I wish to evaluate the expression

knowing that

where a is a constant.  It is not hard to see, assuming enough differentiability,  that the expression evaluates to

I know how to do this when all the derivatives are expressed in terms of the diff() operator.  Here it is:

eq := diff(u(x,t),t) = a^2*diff(u(x,t),x,x);
expr := diff(u(x,t),t,t);
eval['recurse'](expr,[eq]);

However, I would prefer to do the computations when all derivatives are expressed in terms of the D operator but cannot get that to work.  What is the trick?

Consider

> z := Int(f(t-s), s=0..1);

The result is clearly a function of t (and definitely not a function of s, which is a dummy variable).  Let's define

> F := unapply(z, t);

Then

> F(q);

as expected.  However:

> F(s);

which is not correct, as this confuses the argument s of F with the dummy integration variable s.  How would you salvage the situation?

In the following, the diff operator calcuates the derivative correctly, but the D operator doesn't.  A bug?

Here is a worksheet containing the commands above in case you want to try it yourself: mw.mw

In the (r,t) polar coordinates, the graph of the equation r = 1/cos(t) should be a straight vertical line segment but Maple produces junk.  What is going on?

plot(1/cos(t), t=0..Pi/3, coords=polar);

The parametric version

plot([1/cos(t), t, t=0..Pi/3], coords=polar);

produces the same thing.

Is there a way to tell Maple to export a figure to PDF with a proper bounding box, like all of its other graphics export formats?

To export a graphics produced by Maple's plot(), I right-click on the plot, select Export, and then one of the several choices of graphics formats.  All options, other than the PDF, work fine—they produce graphics files whose bounding boxes correspond to the extents of the image.  Exporting to PDF misbehaves—it produces the equivalent of a 8.5''x11'' paper and inserts the graphics somewhere near the upper left corner.  I am absolutely at a loss to see the utility of that.  What in the world is the use of such an export?

Is there a configuration setting that tells Maple to save to PDF with a proper bounding box?  I looked around but couldn't find one.