(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 7.0' *)

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(* Beginning of Notebook Content *)
Notebook[{
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   DynamicModuleBox[{$CellContext`a$$ = 1, $CellContext`b$$ = 
    1, $CellContext`c$$ = 1, $CellContext`CAPB$$ = True, $CellContext`CAPT$$ =
     True, $CellContext`n$$ = 10, $CellContext`q$$ = 0.8, Typeset`show$$ = 
    True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{
      Hold[
       Style["    Top Cap", 13, Bold]], Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`CAPT$$], True, ""}, {True, False}}, {
      Hold[
       Style["    Bottom Cap", 13, Bold]], 
      Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`CAPB$$], True, ""}, {True, False}}, {
      Hold[""], Manipulate`Dump`ThisIsNotAControl}, {
      Hold[""], Manipulate`Dump`ThisIsNotAControl}, {
      Hold[
       Style["                   Density", 13, Bold]], 
      Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`n$$], 10, 
       Style["", 13, Bold]}, 1, 20, 5}, {
      Hold[
       Style["                   Opacity", 13, Bold]], 
      Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`q$$], 0.8, 
       Style["", 13, Bold]}, 0, 2}, {{
       Hold[$CellContext`a$$], 1, 
       Style[
       "\!\(\*\nStyleBox[\"a\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
        Bold]}, -1, 1}, {{
       Hold[$CellContext`b$$], 1, 
       Style[
       "\!\(\*\nStyleBox[\"b\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
        Bold]}, -1, 1}, {{
       Hold[$CellContext`c$$], 1, 
       Style[
       "\!\(\*\nStyleBox[\"c\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
        Bold]}, -1, 1}, {
      Hold[
       Dynamic[
        Column[{
          Style[
          "\!\(\*\nStyleBox[\"Vector\",\nFontColor->RGBColor[0, 0, \
1]]\)\!\(\*\nStyleBox[\" \",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\*\n\
StyleBox[\"Field\",\nFontColor->RGBColor[0, 0, 1]]\)", 15, Bold], 
          Row[{
            Style[
            "\!\(\*\nStyleBox[\"F\",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\*\n\
StyleBox[\"(\",\nFontColor->GrayLevel[0]]\)x,y,z)={\!\(\*\nStyleBox[\"a\",\n\
FontColor->RGBColor[0, 0, 1]]\)x,\!\(\*\nStyleBox[\"b\",\n\
FontColor->RGBColor[0, 0, 1]]\)y,\!\(\*\nStyleBox[\"c\",\n\
FontColor->RGBColor[0, 0, 1]]\)z}=", 15, Bold], 
            Style[
             $CellContext`F[{$CellContext`x, $CellContext`y, $CellContext`z}, \
$CellContext`a$$, $CellContext`b$$, $CellContext`c$$], 15, Bold]}], Null, 
          Null, Null, Null, 
          Row[{
            Style[
            "Lateral Flux=\[Integral]\[Integral]\!\(\*\nStyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]]\)\[CenterDot]\!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"n\",\nFontColor->RGBColor[1, 0, 0]], \"\[RightVector]\"],\n\
FontColor->RGBColor[1, 0, 0]]\)dS=", 15, Bold], 
            Style[$CellContext`FluxLat, 15, Bold]}], Null, 
          If[$CellContext`CAPT$$, 
           Row[{
             Style[
             "Top Cap Flux=\[Integral]\[Integral]\!\(\*\nStyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]]\)\[CenterDot]\!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"n\",\nFontColor->RGBColor[1, 0, 0]], \"\[RightVector]\"],\n\
FontColor->RGBColor[1, 0, 0]]\)dS=", 15, Bold], 
             Style[$CellContext`FluxCap1, 15, Bold], ""}]], Null, 
          If[$CellContext`CAPB$$, 
           Row[{
             Style[
