Maple Tutorial 17:
Vector Calculus

M.M. Yovanovich

TUTORIAL17.MWS

Vector calculus.

> restart:

> with(linalg):

Warning, new definition for norm

Warning, new definition for trace

Define the function f and the vector g.

> f:= exp(-a*y)*cos(a*x); g:= [y, 2 + x + z, z*exp(x)];

Gradient of the function f(x,y)

> gradf:= grad(f, [x,y,z]);

Components of the gradient of f(x,y).

> fx:= gradf[1]; fy:= gradf[2]; fz:= gradf[3];

Laplacian of the function f(x,y).

> laplacian(f, [x,y,z]);

The function is called a harmonic function because the Laplacian is zero.

Divergence of vector g.

> diverge(g, [x,y,z]);

Curl of vector g.

> curl(g, [x,y,z]);

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