Uebungsblatt 1

Uebungen Differential- und Integralrechnung, WS11/12
Andreas Windisch, 21. Oct 2011

ad Aufgabe 2 a

Needs["PlotLegends`"];
Z1=-1+2I;
Z2=3-I;
Z3=Re[Z1];
Z4=Im[Z1];
Z5=Abs[Z1];
Z6=Z1+Z2;
Z7=Z1-Z2;
Z8=Z1/Z2;
Z9=Z1*Z2;
ZP[color_,Z_]:=Graphics[{color,PointSize[0.02],Point[{Re[Z],Im[Z]}]}];
ZL[color_,Z_]:=Graphics[{color,Thickness[0.005],Line[{{0,0},{Re[Z],Im[Z]}}]}];
Z1P=ZP[Red,Z1];
Z1L=ZL[Red,Z1];
Z2P=ZP[Blue,Z2];
Z2L=ZL[Blue,Z2];
Z3P=ZP[Green,Z3];
Z3L=ZL[Green,Z3];
Z4P=ZP[Black,Z4];
Z4L=ZL[Black,Z4];
Z5P=ZP[Magenta,Z5];
Z5L=ZL[Magenta,Z5];
Z6P=ZP[Purple,Z6];
Z6L=ZL[Purple,Z6];
Z7P=ZP[Cyan,Z7];
Z7L=ZL[Cyan,Z7];
Z8P=ZP[Orange,Z8];
Z8L=ZL[Orange,Z8];
Z9P=ZP[Pink,Z9];
Z9L=ZL[Pink,Z9];

LE=Graphics[Legend[{{Graphics[{Red,Disk[{0,0},0.005]}],"Z1"},{Graphics[{Blue,Disk[{0,0},0.005]}],"Z2"},
{Graphics[{Green,Disk[{0,0},0.005]}],"Z3"},
{Graphics[{Black,Disk[{0,0},0.005]}],"Z4"},
{Graphics[{Magenta,Disk[{0,0},0.005]}],"Z5"},
{Graphics[{Purple,Disk[{0,0},0.005]}],"Z6"},
{Graphics[{Cyan,Disk[{0,0},0.005]}],"Z7"},
{Graphics[{Orange,Disk[{0,0},0.005]}],"Z8"},
{Graphics[{Pink,Disk[{0,0},0.005]}],"Z9"}}]];

GraphicsRow[{Show[Z1P,Z1L,Z2P,Z2L,Z3P,Z3L,Z4P,Z4L,Z5P,Z5L,Z6P,Z6L,Z7P,Z7L,Z8P,Z8L,Z9P,Z9L,Axes->True,PlotRange->{{-8,8},{-8,8}},Frame->True],LE}]

ad Aufgabe 2 d

C1=Graphics[{Purple,Opacity[0.2],Disk[{0,0},2]}];
C2=Graphics[{White,Disk[{0,0},1]}];
L1=Graphics[{Red,Thickness[0.005],Line[{{0,0},{3,3}}]}];
L2=Graphics[{Red,Thickness[0.005],Line[{{0,0},{3,-3}}]}];
S1=Graphics[{Orange,Opacity[0.4],Disk[{0,0},2,{-Pi/4,Pi/4}]}];
S2=Graphics[{White,Disk[{0,0},1,{-Pi/4,Pi/4}]}];
LE2=Graphics[Legend[{{Graphics[{Red,PointSize[0.5],Point[{0,0}]}],"|Im Z| <  Re Z"},{Graphics[{Purple,Opacity[0.2],PointSize[0.5],Point[{0,0}]}],"1 ≤ |z|\!\(\*SuperscriptBox[\(\\ \), \(2\)]\) ≤ 4"}}]];

GraphicsRow[{Show[C1,C2,S1,S2,L1,L2,Axes->True,Frame->True,PlotRange->{{-3,3},{-3,3}}],LE2}]

ad Aufgabe 3

D[D[f[x,t],x],x]

D[f[x,t],x]

f[x_,t_]=1/(6t)x^3-x^2+3/2t x;
fprime[x_,t_]=D[f[x,t],x];
f2prime[x_,t_]=D[D[f[x,t],x],x];
Manipulate[Show[{Plot[f[x,t],{x,-3,14},PlotRange->{{-3,14},{-9,9}},PlotStyle->Directive[Thickness[0.005]],PlotLabel->{Row[{Style["x",Italic,10]," = ",Style[x,t,10]    }],
Row[{Style["t",Italic,10]," = ",Style[x,t,10]    }],
Row[{Style["  f[x,t]",Italic,10]," = ",Style[f[x,t],10] }],Row[{Style["  f' [x,t]",Italic,10]," = ",Style[fprime[x,t],10]    }],Row[{Style["  f'' [x,t]",Italic,10]," = ",Style[f2prime[x,t],10]}]}],Plot[fprime[x,t](a-x)+f[x,t],{a,-3,14},PlotStyle->Directive[Thickness[0.005],Red]]}],{x,-3,14},{t,0.001,5}]