(*^
::[	Information =

	"This is a Mathematica Notebook file.  It contains ASCII text, and can be
	transferred by email, ftp, or other text-file transfer utility.  It should
	be read or edited using a copy of Mathematica or MathReader.  If you 
	received this as email, use your mail application or copy/paste to save 
	everything from the line containing (*^ down to the line containing ^*)
	into a plain text file.  On some systems you may have to give the file a 
	name ending with ".ma" to allow Mathematica to recognize it as a Notebook.
	The line below identifies what version of Mathematica created this file,
	but it can be opened using any other version as well.";

	FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2";

	MacintoshStandardFontEncoding; 
	
	fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8,  24, "Times"; 
	fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6,  18, "Times"; 
	fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6,  14, "Times"; 
	fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20,  18, "Times"; 
	fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15,  14, "Times"; 
	fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12,  12, "Times"; 
	fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; 
	fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5,  12, "Courier"; 
	fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; 
	fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5,  12, "Courier"; 
	fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; 
	fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5,  12, "Courier"; 
	fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w218, h221,  12, "Courier"; 
	fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic,  10, "Geneva"; 
	fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = leftheader, inactive, L2,  12, "Times"; 
	fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7,  12, "Times"; 
	fontset = leftfooter, inactive, L2,  12, "Times"; 
	fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; 
	fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	paletteColors = 128; currentKernel; 
]
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
Setup:
:[font = input; noPageBreak; preserveAspect; endGroup]
Clear["Global`*"];
Off[ General::spell ];
Off[ General::spell1];
Off[Clear::wrsym];
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
Load Packages:
:[font = input; noPageBreak; preserveAspect; startGroup]
Needs["LinearAlgebra`Orthogonalization`"]
?LinearAlgebra`Orthogonalization`*
:[font = info; inactive; preserveAspect; endGroup]
GramSchmidt  InnerProduct Normalize    Normalized   Projection
:[font = input; noPageBreak; preserveAspect; startGroup]
Needs["Calculus`VectorAnalysis`"]
?Calculus`VectorAnalysis`*
:[font = info; inactive; preserveAspect; endGroup]
ArcLengthFactor          Div                      phi
Biharmonic               DotProduct               ProlateSpheroidal
Bipolar                  EllipticCylindrical      r
Bispherical              eta                      ScalarTripleProduct
Cartesian                Grad                     ScaleFactors
ConfocalEllipsoidal      JacobianDeterminant      SetCoordinates
ConfocalParaboloidal     JacobianMatrix           Spherical
Conical                  lambda                   theta
CoordinateRanges         Laplacian                Toroidal
Coordinates              mu                       u
CoordinatesFromCartesian nu                       v
CoordinatesToCartesian   OblateSpheroidal         x
CoordinateSystem         ParabolicCylindrical     xi
CrossProduct             Paraboloidal             y
Curl                     ParameterRanges          z
Cylindrical              Parameters
:[font = input; noPageBreak; preserveAspect; startGroup]
Needs["Graphics`PlotField`"]
?Graphics`PlotField`*
:[font = info; inactive; preserveAspect; endGroup]
ListPlotVectorField  PlotHamiltonianField ScaleFactor
MaxArrowLength       PlotPolyaField       ScaleFunction
PlotGradientField    PlotVectorField
:[font = input; noPageBreak; preserveAspect; startGroup]
Needs["Graphics`PlotField3D`"]
?Graphics`PlotField3D`*
:[font = info; inactive; preserveAspect; endGroup; endGroup]
ListPlotVectorField3D PlotVectorField3D     ScaleFunction
MaxArrowLength        ScaleFactor           VectorHeads
PlotGradientField3D
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
Initialization: 
(Don't read this; just execute it)
(Click on the outer bracket--far right--and hit the ENTER key.
:[font = input; noPageBreak; preserveAspect]
Unprotect[{VectorPlot,VectorPlot3D,VectorLength}];
:[font = input; noPageBreak; preserveAspect]
VectorPlot[list__List?VectorQ]:= VectorPlot[{list}];

VectorPlot[list_List?MatrixQ]:= 
Module[{length,totList},
 length=Length[list];
 totList=Table[{{0,0},list[[i]]} ,{i,1,length}];
 Return[
  Show[Graphics[{Thickness[0.015],Line /@ totList }
          ,{GridLines->Automatic
           ,Axes->True
           ,AspectRatio->1}]]
 ]
];
:[font = input; noPageBreak; preserveAspect]
VectorPlot3D[list__List?VectorQ]:= VectorPlot3D[{list}];

VectorPlot3D[list_List?MatrixQ]:= 
Module[{length,totList},
 length=Length[list];
 totList=Table[{{0,0,0},list[[i]]} ,{i,1,length}];
 Return[
  Show[Graphics3D[{Thickness[0.015],Line /@ totList}
          ,{ FaceGrids->{{0,0,-1},{0,1,0},{-1,0,0}}
            ,BoxRatios->{1,1,1}
            ,Axes->True}]]
 ]
];
:[font = input; noPageBreak; preserveAspect]

VectorLength[vector_List?VectorQ]:=Sqrt[vector.vector]
:[font = input; noPageBreak; preserveAspect; endGroup]
Protect[{VectorPlot,VectorPlot3D,VectorLength}];
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
2-D Example:
:[font = input; noPageBreak; preserveAspect; startGroup]
v1={1,0} //Normalize
v2={1,1} //Normalize
v3={0,1} //Normalize
VectorPlot[v1,v2,v3];
:[font = output; output; inactive; noPageBreak; preserveAspect; startGroup]
{1, 0}
;[o]
{1, 0}
:[font = output; output; inactive; noPageBreak; preserveAspect]
{2^(-1/2), 2^(-1/2)}
;[o]
    1        1
{-------, -------}
 Sqrt[2]  Sqrt[2]
:[font = output; output; inactive; noPageBreak; preserveAspect; endGroup; endGroup]
{0, 1}
;[o]
{0, 1}
:[font = input; noPageBreak; preserveAspect; startGroup]
VectorLength /@ {v1,v2,v3,{1,1}}
:[font = output; output; inactive; noPageBreak; preserveAspect; endGroup]
{1, 1, 1, 2^(1/2)}
;[o]
{1, 1, 1, Sqrt[2]}
:[font = input; noPageBreak; preserveAspect; startGroup]
ArcCos[v1.v2]
:[font = output; output; inactive; noPageBreak; preserveAspect; endGroup]
ArcCos[2^(-1/2)]
;[o]
          1
ArcCos[-------]
       Sqrt[2]
:[font = input; noPageBreak; preserveAspect; startGroup]
ArcCos[v1.v2] /Degree //N
:[font = output; output; inactive; noPageBreak; preserveAspect; endGroup; endGroup]
45.00000000000001
;[o]
45.
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
3-D Example:
:[font = input; noPageBreak; preserveAspect; startGroup]
v1={1,0,0} //Normalize
v2={1,1,0} //Normalize
v3={0,1,0} //Normalize
VectorPlot3D[v1,v2,v3];
:[font = output; output; inactive; noPageBreak; preserveAspect; startGroup]
{1, 0, 0}
;[o]
{1, 0, 0}
:[font = output; output; inactive; noPageBreak; preserveAspect]
{2^(-1/2), 2^(-1/2), 0}
;[o]
    1        1
{-------, -------, 0}
 Sqrt[2]  Sqrt[2]
:[font = output; output; inactive; noPageBreak; preserveAspect; endGroup; endGroup]
{0, 1, 0}
;[o]
{0, 1, 0}
:[font = input; noPageBreak; preserveAspect; startGroup]
VectorLength /@ {v1,v2,v3,{1,1,1}}
