{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE " " -1 260 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 } {CSTYLE "" -1 269 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 274 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{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 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 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 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 0 "" }{TEXT 269 38 "Aproximac e funkce Taylorovym polynomem" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 272 0 "" }{TEXT 273 0 "" } {TEXT -1 0 "" }{TEXT 270 10 "Pavel Kriz" }{TEXT -1 2 ", " }{TEXT 271 4 "2002" }}{PARA 0 "" 0 "" {TEXT -1 18 "xkriz@math.muni.cz" }}{PARA 0 "" 0 "" {URLLINK 17 "" 4 "" "" }{URLLINK 17 "www.math.muni.cz/~xkriz/c z" 4 "www.math.muni.cz/~xkriz/cz" "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }}{SECT 1 {PARA 3 "" 0 "" {TEXT 259 18 "Postupnym vypoctem" }}{EXCHG {PARA 0 "" 0 "" {TEXT 268 7 "Zadani:" }{TEXT -1 56 " Vypoctete Tayloru v polynom stupne 3 pro danou funkci. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Definujme funkci f:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:=x->ln(1+x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Spocteme derivace radu 1 az 3 funkce f:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "derivace1:=(D)(f);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "derivace2:=(D@@2)(f);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "derivace3:=(D@@3)(f);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "TayloruvPol ynom[3]:=f(0)+derivace1(0)*x+derivace2(0)*x^2/2+derivace3(0)*x^3/6;" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "Tento postup lze zobecnit pro li bovolnou funkci (splnujici predpoklady definice)." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 59 "TaylorPol:=(f,x0,n)->sum((D@@i)(f)(x0)/i!*(x -x0)^i,i=0..n);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Napoveda k par ametrum funkce taylor(f,x0,n):" }}{PARA 0 "" 0 "" {TEXT -1 16 "f - fun kce,vyraz" }}{PARA 0 "" 0 "" {TEXT -1 42 "x0 - rovnice udavajici stred mocninne rady" }}{PARA 0 "" 0 "" {TEXT -1 29 "n - stupen Taylorova po lynomu" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "TayloruvPolynom:= TaylorPol(f,0,3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Ke kontrole \+ vypoctu muzeme pouzit i funkci taylor:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "taylor(f(x),x=0,4);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 145 "Vyznam parametru je stejny jako u funkce TaylorPol, az na rozd il, ze funkci taylor musime zadat o 1 vetsi stupen pro vypocet stejneh o polynomu. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Tuto radu prevedme na polynom: " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "TayloruvPolynom:=convert(%,p olynom);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Ve vsech trech pripad ech je videt, ze vysledky jsou vzdy stejne." }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 260 28 "Animace Taylorovych polynomu" }}{SECT 1 {PARA 256 "" 0 "" {TEXT -1 31 "Skupina vsech obecnych procedur" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 267 41 "TRada vy tvori Tayloruv rozvoj pro n clenu" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "TRada := proc(f,x0,n ) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " option remember:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " sum((D@@i)(f)(x0)/i!*(x-x0)^i,i=0..n): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "end: " }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 256 67 "TPlots vytvori posloupnost n grafu funkci z 1 az n clenu T. ro zvoje" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "TPlots := proc(f,x0,n,int_x, int_y,degree)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " local p,text,tpl ot,j,bar:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " option remember:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " p:=[]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 " bar:=1/n:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " f or j from 1 to n do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 96 " tplot:= plot(TRada(f,x0,j),x=int_x,y=int_y, thickness=2, color=COLOR(RGB,0+j*b ar,0,1-j*bar));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " if degree th en" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 95 " text:=textplot([op(1,in t_x)+op(2,int_x)/10,op(2,int_y),cat(`Stupen `,j)],align=BELOW); " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " p:=p,[display(tplot,text)] el se " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " p:=p,tplot;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 " " } {TEXT 261 44 "TaylorAnimat a TaylorAnimat2 vytvori animaci" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "TaylorAnimat := proc(f,x0,n,int_x,int_y)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " local p,fplot,tplots:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " p:=TPlots(f,x0,n,int_x,int_y,true):" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 75 " fplot:=display(plot(f(x),x=int_x,y=int_y,col or=aquamarine, thickness=4)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 " \+ tplots:=display(fplot,p,insequence=true):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " display(tplots,fplot);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "TaylorAnimat2 := proc(f,x0, n,int_x,int_y)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " local d,j,fplot ,tplots:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " option remember:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " d:=[]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " for j from 1 to n do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 " d:=d,[display(TPlots(f,x0,j,int_x,int_y,false))] " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 " od: " }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 66 " fplot:=plot(f(x),x=int_x,y=int_y,color=aquamarine , thickness=4):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 " tplots:=displa y(fplot,d,insequence=true):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " di splay(fplot,tplots); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}} {SECT 1 {PARA 0 "" 0 "" {TEXT 262 8 "Funkce " }{TEXT -1 1 " " } {XPPEDIT 18 0 "sin(x) " "6#-%$sinG6#%\"xG" }{TEXT 277 45 " na interva lu [-2Pi; 2Pi], stred Tp v bode 0" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "f:=x->sin(x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "TaylorAnimat(f,0,20,'-2*Pi..2*Pi','-1.5..1.5');" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "TaylorAnimat2(f,0,20,'-2*Pi. .2*Pi','-1.5..1.5');" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 263 9 "Funkce \+ " }{XPPEDIT 18 0 "1/x " "6#*&\"\"\"F$%\"xG!\"\"" }{MPLTEXT 1 0 0 "" }{MPLTEXT 0 21 1 " " }{TEXT 274 39 "na intervalu [-3; 5], stred Tp v b ode 3" }{MPLTEXT 0 21 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f:=x->1/x:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "TaylorAni mat(f,3,9,'-3..5','0..2');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "TaylorAnimat2(f,3,9,'-3..5','0..2');" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 264 6 "Funkce" }{TEXT -1 3 " " }{XPPEDIT 18 0 "sqrt(x) " "6#-% %sqrtG6#%\"xG" }{TEXT 275 40 " na intervalu [0; 4], stred Tp v bode 1 " }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f:=x->sqr t(x): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "TaylorAnimat(f,1, 10,'0..4','0..2');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Taylo rAnimat2(f,1,10,'0..4','0..2');" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 265 6 "Funkce" }{TEXT -1 3 " " }{XPPEDIT 18 0 "ln(1+x); " "6#-%#lnG6 #,&\"\"\"F'%\"xGF'" }{TEXT -1 2 " " }{TEXT 276 39 "na intervalu [-1; \+ 2], stred Tp v bode 0" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:=x->ln(1+x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "TaylorAnimat(f,0,6,'-1..2','-2..2');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "TaylorAnimat2(f,0,6,'-1..2','-2..2');" }}}} {SECT 1 {PARA 0 "" 0 "" {TEXT 266 6 "Funkce" }{TEXT -1 3 " " } {XPPEDIT 18 0 "exp(x) " "6#-%$expG6#%\"xG" }{TEXT 278 42 " na interva lu [-3; 1], stred Tp v bode -2" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f:=x->exp(x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "TaylorAnimat(f,-2,7,'-3..1','0..2.5');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "TaylorAnimat2(f,-2,7,'-3..1','0..2. 5');" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 6 "Funkce" }{TEXT 257 2 " " }{XPPEDIT 18 0 "exp(-x^2)" "6#-%$expG6#,$*$%\"xG\"\" #!\"\"" }{TEXT 279 45 " na intervalu [-1.5; 1.5], stred Tp v bode 0" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:=x->exp(- x^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "TaylorAnimat(f,0,9 ,'-1.5..1.5','0..1.2');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 " TaylorAnimat2(f,0,9,'-1.5..1.5','0..1.2');" }}}}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 93 "Poznamka: Pokud se vyskytne chyba pri vypoctu nebo vyjd e nesmyslny vysledek, pouzijte prikaz " }{HYPERLNK 17 "restart" 2 "res tart" "" }{TEXT -1 33 " pro vymazani interni pameti. " }}}}{MARK "2 " 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }