In addition to the other responses, I have to point out that your attempts to define functions have not been successful.

If you change the command

q(t) := ln( cosh(t) );
diffq(t) := diff( q(t), t$15 ); 

into

q := t -> ln( cosh( t ) );
dq := diff( q(t), t$15 );

If you really want to have the derivative as a function then you should use

Dq := D(q);

 You could also use unapply to create a function from an expression:

D15q := unapply( simplify( diff( q(t), t$15 ) ), t );

Please keep asking questions. That's how we all keep learning.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

@Joe Riel Could you point users to a useful introduction to the Maple Debugger? While it has been in existence for a long time, I don't see many users who are able to use it. If such an introduction does not exist, could you (or someone else at Maplesoft) put together something for the community? I think it would be greatly appreciated.

@Joe Riel Could you point users to a useful introduction to the Maple Debugger? While it has been in existence for a long time, I don't see many users who are able to use it. If such an introduction does not exist, could you (or someone else at Maplesoft) put together something for the community? I think it would be greatly appreciated.

Thank you Robert and Markiyan.

I do not see that the SetColors suggestion helps to draw two solids of revolution with different colors.

The VolumeOfRevolution tutor does provide a nice interface, but the Color can be specified only for the two functions, not the solids obtained by revolution. I agree that there should be a "2nd Volume/Region" (immediately after "Volume/Region").

The displaying of separate SurfaceOfRevolution plots does what I requested. My problem with this is that I want calculus students to create these plots for the lab assignments. Most of the students would not be comfortable putting together plots like this. Of course, you could say that this could be a good learning opportunity. Not only would they learn a little more Maple, but they might actually get a better understanding of solids of revolution. I will pass along this solution to the colleague who posed the original question to me.

I really do hope that this can be improved for a future release.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

Thank you Robert and Markiyan.

I do not see that the SetColors suggestion helps to draw two solids of revolution with different colors.

The VolumeOfRevolution tutor does provide a nice interface, but the Color can be specified only for the two functions, not the solids obtained by revolution. I agree that there should be a "2nd Volume/Region" (immediately after "Volume/Region").

The displaying of separate SurfaceOfRevolution plots does what I requested. My problem with this is that I want calculus students to create these plots for the lab assignments. Most of the students would not be comfortable putting together plots like this. Of course, you could say that this could be a good learning opportunity. Not only would they learn a little more Maple, but they might actually get a better understanding of solids of revolution. I will pass along this solution to the colleague who posed the original question to me.

I really do hope that this can be improved for a future release.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

Thanks, Robert!

The plot in the updated version of your worksheet is much better. It is now very clear exactly where this region lies.

Doug

Very nice (as usual).

I heard this puzzler on the radio and thought it could be a good foundation for a presentation to our new math teachers' circle (http://www.math.sc.edu/schematc/). Robert's analysis goes further than I had initially envisioned. The graphical conclusion is very nice.

I do have one complaint about the plot. Quickly, what are the coordinates of the lower-left corner of the shaded region? I'll guess that a fair number of people said (0,0). In fact, it's (0.25,0). If the 0.2 label had been shown at the left end of the u-axis this would have been much clearer. Personally, I probably would have plotted this on the window [0,1.1]x[0,0.7] (view=[0..1.1, 0..0.7]). 

This is something I think could be imporved in Maple. To make this concrete, execute this command:

plot( (4*u-1)/5, u=0.2..1 );

The label at the left end of the horizontal axis is missing. The presence of the 0 on the vertical axis makes it very easy for someone to assume this intersection 

I also would have asked Maple to use equal scales (scaling=constrained) in the horizontal and vertical directions. This is a personal choice, not a request for a change in Maple.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

I do not see the files that you intended to attach to your question.

If they are only one line, why don't you just include them in your question?

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

@Doug Meade Suspicions confirmed - office system is running Maple 16.00 (Build ID 732982). However, today when I run my worksheet I do not see the error about _PLOTARRAY. But, the real quesion is still unanswered: why does the maplet work in Classic and MapletViewer interfaces but not in Standard interface?

Today, while checking if anyone had responded to my question, I decided to see exactly what happened when I downloaded the worksheet in my question. Much to my surprise, the plots:-display command immediately after the definition of p1, p2, p3, and p4 produced an error - something about _PLOTARRAY. I was surprised because I know this command worked fine when I was digging into this problem last night.

Now that I am at home I could check my memory. Sure enough, the plots:-display command does work fine on my home computer.

What could be different? My home system is running Maple 16.01 (Build ID 744592).

I won't know until the morning if my office system is running Maple 16 or 16.01. I do not see anything explicit in the information about 16.01 to suggest that there was a change in the way arrays of plots are handled.

The real question is still why the Maplet works in the classic interface or the Maplet viewer - but not the standard interface.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

Maple should be able to work with ODEs in implicit form. If you can give us some idea about the actual structure of your equations that should help us to give you a useful result.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

Now that I have downloaded and installed Maple 16, I checked to see if there was any difference in Maple's response to this problem.

On my two Windows systems, one 32-bit (XP) and the other 64-bit (Windows 7). In bothsystems, all output is as reported for Maple 15.

The symbolic results appear to be correct for whatever assumptions are applied to n. It would be nice to have Maple report the different results for n posint or negint and for n=0.

The evaluations for specific values of n are correct for n=-11 .. 11 but incorrect for |n|>11.

That this is not fixed is not a complaint about Maple 16. I reported this problem much too recently to expect this to have been addressed in the released version of Maple 16 - unless it was fixed by some other change. I do hope that this can be fixed in an update that might appear in the next few months.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

@JerJohnson123 What acer is saying is that you should have Maple perform the calculations using more digits than you want in your answer. Once the calculations have been done, then you can use evalf[5] to have the answer displayed with 5 significant digits.

To illustrate, consider:

restart;
Digits;
                               10
1 + 1.123456789 - 2.123456;
                                  -7
                           7.89 10  
evalf[5](%);
                                  -7
                           7.89 10  
Digits := 5;
                               5
1 + 1.123456789 - 2.123456;
                               0.

If you have more questions, please ask.

@JerJohnson123 What acer is saying is that you should have Maple perform the calculations using more digits than you want in your answer. Once the calculations have been done, then you can use evalf[5] to have the answer displayed with 5 significant digits.

To illustrate, consider:

restart;
Digits;
                               10
1 + 1.123456789 - 2.123456;
                                  -7
                           7.89 10  
evalf[5](%);
                                  -7
                           7.89 10  
Digits := 5;
                               5
1 + 1.123456789 - 2.123456;
                               0.

If you have more questions, please ask.

Robert,

I look forward to seeing your contributions as part of the team. But, don't forget to enjoy the "retirement"

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu