# SPACE CURVES    Math II, 11 Sep 96
# 
# We need to include linalg and plots
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> with(linalg):
Warning: new definition for   norm
Warning: new definition for   trace

> with(plots):
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# Set r to be the twisted cubic, and set rd to be its derivative
> r:=vector([t,t**2,t**3]);

                                          2   3
                               r := [ t, t , t  ]
> rd:=map(diff,r,t);

                                                2
                             rd := [ 1, 2 t, 3 t  ]
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# We need to convert r and rd to forms that are usable by plot3d
> v:=convert(r,list);

                                          2   3
                                v := [t, t , t ]
> plot3d(v,t=-2..2,s=0..1,grid=[500,2]);
# In the plot3d command, s is a dummy parameter and the grid option 
# tells MAPLE to plot using 500 subintervals in t and 2 in s.
# 
> vdiff:=convert(rd,list);

                                                  2
                             vdiff := [1, 2 t, 3 t ]
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# 
# Set curve to hold the plot of the space curve
> curve := plot3d(v,t=-2..2,s=0..1,grid=[500,2]):
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# 
# Find the value of the curve and its derivative when t=1
> subs(t=1,v);

                                    [1, 1, 1]
> subs(t=1,vdiff);

                                    [1, 2, 3]
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# 
# We can now plot the derivative when t=1
# The derivative is a vector at [1,1,1] in the direction [1,2,3]
> deriv:=plot3d([1+u,1+2*u,1+3*u],u=0..1,w=0..1,grid=[20,2]):
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# 
# and we display the curve and its derivative on the same plot.
> display({curve,deriv}):
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>