{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "1. Quadriken, 2-dimensional" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "q:=a*x^2 + b*y^2=1;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "(a) beide Eigenwerte positiv (also A posi tiv definit)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "a:=2; b:=5;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "q;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "implicitplot(q,x=-1..1,y=-1..1,thickness=3,color=b lack,scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "((b ) A indefinit, also ein Eigenwert positiv, der zweite negativ" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "a:=2; b:=-5;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 2 "q;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "implicitplot(q,x=-4..4,y=-4..4,thickness=3,color=green,scaling=con strained,numpoints=2000);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "a:=-2; b:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "q;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "implicitplot(q,x=-4..4,y=-4. .4,thickness=3,color=red,scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "(c) singul\344re Matrix, etwa a=0" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "a:=0; b:=4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "q;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "implicitplot(q ,x=-4..4,y=-4..4,thickness=3,color=blue,scaling=constrained);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Fazit: Das ist ein Geradenpaar (w ar ja klar)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{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 26 " 2. Quadriken 3-dimensional" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "q:= a *x^2 + b*y^2 + c*z^2 = 1;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "(a) \+ alle Eigenwerte positiv" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "a:=1; b: =1/4; c:=1/16;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "q;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "implicitplot3d(q,x=-1..1,y= -2..2,z=-4...4,grid=[40,40,40],axes=framed,shading=zhue,style=\npatchc ontour);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "(b) zwei Eigenwerte p ositiv, ein Eigenwert negativ" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "c:=-1/16;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "q;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "implicitplot3d(q,x= -4..4,y=-6..6,z=-10...10,grid=[40,40,40],axes=framed,shading=zhue,styl e=\npatchcontour);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Das ist ein sogenanntes einschaliges Hyperboloid" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "(c) ein Eigenwert positiv, zwei Eigenwert e negativ" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "a:=2; b:= -1; c:= -1; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "q;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "implicitplot3d(q,x=-5..5,y=-5..5,z=-4...4,gr id=[40,40,40],axes=framed,shading=zhue,style=\npatchcontour);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "(d) ein Eigenwert gleich 0 : ellip tische oder hyberbolische Zylinder" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "a:=1/4; b:=1/16; c:=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "q;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "implicitplot3d(q, x=-2..2,y=-4..4,z=-4...4,grid=[40,40,40],axes=framed,shading=zhue,styl e=\npatchcontour);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "a:=1/ 4; b:=-1; c:=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "q;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "implicitplot3d(q,x=-8..8,y= -2..2,z=-4...4,grid=[40,40,40],axes=framed,shading=zhue,style=\npatchc ontour);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "36 " 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }