## 3010 Reputation

19 years, 289 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.

## It's Better With Maple...

Recently, I had to write a brief introduction to the precalculus topic "Vertical Translation of Graphs." Figure 1 ( in black, in red) says just about everything.

 Figure 1   The red curve () is the black curve () vertically translated upward by one unit.

But is the issue all that trivial? Although the curves are vertically separated by one unit, they don't look uniformly spaced. The animation in Figure 2 helps overcome the optical illusion that makes it seem like the black curve bends towards the red curve, even though the curves are congruent.

## Visualizing a Parallel Field in a Curved...

It was 1992 when Mel Maron and I had just published the third edition of Numerical Analysis: A Practical Approach.  One of our editors made the suggestion that a Maple version of an advanced engineering math book should be written. For the next five years I steadfastly resisted the challenge.  Finally, in 1997 I signed a contract with Addison Wesley for a 1000-page AEM text, the manuscript due in two years.

Rose-Hulman Institute of Technology where I was teaching in the math department is on the quarter system, and math faculty normally teach twelve contact hours.  Calculus classes are five hours per week, so for each calculus course taught, a faculty member picks up an extra hour.  To minimize prep time, I wrangled three courses all the same, but they had to be calculus courses, so I was teaching fifteen contact hours and writing what turned out to be a 1200-page text.

After the first two quarters of academic year 1997, I needed to come up for air, so I set aside the project and spent several months putting together a Maple-based tensor calculus course. Happily, I even got to teach it in the following school year. One of the high points for me was animating a parallel vector field along a latitude on a sphere.

## Series and Tests for Their Convergence...

A question was asked in the forums about series tests. I saw that this would also make an excellent weblog entry as well. In answer to the questions: How can I get Maple to determine if a series converges or diverges? and How can I obtain the general representation of a formal power series for a function? I offer the following advice:
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