             "Bottom Cap Flux=\[Integral]\[Integral]\!\(\*\nStyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]]\)\[CenterDot]\!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"n\",\nFontColor->RGBColor[1, 0, 0]], \"\[RightVector]\"],\n\
FontColor->RGBColor[1, 0, 0]]\)dS=", 15, Bold], 
             Style[$CellContext`FluxCap2, 15, Bold], ""}]], Null, 
          Row[{
            Style[
            "Total Flux=\[Integral]\[Integral]\!\(\*\nStyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]]\)\[CenterDot]\!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"n\",\nFontColor->RGBColor[1, 0, 0]], \"\[RightVector]\"],\n\
FontColor->RGBColor[1, 0, 0]]\)dS=", 15, Bold], 
            Style[
             
             Simplify[$CellContext`FluxCap1 + $CellContext`FluxCap2 + \
$CellContext`FluxLat], 15, Bold]}], Null, Null, Null, Null, 
          Row[{
            Style[
            "div\!\(\*\nStyleBox[\"F\",\nFontColor->RGBColor[0, 0, 1]]\)=", 
             15, Bold], 
            Style[
             Simplify[$CellContext`DF], 15, Bold]}], Null, 
          Row[{
            Style[
            "\[Integral]\[Integral]\[Integral]div\!\(\*\nStyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]]\)dV=", 15, Bold], 
            Style[
             Simplify[$CellContext`TrDI], 15, Bold]}]}, Center]]], 
      Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = {
    710., {302., 308.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = False, $CellContext`CAPT$3960$$ = 
    False, $CellContext`CAPB$3961$$ = False, $CellContext`n$3962$$ = 
    0, $CellContext`q$3963$$ = 0, $CellContext`a$3964$$ = 
    0, $CellContext`b$3965$$ = 0, $CellContext`c$3966$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`a$$ = 1, $CellContext`b$$ = 
        1, $CellContext`c$$ = 1, $CellContext`CAPB$$ = 
        True, $CellContext`CAPT$$ = True, $CellContext`n$$ = 
        10, $CellContext`q$$ = 0.8}, "ControllerVariables" :> {
        Hold[$CellContext`CAPT$$, $CellContext`CAPT$3960$$, False], 
        Hold[$CellContext`CAPB$$, $CellContext`CAPB$3961$$, False], 
        Hold[$CellContext`n$$, $CellContext`n$3962$$, 0], 
        Hold[$CellContext`q$$, $CellContext`q$3963$$, 0], 
        Hold[$CellContext`a$$, $CellContext`a$3964$$, 0], 
        Hold[$CellContext`b$$, $CellContext`b$3965$$, 0], 
        Hold[$CellContext`c$$, $CellContext`c$3966$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, 
      "Body" :> ($CellContext`SDB = ParametricPlot3D[
          $CellContext`Surf[$CellContext`v, $CellContext`w], {$CellContext`v, \
$CellContext`Av, $CellContext`Bv}, {$CellContext`w, $CellContext`Aw, \
$CellContext`Bw}, PlotStyle -> Opacity[$CellContext`q$$]]; $CellContext`SCap1 = 
        ParametricPlot3D[
          $CellContext`Cap1[$CellContext`u, $CellContext`v], {$CellContext`u, \
$CellContext`AuC, $CellContext`BTC}, {$CellContext`v, $CellContext`AvC, \
$CellContext`BvC}, PlotStyle -> 
          Opacity[$CellContext`q$$]]; $CellContext`SCap2 = ParametricPlot3D[
          $CellContext`Cap2[$CellContext`u, $CellContext`v], {$CellContext`u, \
$CellContext`AuC, $CellContext`BBC}, {$CellContext`v, $CellContext`AvC, \
$CellContext`BvC}, PlotStyle -> 
          Opacity[$CellContext`q$$]]; $CellContext`DF = $CellContext`a$$ + \
$CellContext`b$$ + $CellContext`c$$; $CellContext`TrDI = $CellContext`DF 
         Integrate[
           Abs[
            Det[
             
             D[{$CellContext`u Cos[$CellContext`v], $CellContext`u 
