# Maplesoft Blogger Profile: Robert Lopez

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## 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.

## Eigenpairs - Live!

by:

You are teaching linear algebra, or perhaps a differential equations course that contains a unit on first-order linear systems. You need to get across the notion of the eigenpair of a matrix, that is, eigenvalues and eigenvectors, what they mean, how are they found, for what are they useful.

Of course, Maple's Context Menu can, with a click or two of the mouse, return both eigenvalues and eigenvectors. But that does not satisfy the needs of the student: an answer has been given but nothing has been learned. So, of what use is Maple in this pedagogical task? How can Maple enhance the lessons devoted to finding and using eigenpairs of a matrix?

In this webinar I am going to demonstrate how Maple can be used to get across the concept of the eigenpair, to show its meaning, to relate this concept to the by-hand algorithms taught in textbooks.

Ah, but it's not enough just to do the calculations - they also have to be easy to implement so that the implementation does not cloud the pedagogic goal. So, an essential element of this webinar will be its Clickable format, free of the encumbrance of commands and their related syntax. I'll use a syntax-free paradigm to keep the technology as simple as possible while achieving the didactic goal.

Notes added on July 7, 2015:

## 14 Additional Clickable Calculus Solutions Posted

by: Maple

Fourteen Clickable Calculus examples have been added to the Teaching Concepts with Maple area of the Maplesoft web site. Four are sequence and series explorations taken from algebra/precalculus, four are applications of differentiation, four are applications of integration, and two are problems from the lines-and-planes section of multivariate calculus. By my count, this means some 111 Clickable Calculus examples have now been posted to the section.

## Additional Clickable Calculus Solutions Posted

by: Maple

Thirteen Clickable Calculus examples have been added to the Teaching Concepts with Maple section of the Maplesoft web site. The additions include examples in algebra, differential and integral calculus, lines-and-planes in multivariate calculus, and linear algebra. By my count, this means some 97 Clickable Calculus examples are now available.

In the Algebra/Precalculus section, examples of an

## Animating a Related-Rate Problem

by: Maple

In a webinar on July 10, 2013, I solved the related rate problem:

Helium is pumped into a spherical balloon at the constant rate of 25 cu ft per min.
At what rate is the surface area of the balloon increasing at the moment when its radius is 8 ft?

A question in the Q&A at the end of the Webinar asked if it were possible to have an animation illustrate the expanding sphere and the rate of change in the surface area thereof.

## Lines and Planes in the Student MultivariateCalculus...

by: Maple 17

In Maple 17, the Student MultivariateCalculus package has been augmented with fifteen new commands relevant for defining and manipulating lines and planes. There already exists a functionality for this in the geom3d package whose structures differ from those in the new Student packages. Students...

## Yet more Clickable Calculus solutions!

by: Maple

Ten more Clickable Calculus solutions have been added to the Teaching Concepts with Maple section of the Maplesoft web site. Solutions to problems include examples in algebra, differential and integral calculus, lines-and-planes in multivariate calculus, linear algebra, and vector calculus.

The algebra additions include an example illustrating how a

## Car Talk Puzzler - September 22, 2012

by: Maple

Revision Note:
I have updated the graph in the attached Maple document based on Doug Meade's comment below.
CarTalkPuzzler_9-22-.mw

Car Talk, a humorous phone-in program in which Tom and Ray Magliozzi (Click and Clack, the Tappet Brothers) diagnose and offer solutions for mysterious auto-related maladies, is carried by National Public Radio...

## 11 New Clickable Calculus Examples added to Teaching...

by: Maple

Eleven new Clickable-Calculus examples have been added to the Teaching Concepts with Maple section of the Maplesoft website. That means some 74 of the 154 solved problems in my data-base of syntax-free calculations are now available. Once again, these examples and associated videos illustrate point-and-click computations in support of the pedagogic message of resequencing skills and concepts.

This message has been articulated in ...

## Further Analysis of a Minimization Problem: Distance...

by: Maple

This post is a further exploration of the optimization problem of finding a point on f(x) = sinh(x) - xe-3x closest to the point (1,7).  The problem is part of our Teaching Concepts with Maple web site, a collection of video examples and Maple worksheets designed to illustrate how Maple can be used to generate...

## Ten new 'Teaching Concepts with Maple' examples...

by: Maple

With the addition of ten new Clickable-Calculus examples to the Teaching Concepts with Maple section of the Maplesoft website, we've now posted 63 of the 154 solved problems in my data-base of syntax-free calculations. Once again, these examples and associated videos illustrate point-and-click computations, but more important, they embody the

by: Maple

My list of problems solved with Clickable-Calculus syntax-free techniques now numbers 154, spread over eight subject areas. Recently, Maplesoft posted to its website 44 of these problems, along with videos of their point-and-click solutions. Not only do these solutions demonstrate Maple functionalities, but they also have a pedagogic message, that is resequencing skills and concepts. They show how Maple can be used to obtain a solution, then show how Maple can be used to implement...

## Teaching Concepts with Maple

by: Maple

Being easy to use is nice, but being easy to learn with is better. Maple’s ease-of-use paradigm, captured in the phrases “Clickable Calculus” and “Clickable Math” provides a syntax-free way to use Maple. The learning curve is flattened. But making Maple easy to use to use badly in the classroom helps neither student nor instructor.

In the mid to late ‘80s,...

## Directional Derivatives in Maple

by: Maple

The directional derivative of a scalar function , computed in the direction u in Cartesian coordinates, is defined by

## Gems 16-20 from the Red Book of Maple Magic

by: Maple

A recent Tips and Techniques article in the Maple Reporter contained the following five "gems" from my Red Book of Maple Magic. These 'gems' are tricks and techniques for Maple that I've discovered in my years here at Maplesoft. The previous 15 gems have appeared in three other issues of the Reporter, as...

## Car Talk Puzzler

by: Maple

National Public Radio in the USA carries Car Talk, a humorous phone-in program in which Tom and Ray Magliozzi (Click and Clack, the Tappet Brothers) diagnose and offer solutions for mysterious auto-related maladies. It's an amusing hour on Saturday mornings.

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