GraphingCalculator 4;
Window 45 0 852 1248;
PaneDivider 445;
FontSizes 18;
BackgroundType 0;
StackPanes 1;
2D.BottomLeft -5.484375 -6.328125;
2D.GraphPaper 0;
Text "Polar coordinates.    Basis vectors and area element.   Derivatives of basis vectors.  Draggable point.

Version 0.36 [10-10-12]
To do:
(i) Box in dA completely?


R – radius; P – azimuthal angle phi; f – dR; g – dP;
R_h – r-hat; P_h – phi-hat; ";
Color 4;
Expr c=3.796875+1.71875*i;
Color 2;
Expr R=abs(c);
Expr P=arg([c]);
Color 3;
Expr f=slider([0,0.2]);
Color 4;
Expr G=slider([0,0.2]);
Color 3;
Expr g=G/R;
Color 5;
Expr function(X,R,P)=vector(R*cos(P),R*sin(P));
Color 6;
Expr function(R_h,P)=vector(cos(P),sin(P)),function(P_h,P)=vector(-sin(P),cos(P));
Color 8;
Expr O=vector(0,0),I=vector(1,0),J=vector(0,1);
Color 2;
Expr function(X,R,P);
Color 17;
Expr O,function(X,R,P);
Text "Shade angle P.   mod takes care of the fact that arg(c) is reported as negative when > pi.";
Color 17;
Expr 0<theta<mod([2*pi+P,2*pi]),0<r<1;
Color 17;
Expr r=abs(function(X,R,P));
Text "Polar and rectangular basis vectors.";
Color 17;
Expr function(X,R,P),function(X,R,P)+function(R_h,P);
Color 17;
Expr function(X,R,P),function(X,R,P)+function(P_h,P);
Color 17;
Expr function(X,R,P),function(X,R,P)+I;
Color 17;
Expr function(X,R,P),function(X,R,P)+J;
Text "Differential area element dA=rdP*dr:";
Color 7;
Expr function(X,R+f*t,P);
Color 7;
Expr function(X,R,P+g*t);
Color 7;
Expr R<r<R+f,P<theta<P+g;
Text "Differential changes in the basis vectors:";
Color 5;
MathPaneSlider 126;
Expr d=slider([0,0.2]);
Color 17;
Expr vector(0,0),function(X,R,P+d);
Color 17;
Expr function(X,R,P+d),function(X,R,P+d)+function(R_h,P+d);
Color 17;
Expr function(X,R,P+d),function(X,R,P+d)+function(P_h,P+d);
Text "Same vectors planted back at P and the corresponding difference vectors:";
Color 17;
Expr function(X,R,P),function(X,R,P)+function(R_h,P+d);
Color 17;
Expr function(X,R,P)+function(R_h,P),function(X,R,P)+function(R_h,P)+d*function(P_h,P);
Color 17;
Expr function(X,R,P),function(X,R,P)+function(P_h,P+d);
Color 17;
Expr function(X,R,P)+function(P_h,P),function(X,R,P)+function(P_h,P)-(d*function(R_h,P));
Text "


<size=16>Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";