               Sin[$CellContext`v], $CellContext`w}, {{$CellContext`u, \
$CellContext`v, $CellContext`w}}]]], {$CellContext`v, $CellContext`Av, \
$CellContext`Bv}, {$CellContext`w, $CellContext`Aw, $CellContext`Bw}, \
{$CellContext`u, 0, 
            $CellContext`f[$CellContext`w]}]; $CellContext`FluxLat = Integrate[
          Dot[
           $CellContext`F[
            $CellContext`Surf[$CellContext`v, $CellContext`w], \
$CellContext`a$$, $CellContext`b$$, $CellContext`c$$], 
           Cross[
            D[
             $CellContext`Surf[$CellContext`v, $CellContext`w], \
$CellContext`v], 
            D[
             $CellContext`Surf[$CellContext`v, $CellContext`w], \
$CellContext`w]]], {$CellContext`v, $CellContext`Av, $CellContext`Bv}, \
{$CellContext`w, $CellContext`Aw, $CellContext`Bw}]; $CellContext`Su = 
        1/$CellContext`n$$; $CellContext`Sv = ($CellContext`Bv - \
$CellContext`Av)/$CellContext`n$$; $CellContext`Sw = ($CellContext`Bw - \
$CellContext`Aw)/$CellContext`n$$; $CellContext`STC = \
$CellContext`BTC/$CellContext`n$$; $CellContext`SBC = \
$CellContext`BBC/$CellContext`n$$; $CellContext`SuC = ($CellContext`BuC - \
$CellContext`AuC)/$CellContext`n$$; $CellContext`SvC = ($CellContext`BvC - \
$CellContext`AvC)/$CellContext`n$$; 
       If[$CellContext`CAPT$$, $CellContext`FluxCap1 = Integrate[
           Dot[
            $CellContext`F[
             $CellContext`Cap1[$CellContext`u, $CellContext`v], \
$CellContext`a$$, $CellContext`b$$, $CellContext`c$$], 
            Cross[
             D[
              $CellContext`Cap1[$CellContext`u, $CellContext`v], \
$CellContext`u], 
             D[
              $CellContext`Cap1[$CellContext`u, $CellContext`v], \
$CellContext`v]]], {$CellContext`u, $CellContext`AuC, $CellContext`BTC}, \
{$CellContext`v, $CellContext`AvC, $CellContext`BvC}], $CellContext`FluxCap1 = 
         0]; If[$CellContext`CAPB$$, $CellContext`FluxCap2 = -Integrate[
            Dot[
             $CellContext`F[
              $CellContext`Cap2[$CellContext`u, $CellContext`v], \
$CellContext`a$$, $CellContext`b$$, $CellContext`c$$], 
             Cross[
              D[
               $CellContext`Cap2[$CellContext`u, $CellContext`v], \
$CellContext`u], 
              D[
               $CellContext`Cap2[$CellContext`u, $CellContext`v], \
$CellContext`v]]], {$CellContext`u, $CellContext`AuC, $CellContext`BBC}, \
{$CellContext`v, $CellContext`AvC, $CellContext`BvC}], $CellContext`FluxCap2 = 
         0]; $CellContext`P1 = Flatten[
          Table[
           Graphics3D[{Red, Arrowheads -> Small, 
             Arrow[{
               $CellContext`Surf[$CellContext`Av + 
                0.5 $CellContext`Sv $CellContext`i, $CellContext`Aw + \
$CellContext`Sw $CellContext`j], $CellContext`Surf[$CellContext`Av + 
                 
                 0.5 $CellContext`Sv $CellContext`i, $CellContext`Aw + \
$CellContext`Sw $CellContext`j] + $CellContext`NrLat[$CellContext`Av + 
                 0.5 $CellContext`Sv $CellContext`i, $CellContext`Aw + \
$CellContext`Sw $CellContext`j]}]}], {$CellContext`i, 1, 
            2 $CellContext`n$$}, {$CellContext`j, 1, $CellContext`n$$}], 
          2]; $CellContext`P2 = Flatten[
          Table[
           Graphics3D[{Blue, Arrowheads -> Small, 
             Arrow[{
               $CellContext`Surf[$CellContext`Av + 
                0.5 $CellContext`Sv $CellContext`i, $CellContext`Aw + \
$CellContext`Sw $CellContext`j], $CellContext`Surf[$CellContext`Av + 
