I guess you don't sell as much product with "This program is very powerful, but it takes a long time to learn how to use it effectively, and even then you must be clever. Oh, and a postgraduate degree in math might help too."

I guess you don't sell as much product with "This program is very powerful, but it takes a long time to learn how to use it effectively, and even then you must be clever. Oh, and a postgraduate degree in math might help too."

That makes a big difference. Can you see a pattern if you look at A, A^2, A^3, ... ?

That makes a big difference. Can you see a pattern if you look at A, A^2, A^3, ... ?

Have been presented, by whom? Where? If you're looking for accurate numerical approximations for a continuous function on an interval, you generally should not bother with Taylor series. Try Chebyshev series, or Chebyshev-Pade, or the Remez algorithm. See the numapprox package in Maple.

If you look at your function, the first term changes by over 6.5e7 when t changes by Pi/20.952 or about .15, or about 0.00029 of 524. Roundoff error in calculating 20.952*524 at Digits = 4 or 5 can easily account for that much change.

This has nothing to do with piecewise or vectors. The t in p1 and p2 is the global t, which has nothing to do with the formal parameter t in the definition of r. It's just like:

> p := t;
  r := t -> p;
  r(1);

t

This has nothing to do with piecewise or vectors. The t in p1 and p2 is the global t, which has nothing to do with the formal parameter t in the definition of r. It's just like:

> p := t;
  r := t -> p;
  r(1);

t

That requires the degree to be exactly 1, not <= 1.

> type(1, linear([e1,e2,e3,e4,e5,e6,e7]));

false

That requires the degree to be exactly 1, not <= 1.

> type(1, linear([e1,e2,e3,e4,e5,e6,e7]));

false

This is definitely a problem in all versions of Maple. Searching for Text in the Help system is often useful, but not always, particularly because you might be using different terminology to describe your problem than what Maple uses. Allowing more sophisticated help searches (e.g. search for word1 near word2 but not word3) might be worthwhile, but I don't think even that would solve the problem.

This is definitely a problem in all versions of Maple. Searching for Text in the Help system is often useful, but not always, particularly because you might be using different terminology to describe your problem than what Maple uses. Allowing more sophisticated help searches (e.g. search for word1 near word2 but not word3) might be worthwhile, but I don't think even that would solve the problem.

dsolve(des,ics) is incorrect syntax for dsolve. In Maple 11.02 this gave me an error message. In Maple 9.5 it gave me a solution, but containing arbitrary constants (thus the initial conditions were ignored).

dsolve(des,ics) is incorrect syntax for dsolve. In Maple 11.02 this gave me an error message. In Maple 9.5 it gave me a solution, but containing arbitrary constants (thus the initial conditions were ignored).

You could try a numerical global optimization to see if the derivative is ever positive. With gmax in my Maple Advisor Database:

> Q:= arctan(x)/(1+x^2):
  gmax(diff(Q,x), x=1 .. infinity, 'x0');

-0.

> x0;

{infinity, .1889785610e12} You could also try Optimization[Maximize](..., method=branchandbound), but this requires a finite interval. Well, let's try transforming to a finite interval.

> Q1:= eval(Q, x = tan(t)):
  Optimization[Maximize](diff(Q1,t), t=Pi/4 .. Pi/2,
    method=branchandbound);

[-.102712384246536857e-13, [t = 1.57079632679490012]] Note that, due to roundoff error, the result could quite easily have ended up slightly positive rather than slightly negative. Unfortunately, it's hard to tell just how big a value should be considered as "really" positive.