Maplesoft Blogger Profile: Robert Lopez

Maple Fellow

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.

Posts by Robert Lopez

On November 22, Joe Riel posted an implicit differentiation problem that caught my attention. It took the manipulations typically learned in an Advanced Calculus course one step further, but the devices learned in such a course could readily be applied. Joe's solution was expressed in terms of exterior...

 

 

This is the Classroom Tips & Techniques article for the May, 2011 Maplesoft Reporter, which, after publication, finds...

Each of my two previous two blog posts (Maple Gems, More Maple Gems) contained five "gems" from my Little Red Book of Maple Magic, a red ring-binder in which I record...

In a recent blog post, I discussed five "gems" in my Little Red Book of Maple Magic, a notebook I use to keep track of the Maple wisdom I glean from interactions with the Maple programmers in the building. Here are five more such "gems" that appeared in a Tips & Techniques column in a recent issue of the ...

 

Update - April 4, 2011: I corrected a typo in Table 2, first column, bottom row.  What was sqrt(6) has been changed to sqrt(5).

 

Since coming to Maplesoft in 2003, I've kept a notebook of "gems" I've gleaned from consulting with the programmers in the building. I call it my "Little Red Book of Maple Magic." It really is red. The first spiral-bound notebook was little, and it was red. When it overflowed, I moved the notes to a red ring-binder. But it's not so little any more.

I have always preferred the notation  for the derivative of

I spent this past week preparing a Webex presentation to a client who was interested in using Maple for a physics course in chaos. Of the two texts selected for the course, I had one on my own bookshelf. So I scanned Steven Strogatz' text Nonlinear Dynamics and Chaos (Addison Wesley, 1994) for topics that would profit from investigation with Maple.

The hardest and/or most important part of answering a question is making sure the real question is understood. The July 1, 2010 question Using fsolve with a dispersion relation posted to MaplePrimes seemed to be about obtaining a numeric solution of an equation. Turns out it was more a question about the behavior of an implicit function.

The greatest benefits from bringing Maple into the classroom are realized when the static pedagogy of a printed textbook is enlivened by the interplay of symbolic, graphic, and numeric calculations made possible by technology.  It is not enough merely to compute or check answers with Maple.  To stop after noting that indeed, Maple can compute the correct answer is not a pedagogical breakthrough.

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In a recent blog post, I pointed out that Maple did not have a built-in functionality for drawing graphs that arise in computing volumes by slices. However, I did provide several examples of ad-hoc visualizations that one could build with the graphing tools in Maple.

 

Recently, a user called attention to a weakness in the Student Calculus 1 command, VolumeOfRevolution. This command (and the tutor built on it) will draw a surface of revolution bounded by the surfaces generated by revolving the graph of one or two functions.

Points and lines, and the relationships between them, are essential ingredients of so many problems in, for example, calculus. In particular, obtaining the equation of the perpendicular bisector of a line segment, dropping a perpendicular from a point to a given line, and calculating the distance from a point to a line are three tasks treated in elementary analytic geometry that recur in the applications....

Back in July of 2005, one of the early Tips & Techniques articles (since updated) in the Maple Reporter was a comparison of two different approaches to fitting a circle to 3D data points. The impetus for the comparison was Carl Cowen's article on the subject. His approach was algebraic - he used the singular value decomposition to obtain a basis for the...

In 1988, Keith Geddes and others involved with the Maple project at the University of Waterloo published a Maple Calculus Workbook of interesting calculus problems and their solutions in Maple. Over the years, I've paged through this book, extracting some of its more unique problems. Recently, I extracted the following problem from this book, and added it to my Clickable Calculus collection, which I use for workshops and web-based presentations.

Three recent articles in the Tips & Techniques series addressed the question of stepwise solutions in Maple. Just what is it that Maple provides by way of stepwise solutions for standard calculations in the mathematical curricula? There are commands, assistants, tutors, and task templates that provide stepwise calculations in precalculus, calculus, linear algebra, and vector calculus. In addition, since Maple can implement nearly any mathematical operation, any stepwise calculation can be reproduced in Maple by assembling the appropriate intermediate steps, just as they would be assembled when working with pencil and paper.

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