Page 815 - Advanced_Engineering_Mathematics o'neil

APPENDIX A A MAPLE Primer
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use
∗
∗
F:= VectorField(<x y z,x - y,yz>);
Take the divergence of F as the dot product of del with F.
DotProduct(Nabla,F);
or
DotProduct(Del,F);
For the curl, take the cross product of the del operator with the vector field:
CrossProduct(Nabla,F);
or
CrossProduct(Del,F);
The output from this command will have the appearance
0e x + xye y + (1 − xz)e z .
In MAPLE, unit vectors along the coordinate axes are denoted e α where α denotes the coordinate.
In rectangular coordinates, e x =i, e y =j, and e z =k. In spherical coordinates, these vectors would
be denoted e ρ , e θ , and e ϕ .
We can also carry out vector operations in other curvilinear coordinate systems. We will
illustrate these for cylindrical and spherical coordinates.
To work in cylindrical coordinates, begin with
SetCoordinates(‘cylindrical’ [r,theta,z]);
As an example, define a vector field G(r,θ, z) by
∗
∗
∗
∗
G:=VectorField(<(r∧2) cos(theta),r z cos(theta) sin(theta),
(z∧2)>);
This will produce the output
2
2
G :=r cos(θ)e r +rz cos(θ)sin(θ)e θ + z e z .
For the divergence, enter
Divergence(G);
resulting in the output
2
2
2
3r cos(θ) −rz sin(θ) +rz cos(θ) + 2rz
.
r
Of course, we can divide out the r in the denominator. For the curl of G, enter
Curl(G);
to obtain
2
2rz cos(θ)sin(θ) +r sin(θ)
−r cos(θ)sin(θ)e r + e z .
r
We would divide out the r in the e z component. MAPLE does not automatically simplify all
output.
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