SkalarproduktFunktionen

Buch:Höhere Mathematik sehen und verstehen, Haftendorn, Riebesehl, Dammer, 
Springer Spektrum, Feb. 2021
Datei fkt-skalar.nb zu Abschnitt 2.1.6.2 Seite 144, Abb. 2.7

g[x_]:=(1/2)+(1/2)(((1-x))^2)

f[x_]=(1/2)+(1/8)(((2-x))^3)(*f[x_]:=(3/2)-(1/2)x*)

{4f[x],4g[x]}//Simplify

Plot[{f[x],g[x]},{x,0,2}]

f[x]

f[x]/.x->1

Table[f[x],{x,0,2,(1/2)}]

fvdv=Table[4f[x],{x,0,2,(1/2)}]

gvdv=Table[4g[x],{x,0,2,(1/2)}]

fvdv.gvdv

%//N

(1/2)fvdv.gvdv
%//N

fv10dv=Table[4f[x],{x,0,2,(1/5)}]

gv10dv=Table[4g[x],{x,0,2,(1/5)}]

(1/5)fv10dv.gv10dv
%//N

(∫_0^2)16f[x]g[x]\[DifferentialD]x

%//N

rects=ParametricPlot3D[{{x,t f[x],0},{x,t f[x],g[x]},{x,0,t g[x]},{x,f[x],t g[x]}},{x,0,2},{t,0,1},BaseStyle->{Opacity[1],Thickness[0.005],FontSize->30},PlotRange->All,Boxed->False,MeshFunctions->{#1&},Mesh->10,MeshShading->{Opacity[0.5]},Axes->{True,False,False},Ticks->{{{0,"a"},{2,"b"}},None}];

rectsleer=ParametricPlot3D[{{x,t f[x],0},{x,t f[x],g[x]},{x,0,t g[x]},{x,f[x],t g[x]}},{x,0,2},{t,0,1},BaseStyle->{Opacity[1],Thickness[0.005],FontSize->30},PlotRange->All,Boxed->False,MeshFunctions->{#1&},Mesh->10,MeshShading->{Opacity[0]},Axes->{True,False,False},Ticks->{{{0,"a"},{2,"b"}},None}];

lines0=ParametricPlot3D[{{x,0,0},{x,0, g[x]},{x,f[x],0}},{x,0,2},PlotStyle->{{Thickness[0.009],Red},{Thickness[0.009],Blue},{Thickness[0.009],Green}},BaseStyle->{Thickness[0.008]},PlotRange->All,Boxed->False,Mesh->None];

lines=ParametricPlot3D[{{x,0,0},{x,0, g[x]},{x,f[x],0},{x, f[x],g[x]}},{x,0,2},
PlotStyle->{{Thickness[0.011],Red},{Thickness[0.009],Blue},{Thickness[0.009],Green},{Thickness[0.009],RGBColor[0.8,0,1]}},BaseStyle->{Thickness[0.008]},PlotRange->All,Boxed->False,Mesh->None];

extra=Graphics3D[{Line[{{0,0,0},{0,f[0],0},{0,f[0],g[0]},{0,0,g[0]},{0,0,0}}],Line[{{2,0,0},{2,f[2],0},{2,f[2],g[2]},{2,0,g[2]},{2,0,0}}]}];

allrects=Graphics3D[{EdgeForm[Thickness[0.007]],FaceForm[RGBColor[0,1,1]],Opacity[0.5],Table[Polygon[{{x,0,0},{x,f[x],0},{x,f[x],g[x]},{x,0,g[x]},{x,0,0}}],{x,0,2,0.2}]},Boxed->False];

allvects=Graphics3D[{Thickness[0.007],Table[{Arrow[{{x,0,0},{x,f[x],0}}],Arrow[{{x,0,0},{x,0,g[x]}}]},{x,0,2,0.2}]},Boxed->False];

allboxes=Graphics3D[{EdgeForm[Thickness[0.003]],FaceForm[RGBColor[1,1,1]],Opacity[0.3],Table[Cuboid[{x,0,0},{x+0.2,f[x],g[x]}],{x,0,2,0.2}]},Boxed->False];

Show[rectsleer,extra,lines0]

.1

Show[rects,lines,extra]

Show[allrects,lines,Axes->{True,False,False},BaseStyle->{FontSize->30,Thickness[0.007]},Ticks->{{{0,"a"},{2,"b"}},None},PlotRange->All]

Show[allvects,lines0,Axes->{True,False,False},BaseStyle->{FontSize->30,Thickness[0.007]},Ticks->{{{0,"a"},{2,"b"}},None},PlotRange->All]

Show[allboxes,lines,lines,Axes->{True,False,False},BaseStyle->{FontSize->30,Thickness[0.007]},Ticks->{{{0,"a"},{2,"b"}},None}]