{VERSION 6 0 "IBM INTEL NT" "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 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 } {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 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{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 "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 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 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "with(plottools): wit h(plots):" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 64 "Zu Kap. 7.6: Ausgle ichsgerade (Least-Square, Moore'sches Gesetz)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "with(linalg): with(plots):" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 179 "Vier Datenpunkte (xi,yi), durch die wir eine Ausg leichsgerade legen wollen:\n[Anwendungsfall Moore'sches Gesetz: xi sei en Jahre und yi sei log2(Speicherkapazit\344t bestimmter Chips)]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "npts:=5: \nxi:=[2,2.5,3,3.5, 4]:\nyi:=[1,1.7,2.9,2.0,3.8]:\nvi:=seq([xi[i],yi[i]],i=1..npts);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "p1:=plot([vi],x=2..4,0..5,st yle=point,symbol=CIRCLE,symbolsize=20,transparency=1):\ndisplay(p1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A:=matrix(npts,2,transpos e([xi,yi]));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Die Kovarianzmatr ix der Datenpunkte:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "C:=e valm(transpose(A) &* A);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Die r echte Seite des LGS:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "sx: =sum(xi[i],i=1..npts):\nsy:=sum(yi[i],i=1..npts):\nrechts:=transpose(m atrix(1,2,[sx,sy]));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "p:= 'p': p:=linsolve(C,rechts);\na:=p[1,1];\nb:=p[2,1];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Die Gleichung ax+by=1 aufgel\366st nach y=gerad :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "gerad:=x->1/b-a/b*x;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "Als Ergebnis plotten wir die Da tenpunkte zusammen mit der Ausgleichsgeraden in Blau:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "p2:=plot(gerad(x),x=2..4,0..5,lines tyle=[1],thickness=[3],color=[blue]):\ndisplay(p1,p2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 112 "Ergebnis anwenden:\nWenn y=log2(MegaByte ) und x=Jahre, dann ist die Steigung von y(x) gleich der Verdopplungsz eit" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "tDoppel:=evalf(-a/b) ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Alle 1.56 Jahre verdoppelt s ich die Speicherkapazit\344t dieser Chips." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 26 "gerad(5); MB5:=2^gerad(5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 " Im Jahre 5 erwarten wir eine Speicherkapazit\344t von 50.4 MB." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "#Jetzt noch ei nen 5. Pkt. dazu und neu fitten" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 46 "Aufgabe 5.5B (Gauss- Elimination mit Parameter)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart:\nwith(linalg): " }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, \+ the protected names norm and trace have been redefined and unprotected \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "A:=matrix(3,3,[[1,2,- 4],[0,4,2],[1,6,lambda]]);\nb:=vector([1,0,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7%7%\"\"\"\"\"#!\"%7%\"\"!\"\"%F+7%F* \"\"'%'lambdaGQ(pprint06\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGK% 'vectorG6#7%\"\"\"\"\"!F)Q(pprint16\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Aufgabe 1.4 (a): keine eindeutige L\366sung, wenn det(A)= 0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(det(A)=0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#!\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Aufgabe 1.4 (b): L\366sung f\374r " }{XPPEDIT 18 0 "lambda <> - 2;" "6#0%'lambdaG,$\"\"#!\"\"" }{TEXT -1 64 ": (Etwas bedenklich ist, \+ dass Maple nicht auf die Notwendigkeit " }{XPPEDIT 18 0 "lambda <> -2; " "6#0%'lambdaG,$\"\"#!\"\"" }{TEXT -1 12 " hinweist!!)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "x:='x': lambda:='lambda': x:=linsol ve(A,b);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xGK%'vectorG6#7%\"\" \"\"\"!F*Q(pprint26\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "L\366sun g f\374r" }{XPPEDIT 18 0 "lambda = -2;" "6#/%'lambdaG,$\"\"#!\"\"" } {TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "Am2:=matri x(3,3,[[1,2,-4],[0,4,2],[1,6,-2]]);\nx:='x': x:=linsolve(Am2,b);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Am2GK%'matrixG6#7%7%\"\"\"\"\"#!