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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


Would it not be more precise to say that while p(t) has an antiderivative, its representation can't be given in terms of any functions known at this time?


I responded by sending the worksheet as an attachment to a private response to your email address, then I sent a second email stating that the attachment was on its way. I asked that you respond to me directly if you did not get the email with the attachment. What went wrong with this process?

There's no need for me to upload a worksheet. Take Acer's last worksheet, execute it, then append the following commands.



As I understand your problem, you need not only the values of lambda, but the algorithm by means of which they were found. The fsolve command uses mostly a Newton iteration, but if you use the NewtonsMethod command in the Student Calculus1 package, you will get the same values that Acer got, but you can confidently state that they were obtained by Newton's method. I actually did this, and the values are the same as those produced by fsolve as implemented by Acer.


Unfortunately, the "Large Operators" are not operators, at least not the contour and surface integral symbols. To behave as operators, the symbols would need a way to capture all the information needed for constructing line and surface integrals. For example, the differential area element in a surface integral needs a description of the surface before it can be meaningful. Maybe in another lifetime? 

The implicitplot command is applied to the expression in (11). It contains L[2], L[3], and mu. At best you would need to use implicitplot3d, but the command you did use has ranges for L[1] and mu. There is a big disconnect here.

Are the functions f(x) = (x^2-1)/(x-1) and g(x) = x+1 the same? Are the equations y/x = 1 and y = x the same?

In the first case, what is the role of domains in defining a function? In the second, what is the role of solution sets in defining equivalent equations?

Mathematica's second "solution," namely, Y2=(x+2)^2 does not satisfy the ode for x>-2.

Indeed, substitution into the ode yields on the left, -x*(x+2), but on the right, x*abs(x+2). (Please note that the symbol sqrt(u) is a single positive number. It does not mean the pair of numbers +/-.)

A graph of the left and right sides shows that the two sides match for x<= -2, and for x=0. And nowhere else. 


I noticed your question to the OP, and the lack of a clear response to it. However, as far as my experience goes, the missing ingredient was the Suppress command from Typesetting. I had immediate success with D(f)(x)(0) and did not question whether there might be an even simpler form. Thanks for pointing that out.

@Scot Gould 


My ODE webinar in the Clickable series (check Youtube) has a pretty sophisticated eigenvalue problem solved numerically. And it's all done with point-and-click operations (2D math, palettes, Context Panel).

When exploring how I might solve a problem in Maple, I often try stuff via the Context Panel, thus avoiding the need to name things, look up syntax, etc. The ease-of-use features are useful.

The transition from point-and-click to learning commands is (in my view) easily done if the Context Panel is invoked in a worksheet where the underlying commands are then displayed. A user doing that can then determine if it's worth learning the syntax or not. Might even learning it without trying to.

I guess the bottom line is that when faced with a computational task, one asks "How do I do thus-and-such in Maple?" It's at that point that the ability to experiment, look things up, try things comes into play. And since Maple 10 when the Context Menu began to be useful, I've found the syntax-free tools to be more and more helpful.

@Scot Gould 

Scot, thanks for dragging me into what might become an endless morass. So, let me just say my piece and point out that I will not be drawn into the fray any further.

I had 15 years experience with Maple in the classroom at a time when learning syntax was the only way to go. It was a chore convincing students to learn the Maple language in order to "learn the math language." When Maplesoft introduced the beginnings of "syntax-free" computing, I was then working for Maplesoft and I immediately saw the benefits of students not having to learn syntax in order to implement math calculations. I pushed Maplesoft to improve its capabilities in that direction because I believed it would benefit students.

For students who will make use of Maple far into their careers, learning syntax is probably necessary. But for students who need Maple to "get through" their required math courses, and who will probably not take math courses beyond those, why add the burden of syntax if it can be avoided?

For the instructor who wants students to master syntax, just operate in a worksheet (even using 2D math input) and use a Context Panel operation. The underlying syntax will be displayed. Is there a faster way to learn syntax?

So, I guess the moral of the story is that necessity is the mother of invention. Adopt the usage that best serves the student. And now we can debate the meaning of "best."

PS. I think what Paul did to solve the inequalities was clever, and the graph he drew meaningful (if not subtle). That he was smart enough to ask if there was a better way shows what happens when there's a tool allowing different approaches to be implemented.


Have you looled at the built-in Programming Guide, available in the help system?

The assignment operator in Maple is :=, not just =.

The imaginary unit is upper-case i, so it looks like I in this font.

The construct i(... needs to be changed to I*(

Generally, you want to apply the evalc command to a complex espression to break it into its real and imaginary parts. When I tried that with h1*h2, the resulting expression got very large, and it was evident that the sizes of a and lambda determined the form of the result. You will have to make appropriate assumptions on these parameters to achieve any kind of useful outcome.


add in the command "with(plots)" so you get access to implicitplot3d, then change Kitonum's Explore command to


You will get an animation of some of the level surfaces. You will have to modify the bounds and ranges to fit your needs.

The "sub-Wronskians" cannot be calculated as 3x3 matrices with one column zero. Check the definitions of W1, W2, and W3. They are the determinants of appropirate 2x2 matrices formed by deleting the i-th row and column from the Wronskian matrix W, thereby defining W_i.


Both work-arounds eliminate the long fraction bar, but neither actually produces the "textbook" version (a+b)/c. But I guess the second uses the least horizontal space.

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