:[font = output; output; inactive; noPageBreak; preserveAspect; endGroup]
{1, 1, 1, 3^(1/2)}
;[o]
{1, 1, 1, Sqrt[3]}
:[font = input; noPageBreak; preserveAspect; startGroup]
CrossProduct[v1,v2] //Normalize
:[font = output; output; inactive; noPageBreak; preserveAspect; endGroup]
{0, 0, 1}
;[o]
{0, 0, 1}
:[font = input; noPageBreak; preserveAspect]
VectorPlot3D[v1,v2,CrossProduct[v1,v2]];
:[font = input; noPageBreak; preserveAspect; startGroup]
{CrossProduct[v1,v2].v1,CrossProduct[v1,v2].v2}
:[font = output; output; inactive; noPageBreak; preserveAspect; endGroup]
{0, 0}
;[o]
{0, 0}
:[font = input; noPageBreak; preserveAspect; startGroup]
vx={1,0,0};
vy={0,1,0};
vz={0,0,1};
VectorPlot3D[vx,vy,vz];
{CrossProduct[vx,vy].vz,CrossProduct[vz,vy].vx}
:[font = output; output; inactive; noPageBreak; preserveAspect; endGroup; endGroup]
{1, -1}
;[o]
{1, -1}
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
Gradient:
:[font = input; noPageBreak; preserveAspect]
?Grad
:[font = input; noPageBreak; preserveAspect]
Plot3D[x^2+y^2+z^2 /.{z->0} 
      ,{x,0,1}
      ,{y,0,1}
      ,BoxRatios->{1,1,1}
      ];
:[font = input; noPageBreak; preserveAspect]
ContourPlot[- (x^2+y^2+z^2) /.{z->0} //Evaluate
      ,{x,0,1}
      ,{y,0,1}
      ];
:[font = input; noPageBreak; preserveAspect; startGroup]
Grad[x^2+y^2+z^2]
:[font = output; output; inactive; noPageBreak; preserveAspect; endGroup]
{2*x, 2*y, 2*z}
;[o]
{2 x, 2 y, 2 z}
:[font = input; noPageBreak; preserveAspect]
PlotGradientField[x^2+y^2+z^2 /.{z->0} //Evaluate
   ,{x,0,1}
   ,{y,0,1}
   ,VectorHeads->True
   ,PlotPoints->4
   ,Axes->True
   ];
:[font = input; noPageBreak; preserveAspect; endGroup]
PlotGradientField3D[x^2+y^2+z^2
   ,{x,0,1}
   ,{y,0,1}
   ,{z,0,1}
   ,VectorHeads->True
   ,PlotPoints->4
   ,Axes->True
   ];
:[font = section; inactive; noPageBreak; preserveAspect]
Div:
:[font = section; inactive; noPageBreak; preserveAspect]
Curl:
:[font = section; inactive; noPageBreak; preserveAspect]
Multiple Operations:
:[font = section; inactive; noPageBreak; preserveAspect]
Grad[x^2+y^2+z^2]
:[font = section; inactive; noPageBreak; preserveAspect]
Div[{x,0,0}]
:[font = section; inactive; noPageBreak; preserveAspect]
Curl[{y,-x,0}]
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
Dirac Delta:
:[font = input; noPageBreak; preserveAspect]
f[1]= n/Sqrt[Pi] Exp[-n^2 x^2];
f[2]=n/Sqrt[Pi] 1/(1+n^2 x^2);
f[3]=Sin[n x]/(Pi x);
:[font = input; noPageBreak; preserveAspect; endGroup]
Do[

Print["================================"];

ftemp=f[i]; Print["f[",i,"] =  ",ftemp];

Plot[ Table[ ftemp ,{n,2,10,2}] //Evaluate 
  ,{x,-1,1}
  ,PlotRange->All];
  
iftemp= Integrate[ftemp,x]; Print["int-f[",i,"] =  ",iftemp];

Plot[ Table[ iftemp ,{n,2,10,2}] //Evaluate 
  ,{x,-1,1}
  ,PlotRange->All];
  
,{i,1,3}]
^*)