                 0.5 $CellContext`Sv $CellContext`i, $CellContext`Aw + \
$CellContext`Sw $CellContext`j] + 0.5 $CellContext`F[
                  $CellContext`Surf[$CellContext`Av + 
                   0.5 $CellContext`Sv $CellContext`i, $CellContext`Aw + \
$CellContext`Sw $CellContext`j], $CellContext`a$$, $CellContext`b$$, \
$CellContext`c$$]}]}], {$CellContext`i, 1, 
            2 $CellContext`n$$}, {$CellContext`j, 1, $CellContext`n$$}], 
          2]; $CellContext`P3 = Flatten[
          Table[
           Graphics3D[{Red, Arrowheads -> Small, 
             Arrow[{
               $CellContext`Cap1[$CellContext`AuC + $CellContext`STC \
$CellContext`i, $CellContext`AvC + 
                0.5 $CellContext`SvC $CellContext`j], \
$CellContext`Cap1[$CellContext`AuC + $CellContext`STC $CellContext`i, \
$CellContext`AvC + 
                 0.5 $CellContext`SvC $CellContext`j] + \
$CellContext`NrCap1[$CellContext`AuC + $CellContext`STC $CellContext`i, \
$CellContext`AvC + 0.5 $CellContext`SvC $CellContext`j]}]}], {$CellContext`i, 
            1, $CellContext`n$$}, {$CellContext`j, 1, 2 $CellContext`n$$}], 
          2]; $CellContext`P4 = Flatten[
          Table[
           Graphics3D[{Blue, Arrowheads -> Small, 
             Arrow[{
               $CellContext`Cap1[$CellContext`AuC + $CellContext`STC \
$CellContext`i, $CellContext`AvC + 
                0.5 $CellContext`SvC $CellContext`j], \
$CellContext`Cap1[$CellContext`AuC + $CellContext`STC $CellContext`i, \
$CellContext`AvC + 0.5 $CellContext`SvC $CellContext`j] + 0.5 $CellContext`F[
                  $CellContext`Cap1[$CellContext`AuC + $CellContext`STC \
$CellContext`i, $CellContext`AvC + 
                   0.5 $CellContext`SvC $CellContext`j], $CellContext`a$$, \
$CellContext`b$$, $CellContext`c$$]}]}], {$CellContext`i, 
            1, $CellContext`n$$}, {$CellContext`j, 1, 2 $CellContext`n$$}], 
          2]; $CellContext`P5 = Flatten[
          Table[
           Graphics3D[{Red, Arrowheads -> Small, 
             Arrow[{
               $CellContext`Cap2[$CellContext`AuC + $CellContext`SBC \
$CellContext`i, $CellContext`AvC + 
                0.5 $CellContext`SvC $CellContext`j], \
$CellContext`Cap2[$CellContext`AuC + $CellContext`SBC $CellContext`i, \
$CellContext`AvC + 
                 0.5 $CellContext`SvC $CellContext`j] + \
$CellContext`NrCap2[$CellContext`AuC + $CellContext`SBC $CellContext`i, \
$CellContext`AvC + 0.5 $CellContext`SvC $CellContext`j]}]}], {$CellContext`i, 
            1, $CellContext`n$$}, {$CellContext`j, 1, 2 $CellContext`n$$}], 
          2]; $CellContext`P6 = Flatten[
          Table[
           Graphics3D[{Blue, Arrowheads -> Small, 
             Arrow[{
               $CellContext`Cap2[$CellContext`AuC + $CellContext`SBC \
$CellContext`i, $CellContext`AvC + 
                0.5 $CellContext`SvC $CellContext`j], \
$CellContext`Cap2[$CellContext`AuC + $CellContext`SBC $CellContext`i, \
$CellContext`AvC + 0.5 $CellContext`SvC $CellContext`j] + 0.5 $CellContext`F[
                  $CellContext`Cap2[$CellContext`AuC + $CellContext`SBC \
$CellContext`i, $CellContext`AvC + 
                   0.5 $CellContext`SvC $CellContext`j], $CellContext`a$$, \
$CellContext`b$$, $CellContext`c$$]}]}], {$CellContext`i, 
            1, $CellContext`n$$}, {$CellContext`j, 1, 2 $CellContext`n$$}], 
          2]; If[
         And[$CellContext`CAPT$$, $CellContext`CAPB$$], 
         Framed[
          
          Show[$CellContext`P1, $CellContext`P2, $CellContext`P3, \
