{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 146 "Datum: 28.1.97\nAutor: Ja n K\344stle\nSchule: Isolde-Kurz-Gymnasium, 72766 Reutlingen\nDateinam e: linaprox\nDateigr\366\337e: 7 KB\nThema: Lineare Approximation" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart: with(plot s):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "f:=t->a*t^4+b*t^3+c* t^2+d*t+e;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"tG6\"6$%)ope ratorG%&arrowGF(,,*&%\"aG\"\"\"9$\"\"%F/*&%\"bGF/F0\"\"$F/*&%\"cGF/F0 \"\"#F/*&%\"dGF/F0F/F/%\"eGF/F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "1. Errechnen der Gleichung f\374r f(t) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "g:=f(x1)=y1: h:=f(x2)=y2: i:=f(x3)=y3: j:=f(x4)=y4 : k:=f(x5)=y5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "x1:=0: y1 :=0.: x2:=1.: y2:=2.: x3:=2: y3:=3: x4:=4.: y4:=4: x5:=5.: y5:=6:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(\{g,h,i,j,k\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<'/%\"eG\"\"!/%\"cG$!+nmmm^!#5/%\"bG$! +LLLLL!#6/%\"aG$\"+nmmm;F0/%\"dG$\"+LLLLD!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "kurve:=plot(f(t),t=-5..5,-5..5,scaling=constrained,th ickness=4,color=green):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " display(kurve);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "2. Ann\344heru ng an die Kurve durch Strecken" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "Punkte:=[[x1,y1],[x2,y2],[x3,y3],[x4,y4],[x5,y5]]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "strecken:=plot(Punkte,thickness=2): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "display(kurve,strecken) ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "3. Ausrechnen der Steigung d er Streckenteile" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "ZPF1:=( y-y1)/(x-x1)=(y2-y1)/(x2-x1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "ZPF2:=(y-y2)/(x-x2)=(y3-y2)/(x3-x2):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 36 "ZPF3:=(y-y3)/(x-x3)=(y4-y3)/(x4-x3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "ZPF4:=(y-y4)/(x-x4)=(y5-y4)/(x5-x4) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ZPF4G/*&,&%\"yG\"\"\"!\"%F)F), &%\"xGF)$F*\"\"!F)!\"\"$\"+++++?!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(ZPF1,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$% \"xG$\"\"#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(ZP F2,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"\"\"\"\"!F%%\"xGF%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(ZPF3,y);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,&$\"\"#\"\"!\"\"\"%\"xG$\"+++++]!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(ZPF4,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG$\"\"#\"\"!$!\"%F'\"\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 6 "m1:=2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "m2:=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "m3:=1/2:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "m4:=2:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 66 "Geschw:=[[0,m1],[1,m1],[1,m2],[2,m2],[2,m3],[3 ,m3],[3,m4],[4,m4]]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "v:= plot(Geschw):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "v;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "4. Ersetzen der Stufen durch eine \+ Kurve p(x)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "unassign('x1' ,'y1','x2','y2','x3','y3','x4','y4','x5','y5');" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 66 "x1:=0.5: y1:=2: x2:=1.5: y2:=1: x3:=2.5: y3:=1 /2: x4:=3.5: y4:=2: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "pun kte2:=[[x1,y1],[x2,y2],[x3,y3],[x4,y4]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(punkte2G7&7$$\"\"&!\"\"\"\"#7$$\"#:F)\"\"\"7$$\"#DF)#F.F*7$$ \"#NF)F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "p:=x->a1*x^3+b1 *x^2+c1*x+d1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG:6#%\"xG6\"6$%) operatorG%&arrowGF(,**&%#a1G\"\"\"9$\"\"$F/*&%#b1GF/F0\"\"#F/*&%#c1GF/ F0F/F/%#d1GF/F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "l:=p(x 1)=y1: m:=p(x2)=y2: n:=p(x3)=y3: o:=p(x4)=y4:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "loesung:=solve(\{l,m,n,o\},\{a1,b1,c1,d1\}):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "loesung;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#<&/%#a1G$\"+++++D!#5/%#c1G$!++++]i!#6/%#b1G$!++++]()F (/%#d1G$\"+++v=A!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "ass ign(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot2:=plot(p(x ),x,color=blue,thickness=2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "display(v,plot2,view=[0..5,0..4]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "5. Vergleich der beiden Kurven" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$%\"tG \"\"%$\"+nmmm;!#6*$F%\"\"$$!+LLLLLF)*$F%\"\"#$!+nmmm^!#5F%$\"+LLLLD!\" *" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "p(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$%\"xG\"\"$$\"+++++D!#5*$F%\"\"#$!++++]()F)F%$!++ ++]i!#6$\"+++v=A!\"*\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "plot1:=plot(f(t),t,color=green,thickness=2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "display(plot1,plot2,view=[0..8,0..8]);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "6. Ergebniss" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 221 "Man bekommt die Kurve der Geschwindigkeit durch A bleiten von der ersten Kuve,d.h.:man nimmt den koeffizienten mit der H ochzahl mal und verringert die Hochzahl anschlie\337end um eins (In di esem Fall stimmt da\337 nur ungef\344hr)." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "diff( .1666666667e-1*t^4-.3333333333e-1*t^3-.5166666667*t^2+2.533333333*t,t) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$%\"tG\"\"$$\"+ommmm!#6*$F%\" \"#$!+**********F)F%$!+LLLL5!\"*$\"+LLLLDF0\"\"\"" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }