<Text-field style="Heading 1" layout="Heading 1">div and curl in VectorCalculus</Text-field>

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Examples from Wednesday

I) Using vector calculus to find divergence and curl

First load the VectorCalculus package

with(VectorCalculus);

You then want to set the coordinate system and name the coordinates. I will do standard Cartesian 3D.

I also set the BasisFormat command to false because I like vector format ratehr than linear combination format.

SetCoordinates(cartesian[x,y,z]); BasisFormat(false);

Next you define a VectorField. This is a data type used by the commands in the package.

vf := VectorField(<x, x^2*y, z*y*z>);

Now the commands are straightforward.

Del.vf; Curl(vf); Divergence(vf);

LinearAlgebra[CrossProduct](Del, vf);

<Text-field style="Heading 1" layout="Heading 1">Plotting Polar Functions</Text-field>

The question was asked about graphing functions converted to polar format.

func:= (x, y) -> x^2*y/(x^2+y^2);

makepolar := g -> simplify(subs({x=r*cos(theta), y=r*sin(theta)}, g));

polarfunc := makepolar(func(x,y));

plot3d(func(x,y),x=-1..1, y=-1..1, style=patchcontour, axes=boxed);

plot3d([r,theta, polarfunc], r=0..1, theta=0..2*Pi, coords=cylindrical, style=patchcontour, axes=boxed);

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