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PaneDivider 479;
FontSizes 18;
BackgroundType 0;
StackPanes 1;
2D.Scale 0.1 0.25 5 1;
2D.BottomLeft -3.75 -0.44375;
2D.GraphPaper 0;
Text "Dirac delta function

Area under (approximation to) the delta function is 1.";
Color 2;
Expr function(d,x)=branch(if(1/a,abs(x)<a/2),if(0,abs(x)>a/2));
MathPaneSlider 30;
Expr a=slider([sn(1,-2),1]);
Color 4;
MathPaneSlider 31;
Expr s=slider([-5,5,40]);
Color 3;
Expr function(d,x-s);
Color 5;
Expr 0<y<function(d,x-s);
Color 17;
Expr x=s;
Color 17;
Expr x=s,y>0;
Text "A test function";
Color 6;
Expr function(f,x)=-(5*sin(2*x)*e^(-[x-2]^2/2));
Color 8;
Expr function(f,x);
Color 17;
Expr function(f,x)*function(d,x-s);
Color 17;
Expr function(f,s)*function(d,x-s);
Color 17;
Expr function(f,x)*function(d,x-s)*a;
Text "Heaviside step function";
Color 5;
Expr function(T,x)=branch(if(1,x>0),if(1/2,x=0),if(0,x<0));
Color 17;
Expr function(T,x-s);
Text "Approximation to Heaviside step function.    The derivative of D(x) is d(x)!   (The derivative of the Heaviside function is the delta function.)";
Color 2;
Expr m=1/a;
Color 7;
Expr function(D,x)=branch(if(1,x>a/2),if(m*x+1/2,-a/2<x<a/2),if(0,x<-a/2));
Color 17;
Expr function(D,x-s),y>-10^(-8);
Color 17;
Expr function(D,x-s);
Text "All of these also have the delta-function as their a->0 limit:";
Color 3;
Expr function(d_1,x)=1/(2*a)*e^(-abs(x)/a);
Expr function(d_2,x)=1/pi*(a/(x^2+a^2));
Color 3;
Expr function(d_3,x)=1/(a*sqrt(pi))*e^(-x^2/a^2);
Color 4;
Expr function(d_4,x)=1/pi*(sin([x/a])/x);
Color 6;
Expr function(d_5,x)=a/pi*(sin([x/a])^2/x^2);
Color 17;
Expr function(d_1,x-s);
Color 17;
Expr function(d_2,x-s);
Color 17;
Expr function(d_3,x-s);
Color 17;
Expr function(d_4,x-s);
Color 17;
Expr function(d_5,x-s);
Text "

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