rlopez

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14 years, 286 days

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

Doug pointed this out to me privately by email, and I immediately modified the graph by adding a view option to the plot command. As soon as the original file is replaced with the modified one, downloads will not have this "glitch" in the graph.

I raised Doug's point with our graphics people. Apparently, I've already hit on the best cure by adding the view option.

RJL Maplesoft

To get multiple lines of input to reside in a single execution group, terminate the line with Shift+Enter.

Of course, if the code for the loop has been typed already and resides in separate execution groups, then follow van der Meer's advice and use the Edit menu to join execution groups.

RJL Maplesoft

To get multiple lines of input to reside in a single execution group, terminate the line with Shift+Enter.

Of course, if the code for the loop has been typed already and resides in separate execution groups, then follow van der Meer's advice and use the Edit menu to join execution groups.

RJL Maplesoft

@gdorsch Look up the try/catch mechanism. It will let you branch upon detection of specific errors, or upon detection of any error.

@gdorsch Look up the try/catch mechanism. It will let you branch upon detection of specific errors, or upon detection of any error.

@mzh 

The first part of the demo shows how to obtain the solution via a task template. The second part shows how to obtain the solution from first principles. I just reviewed both parts. The second part, the solution from first principles, is a pretty thorough explanation of how to obtain the solution. It clearly shows why there are two integrals, and how these two integrals are to be obtained.

A visual demonstration of the derivative as the linear approximation of the rate of change is an excellent suggestion. There are several ways to create such a graph in Maple. The Explore command applied to a plot command is one of them. The interactiveparams command in the plots package is another, but both these alternatives require knowledge and use of syntax. A syntax-free (or clickable) way to build the same animation is through the Plot Builder, launched from the Context Menu. Selection of the animation option or the "Interactive Plot with 1 Parameter" option would lead to equivalent visuals.

RJL Maplesoft

@Alex Smith 

Yes, its just a different philosophy of learning. My experience in the classroom (35 years) convinced me that I best served my students if I helped them to avoid mistakes. I always found that I had the hardest time learning something I had previously gotten a wrong impression of. Unlearning is hard, so I always tried to get my students to "get it right" right from the beginning.

Just a different perspective on what works best for both student and instructor. But it's good to be reminded that others have different views, and that these differences for the most part need to be respected.

@Alex Smith 

Let's see if I correctly understand this comment. Does it suggest that the chance for cognitive conflict is diminished with a tool that makes it easier to make the exact same mistake described in the example?

Suppose the student wrote the same wrong expression for the tangent line, and then added it to a graph of the function via drag-and-drop instead of via some more complex syntax. The same cognitive conflict would arise, only it would happen faster and more easily with "syntax-free" computing. And with syntax-free computing, the student wouldn't have to check out the detour "Is my syntax correct, or is the error in my math?"

Bottom line: I don't see that ease-of-use in any way reduces the pedagogical opportunities afforded by cognitive conflict. Am I missing something?

@Markiyan Hirnyk 

The subject areas touched by the 44 problems posted so far are those that the "typical" college student in math and science programs meet in their first two years of study. The point of the work is to show both a pedagogical approach and to demonstrate how to implement this pedagogy in a syntax-free manner.

There are more than 100 additional problems in the pipeline, and as of this moment, more than half that have now been recorded and are being readied for posting. But initially, the six subject areas themselves will be augmented with problems only from precalculus math (algebra and trig).

Beyond that, where the "clickable" paradigm works, problems from additional areas can be considered. But it would be useful to understand that the primary goal of this collection of activities is to demonstrate an approach to the use of technology in teaching and learning college-level mathematics, and to show that the ease-of-use techniques in Maple that flatten itslearning curve make it possible for this pedagogy to be implemented in a syntax-free manner.

Maple is certainly a useful tool in many other subject areas of mathematics. The pedagogy advocated in the problems so far posted is certainly applicable, and has already been demonstrated in my Advanced Engineering Mathematics ebook. However, not all of what's in that volume is easily rendered in a syntax-free form. Perhaps there is need for a separate web area reserved for problems in which the "clickable" paradigm is less well-developed.

By the way, a number of improvements in the syntax-free environment of Maple have come from pushing the boundaries of what could and could not be captured in this format. So, perhaps one outcome of extending this project to other subject areas will be the augmentation of the syntax-free tools in Maple. Is this something our user-community can contribute to?

@Axel Vogt 

 

Axel,

I agree that a worksheet full of 2D math and slated for Application Center, makes a poor post to MaplePrimes. Henceforth, I intend to do what you suggest - summarize for Primes and leave the worksheet for download.

 

As to "Why can't I have..." I must tell you that I was hired by Maplesoft to reflect the perspective of the classroom user of Maple, not as a programmer. I have little influence on the actual code in Maple. I make recommendations, I ask for things, and even sometimes resort to begging and bribing. I, as much as you, would like Maple to be as intuitive as possible. I'm not the one to answer your second question. But don't stop asking it. Maplesoft does say it listens to its users.

 

RJL

@Torre 

Thanks for the pointer to the DG worksheet. I'll have to study that for a bit. My 1970 PhD thesis was in relativistic cosmology, so at one time I knew some differential geometry and continuous group theory, but that was a long time ago.

I've looked at the DG package, but there's so much in it that I'm not sure I'll ever master it. Every bit of digging helps, though.

RJL

@Torre 

It would certainly be useful if this comment were expanded to a full demonstration showing how one might use such a basis in the DifferentialGeometry package. For sure, I would appreciate being shown how.

RJL

Simply work in the Student LinearAlgebra package where all quantities are assumed to be real. Also, the VectorCalculus packages do not conjugate for dot products.

RJL Maplesoft

I've looked at the two worksheets supplied in this question, but they import data from Excel files that weren't provided. I've privately requested access to the data. If I get the data, I'll explore the calculations to try finding out why there's a problem. I'd like the conversation to be off-line until I have something to report. Meanwhile, if anyone else can spot what's happening in the failed calculation, please enlighten us all.

 RJL Maplesoft

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