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Dr. Robert J. Lopez, Emeritus Professor of Mathematics at the Rose-Hulman Institute of Technology in Terre Haute, Indiana, USA, is an award winning educator in mathematics and is the author of several books including Advanced Engineering Mathematics (Addison-Wesley 2001). For over two decades, Dr. Lopez has also been a visionary figure in the introduction of Maplesoft technology into undergraduate education. Dr. Lopez earned his Ph.D. in mathematics from Purdue University, his MS from the University of Missouri - Rolla, and his BA from Marist College. He has held academic appointments at Rose-Hulman (1985-2003), Memorial University of Newfoundland (1973-1985), and the University of Nebraska - Lincoln (1970-1973). His publication and research history includes manuscripts and papers in a variety of pure and applied mathematics topics. He has received numerous awards for outstanding scholarship and teaching.

MaplePrimes Activity

These are replies submitted by rlopez


The function of a matrix is not the same as mapping that function onto the entries of the matrix. Use the square root function to convince yourself of this. The square root of a matrix is a matrix whose product with itself is the original matrix. That will not be the case if you simply map the square root onto the elements of the matrix.

I just ran your three lines of code in Maple, obtaining three solutions: x~-36, 30, 2006. Graphical and numeric investigation shows no solution anywhere near x=94. I suggest you double-check everything, including what Excel is giving. (When I pasted your code into Maple as 1D math, I had to insert explicit multiplication operators to the left of each x in eq2. So, are you working in 1D input or 2D input?)

RJL Maplesoft

@Markiyan Hirnyk



Student:-MultivariateCalculus:-Plane(Vector(3, {(1) = u, (2) = v, (3) = w}), [a, b, c], variables = [x, y, z], id = 1)








Download Distance-M18.mw


@Markiyan Hirnyk 

Unfortunately, what worked in Maple 18, broke in Maple 2015 and 2015.1. It's been fixed for a later dot-releaase and for the next full version of Maple.


I received the worksheet attached to an email sent directly to me. For anyone else on this forum who wanted to interact with this question, the worksheet itself is essential. Use the green upward-pointing arrow in the toolbar to upload the worksheet.

In a private email, I corrected the issue with eval, the correction I suggested at the very beginning of this thread.

The expression to be evaluated is called f, and it contains at least five parameters such as delta, and C. The values of these parameters are read from math containers by the Evaluate-at-parameters button. However, the values are assigned to the names themselves so that it is now not possible to use these names in the eval command. My modification was to read in the values, but assign to new names such as Xdelta, and XC. Then, I removed the value command wrapped around the read statements. Finally, I adjusted the eval command to the proper syntax:


So, the code ended up looking like this:



So, this is the style in which I would have written the App. If anyone else can see a more efficient way to do all this, have at it. Perhaps we all could learn something about coding.

Please save all of us the trouble of reconstructing the App. Post the worksheet you are using to build the App.

The syntax of the eval command should be fixed: after the expression to be evaluated, use a list of equations, not merely the names.


Unfortunately, the order of output for commands like solve can change. Sometimes repeated execution of the command will cause the change in order, sometimes it takes a new version of Maple to cause the order to change. So, unless the calculation is interactive and to be used just onece, picking out a member of a sequence of solutions by position in the sequence is not necessarily the best way. Selection based on a property of that member is the safest way, even if it is a bit more difficult.

My experience in maintaining the Advanced Engineering Math ebook is what prompts this note. One of the worst offenders against canonical ordering is the dsolve command, but over the years, more and more cases of fickleness in the solve command have had to be corrected with the addition of special code to make the choice of solution unique.

RJL Maplesoft


Check the recorded demos available on the following page.


There are more recorded demos here:




First, the question asks about rotating about the line "theta-pi/2" but apparently, the minus sign should be taken as an equal sign. At least, that is what was done in the several answers already given.

More important: A volume of revolution is created by rotating a region about an axis that does not intersect the region. If the region is the area bounded by the given cardioid, then the problem is what does it mean to create a solid by rotating the region about an axis that passes through the region? In other words, meaning must be given to the doubling over of such a region on itself when it is rotated. Is the volume to be counted twice? If not, provision has to be taken in the integration to ensure that this doubling of volume is not computed.

RJL Maplesoft

Maple and the Putnam Competition

Philippe Dumas and Bruno Salvy

page 63, MapleTech, Volume 2, Number 2, 1995


All 12 problems of the 1993 competition were examined with the conclusion that six fell to the axe of Maple, five did not appear to yield to a computer algebra system, and one could profitably be explored with Maple.

Unfortunately, this Birkhauser publication no longer exists. Perhaps copies can be found on the shelf of an early Maple enthusiast who hasn't yet retired.

RJL Maplesoft



Let's make sure you can at least insert a Task Template into your worksheet.

From the Tools menu, select Tasks, then Browse. This brings up the Table of Contents for the task templates. Find the one you want. Then click one of the two Insert buttons at the top. Insert default content means you insert all the verbiage that goes along with the template. Insert Minimal Content means you get enough to make the template work.

The templates in the Table of Contents don't work. They have to be installed into the worksheet to function.

If you are having problems inserting the task template into the worksheet, then something is really wrong. Let us know - this is important.




Yes, you are experiencing a bug that has finally been removed for the next release of Maple. Meanwhile, you can get the blue border to go away by clicking in the box "adroitly." There are places inside the box where the click "takes" and the border goes away. It drives me nuts also, but the task template does work, eventually.

Alternatively, if you watch the whole video, there's a solution from first principles given for drawing tangent and normal lines. This solution uses the syntax-free paradigm, so it can be implemented through the palettes and the Context Menu.


For any integer n, the nth-degree Taylor polynomial for exp(x) has n zeros. Yet, exp(x) has neither real nor complex zeros. With this behavior of the limit of a sequence of polynomial approximations in mind, the request to find the zeros of a polynomial of infinite degree strikes me as problematic, and really calls for some precise definitions.

RJL Maplesoft

@Markiyan Hirnyk 

Markiyan, thanks for your care in reading my response. You are again correct - when x=3, the edge of the triangle is being searched and the "max" is at a vertex. I failed to note the three coordinates of the point I located. Had I done so, I'd have seen the error you so quickly spotted. Thanks again.

@Markiyan Hirnyk 

Markiyan is completely correct in pointing out that the "maximum" does not exist.

But to conclude that the maximum does not exist on the given set, one has to go through my calculations first.

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