$CellContext`P4, $CellContext`P5, $CellContext`P6, $CellContext`SDB, \
$CellContext`SCap1, $CellContext`SCap2, ImageSize -> {700, 600}]], 
         If[$CellContext`CAPT$$, 
          Framed[
           
           Show[$CellContext`P1, $CellContext`P2, $CellContext`P3, \
$CellContext`P4, $CellContext`SDB, $CellContext`SCap1, 
            ImageSize -> {700, 600}]], 
          If[$CellContext`CAPB$$, 
           Framed[
            
            Show[$CellContext`P1, $CellContext`P2, $CellContext`P5, \
$CellContext`P6, $CellContext`SDB, $CellContext`SCap2, 
             ImageSize -> {700, 600}]], 
           Framed[
            
            Show[$CellContext`P1, $CellContext`P2, $CellContext`SDB, 
             ImageSize -> {700, 600}]]]]]), "Specifications" :> {
        Style[
        "    Top Cap", 13, Bold], {{$CellContext`CAPT$$, True, ""}, {
         True, False}}, 
        Style[
        "    Bottom Cap", 13, Bold], {{$CellContext`CAPB$$, True, ""}, {
         True, False}}, Delimiter, "", "", 
        Style["                   Density", 13, Bold], {{$CellContext`n$$, 10, 
          Style["", 13, Bold]}, 1, 20, 5}, 
        Style[
        "                   Opacity", 13, Bold], {{$CellContext`q$$, 0.8, 
          Style["", 13, Bold]}, 0, 2}, {{$CellContext`a$$, 1, 
          Style[
          "\!\(\*\nStyleBox[\"a\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
           Bold]}, -1, 1}, {{$CellContext`b$$, 1, 
          Style[
          "\!\(\*\nStyleBox[\"b\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
           Bold]}, -1, 1}, {{$CellContext`c$$, 1, 
          Style[
          "\!\(\*\nStyleBox[\"c\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
           Bold]}, -1, 1}, 
        Dynamic[
         Column[{
           Style[
           "\!\(\*\nStyleBox[\"Vector\",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\
\*\nStyleBox[\" \",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\*\n\
StyleBox[\"Field\",\nFontColor->RGBColor[0, 0, 1]]\)", 15, Bold], 
           Row[{
             Style[
             "\!\(\*\nStyleBox[\"F\",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\*\n\
StyleBox[\"(\",\nFontColor->GrayLevel[0]]\)x,y,z)={\!\(\*\nStyleBox[\"a\",\n\
FontColor->RGBColor[0, 0, 1]]\)x,\!\(\*\nStyleBox[\"b\",\n\
FontColor->RGBColor[0, 0, 1]]\)y,\!\(\*\nStyleBox[\"c\",\n\
FontColor->RGBColor[0, 0, 1]]\)z}=", 15, Bold], 
             Style[
              $CellContext`F[{$CellContext`x, $CellContext`y, \
$CellContext`z}, $CellContext`a$$, $CellContext`b$$, $CellContext`c$$], 15, 
              Bold]}], Null, Null, Null, Null, 
           Row[{
             Style[
             "Lateral Flux=\[Integral]\[Integral]\!\(\*\nStyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]]\)\[CenterDot]\!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"n\",\nFontColor->RGBColor[1, 0, 0]], \"\[RightVector]\"],\n\
FontColor->RGBColor[1, 0, 0]]\)dS=", 15, Bold], 
             Style[$CellContext`FluxLat, 15, Bold]}], Null, 
           If[$CellContext`CAPT$$, 
            Row[{
              Style[
              "Top Cap Flux=\[Integral]\[Integral]\!\(\*\nStyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]]\)\[CenterDot]\!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"n\",\nFontColor->RGBColor[1, 0, 0]], \"\[RightVector]\"],\n\
FontColor->RGBColor[1, 0, 0]]\)dS=", 15, Bold], 
              Style[$CellContext`FluxCap1, 15, Bold], ""}]], Null, 
           If[$CellContext`CAPB$$, 
            Row[{