\"% 7%\"\"!\"\"%F+7%F*\"\"'!\"#Q(pprint36\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xGK%'vectorG6#7%,&\"\"\"F**&\"#5F*&%#_tG6#F*F*!\"\"F-,$*&\" \"#F*F-F*F0Q(pprint46\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "ACHTUN G: Die Zuweisung lambda:=-2 f\374hrt leider NICHT automatisch zur \304 nderung von A:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "x:='x': l ambda:=-2: evalm(A); x:=linsolve(A,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7%7%\"\"\"\"\"#!\"%7%\"\"!\"\"%F)7%F(\"\"'%'lambdaGQ (pprint56\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xGK%'vectorG6#7%\" \"\"\"\"!F*Q(pprint66\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Erst w enn wir den A-matrix-Befehl wiederholen, bekommt " }{XPPEDIT 18 0 "lam bda;" "6#%'lambdaG" }{TEXT -1 24 " in A einen festen Wert:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "A:=matrix(3,3,[[1,2,-4],[0,4,2],[1, 6,lambda]]);\nx:='x': x:=linsolve(A,b);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7%7%\"\"\"\"\"#!\"%7%\"\"!\"\"%F+7%F* \"\"'!\"#Q(pprint76\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xGK%'vect orG6#7%,&\"\"\"F**&\"#5F*&%#_tG6#F*F*!\"\"F-,$*&\"\"#F*F-F*F0Q(pprint8 6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Aufgabe 1.4(c): Zu fordern ist _t1 = 1/4, also ist " }{XPPEDIT 18 0 "(x_1, x_2, x_3) = ((-6)/4, \+ 1/4, (-2)/4);" "6#/6%%$x_1G%$x_2G%$x_3G6%*&,$\"\"'!\"\"\"\"\"\"\"%F,*& F-F-F.F,*&,$\"\"#F,F-F.F," }{TEXT -1 13 " eine L\366sung." }}{PARA 0 " " 0 "" {TEXT -1 17 "Die Probe stimmt:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "xc:=vector([-6/4,1/4,-2/4]):\nmultiply(Am3,xc)=evalm( b);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 127 "Das Package LinearAlgebra ist nicht besser. Ist lambda ein freier Parameter, dann wird die L \366sung zur\374ckgeliefert, die nur f\374r " }{XPPEDIT 18 0 "lambda < > -2;" "6#0%'lambdaG,$\"\"#!\"\"" }}{PARA 0 "" 0 "" {TEXT -1 77 "gilt: (BEACHTE: Die Matrix ist bei LinearAlgebra SPALTENweise zu definieren !)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "with(LinearAlgebra): lambda:='lambda':\nAA := <<1,0,1>|<2,4,6>|<-4,2,lambda>>; BB:=<<1,0,1> >;\nx:='x': x:=LinearSolve(AA,BB);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#AAG-%'RTABLEG6%\"*C3O\\\"-%'MATRIXG6#7%7%\"\"\"\"\"#!\"%7%\"\"!\"\" %F/7%F.\"\"'%'lambdaG%'MatrixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#B BG-%'RTABLEG6%\"*k`S\\\"-%'MATRIXG6#7%7#\"\"\"7#\"\"!F-%'MatrixG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'RTABLEG6%\"*KQj\\\"-%'MATRIXG 6#7%7#\"\"\"7#\"\"!F/%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 " Ist " }{XPPEDIT 18 0 "lambda = -2;" "6#/%'lambdaG,$\"\"#!\"\"" }{TEXT -1 49 ", dann erscheint die L\366sung mit freiem Parameter:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "lambda:=-2: AA := <<1,0,1>|< 2,4,6>|<-4,2,lambda>>; BB:=<<1,0,1>>;\nx:='x': x:=LinearSolve(AA,BB); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#AAG-%'RTABLEG6%\"*;:6[\"-%'MATR IXG6#7%7%\"\"\"\"\"#!\"%7%\"\"!\"\"%F/7%F.\"\"'!\"#%'MatrixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#BBG-%'RTABLEG6%\"*3]B\\\"-%'MATRIXG6#7%7# \"\"\"7#\"\"!F-%'MatrixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'R TABLEG6%\"*S\"*))\\\"-%'MATRIXG6#7%7#,&\"\"\"F/*&\"\"&F/&%$_t1G6$F/F/F /F/7#,$*&#F/\"\"#F/F2F/!\"\"7#F2%'MatrixG" }}}}{SECT 1 {PARA 3 "" 0 " " {TEXT -1 29 "Aufgabe 5.6B (Inverse Matrix)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "AB:=matrix(3,6,(1/6)*[[1,-1,1,6,0,0],[1,0,-2,0,6,0],[ 1,1,1,0,0,6]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ABGK%'matrixG6#7 %7(#\"\"\"\"\"'#!\"\"F,F*F+\"\"!F/7(F*F/#F.\"\"$F/F+F/7(F*F*F*F/F/F+Q) pprint446\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "gaussjord(AB );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7%7(\"\"\"\"\"!F)\" \"#F*F*7(F)F(F)!\"$F)\"\"$7(F)F)F(F(!\"#F(Q)pprint456\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A:=1/6*<<1,1,1>| <-1,0,1> |<1,-2,1> >;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'RTABLEG6%\"*gcy\\\"-%'M ATRIXG6#7%7%#\"\"\"\"\"'#!\"\"F0F.7%F.\"\"!#F2\"\"$7%F.F.F.%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "IA:=MatrixInverse(A);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#IAG-%'RTABLEG6%\"*O$>)\\\"-%'MATRIX G6#7%7%\"\"#F.F.7%!\"$\"\"!\"\"$7%\"\"\"!\"#F4%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "IA . A;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*;Wl\\\"-%'MATRIXG6#7%7%\"\"\"\"\"!F-7%F- F,F-7%F-F-F,%'MatrixG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }