" }}}{EXCHG {PARA 391 "> \+ " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "with(powseries); #procedury, slouzici k praci s mocninnymi rad ami\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#78%(composeG%(evalpowG%(inver seG%*multconstG%)multiplyG%)negativeG%'powaddG%'powcosG%*powcreateG%(p owdiffG%'powexpG%'powintG%'powlogG%(powpolyG%'powsinG%)powsolveG%(pows qrtG%)quotientG%*reversionG%)subtractG%)templateG%(tpsformG" }}} {EXCHG {PARA 393 "> " 0 "" {MPLTEXT 1 0 23 "powcreate(f(n)=a^n/n!);" } }}{EXCHG {PARA 394 "> " 0 "" {MPLTEXT 1 0 36 "powcreate(g(n)=(-1)^(n+1 )/n,g(0)=0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f(2);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"#!\"\"%\"aGF%\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "f_series:=tpsform(f,x,5);\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)f_seriesG+/%\"xG\"\"\"\"\"!%\"a GF',$*&\"\"#!\"\"F)F,F'F,,$*&\"\"'F-F)\"\"$F'F1,$*&\"#CF-F)\"\"%F'F5-% \"OG6#F'\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "g_series:= tpsform(g,x,5);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)g_seriesG+-%\" 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