              Style[
              "Bottom Cap Flux=\[Integral]\[Integral]\!\(\*\nStyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]]\)\[CenterDot]\!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"n\",\nFontColor->RGBColor[1, 0, 0]], \"\[RightVector]\"],\n\
FontColor->RGBColor[1, 0, 0]]\)dS=", 15, Bold], 
              Style[$CellContext`FluxCap2, 15, Bold], ""}]], Null, 
           Row[{
             Style[
             "Total Flux=\[Integral]\[Integral]\!\(\*\nStyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]]\)\[CenterDot]\!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"n\",\nFontColor->RGBColor[1, 0, 0]], \"\[RightVector]\"],\n\
FontColor->RGBColor[1, 0, 0]]\)dS=", 15, Bold], 
             Style[
              
              Simplify[$CellContext`FluxCap1 + $CellContext`FluxCap2 + \
$CellContext`FluxLat], 15, Bold]}], Null, Null, Null, Null, 
           Row[{
             Style[
             "div\!\(\*\nStyleBox[\"F\",\nFontColor->RGBColor[0, 0, 1]]\)=", 
              15, Bold], 
             Style[
              Simplify[$CellContext`DF], 15, Bold]}], Null, 
           Row[{
             Style[
             "\[Integral]\[Integral]\[Integral]div\!\(\*\nStyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]]\)dV=", 15, Bold], 
             Style[
              Simplify[$CellContext`TrDI], 15, Bold]}]}, Center]]}, 
      "Options" :> {
       ControlPlacement -> Left, FrameLabel -> 
        "\!\(\*\nStyleBox[\"\[Copyright]\",\nFontSize->14]\)\!\(\*\nStyleBox[\
\" \",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"N\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\".\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"Bykov\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\",\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"SJ\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"Delta\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"College\",\n\
FontColor->RGBColor[0, 0, 1]]\)"}, "DefaultOptions" :> {}],
     ImageSizeCache->{984., {341., 346.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>({{$CellContext`SDB = Graphics3D[
           GraphicsComplex[CompressedData["
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           Axes -> True, 
            PlotRange -> {{-1.732050766329572, 
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             1.7320507663295281`}, {1.0000001428571428`, 2.999999857142857}}, 
            PlotRangePadding -> {
              Scaled[0.02], 
              Scaled[0.02], 
              Scaled[0.02]}}], $CellContext`Surf[
           Pattern[$CellContext`u, 
            Blank[]], 
           Pattern[$CellContext`v, 
            Blank[]], 
           Pattern[$CellContext`w, 
            Blank[]]] := {$CellContext`u (2 
            Cos[$CellContext`v]), $CellContext`u (2 
            Sin[$CellContext`v]), $CellContext`w (
            1 - $CellContext`u^2)}, $CellContext`Surf[
           Pattern[$CellContext`v, 
            Blank[]], 
           Pattern[$CellContext`w, 
            Blank[]]] := {$CellContext`f[$CellContext`w] 
           Cos[$CellContext`v], $CellContext`f[$CellContext`w] 
           Sin[$CellContext`v], $CellContext`w}, $CellContext`f[
           Pattern[$CellContext`w, 
            Blank[]]] := Sqrt[$CellContext`w], $CellContext`Av = 
         0, $CellContext`Bv = 2 Pi, $CellContext`Aw = 1, $CellContext`Bw = 
         3, $CellContext`SCap1 = Graphics3D[
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