rlopez

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16 years, 364 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

@Rouben Rostamian  

What if the equations f=0, diff(f,p)=0 are so entangled that there is no explicit solution for x(p) and y(p)? These functions would have to be determined numerically, making the whole computation more difficult.

@mmcdara 

An internet search for "method of lines" brings up many links. In particular, Wikipedia has a substantial article on the method.

One surprising result I found in Dr. Dao's work was the use of this method in conjunction with Ritz/Galerkin and collocation techniques.

In none of my readings on MoL did I find reference to the method of characteristics.

 

@mmcdara 

I save my Maple worksheets as mw files, and search through them with Advanced Find and Replace from Abacre Software.

If you open a mw worksheet in a text editor, you find many things written in plain text, and many things in some strange coding. The search software finds what's in plain text, but not what's in code. So some things won't be found with this tool. But enough can be found so that it's worth using. There has never been something I've searched for that this tool has been unable to help me find. (I guess that means I've never searched for one of those "impossible" items.)

 

@Carl Love 

Could you show how to form a subscripted symbol with a subscript that is not italicized?

@C_R 

Substitute Into is an option in the Context Panel. It is available for an equation or a set/list of equations, and is equivalent to the eval command. The eval command admits an equation label, but Substitute Into does not. That is the inadequacy I'd like to see corrected.

It might require a total rethink to how equation labels are implemented in Maple, but the utility of such labels would be greatly enhanced if they could be use in some of the pop-ups from the Context Panel and as inputs to Embedded Components.

One instance of the former is "Substitute Into" where you can only substitute into somthing that already has a name, not just an equation label.

@Carl Love 

Thanks for this insight.

with(plots):

with(Student:-VectorCalculus):

animate(PlotVector,[<cos(t),sin(t)>],t=0..2*Pi);

These commands generate the same animation without the headache of premature evaluation. The PlotVector command has many advantages over the use of the plots package arrow command.

However, the example given amply illustrates the evaluation issue and clearly explains how to deal with it.

 

@lemelinm 

Equation (14) needs a multiplicative "c" on the left. (See equation (3).) Then the lettered equations in red make sense.

https://www.mapleprimes.com/posts/208379-Double-Integral-Over-A-Nonrectangular-Domain

On July 5, 2017, Kitonum provided code for using Green's theorem to obtain the area of a plane region. This would make a useful tool in Maple, but presently it's neither a Task Template nor a Math Apps.

I knew I had saved this code but nothing I searched for in the Primes search engine led me back to it. I had to hunt on my hard drive for this link. Searches with words such as "area" or "enclosed" led nowhere useful.

@acer 

I read and experimented with these four solutions, and I still don't understand why they work. What's going on behind the scene so that after the second Explore where a:=2, the first Explore still uses a=1?

I look at solutions in MaplePrimes and ask myself what I would have done if I faced a similar issue. If it's an issue I don't think I would ever face, I tend to ignore the proposed Maple syntax. If it's an issue I think I might face, I then try to understand what the proposed syntax is doing, and how I might have solved the problem with what I know about Maple. (I don't know anywhere as much about Maple coding as some of the habitual respondants do.)

In this particular instance, I probably would have used one Explore, but would have added a second slider for "a".

Just tried the following syntax, and it seems to work just fine. Is ignorance actually bliss?

Explore(plot(a*x + y, x = -10 .. 10, -20 .. 20), a = 1 .. 5, y = -10 .. 10.)

The RationalFunctionPlot command in the Student Precalculus package will graph the rational function without the need for discont, and will draw in all asymptotes. The functionality exists in the Rational Functions tutor, available from Tools/Tutors/Precalculus/RationalFunctions.

Acer's syntax for the piecewise function is far simpler than what I had used. The time-stamps show our posts were almost simultaneous.

@janhardo 

You are correct about there being no curl in 2 dimensions. The difference of the "cross partials" is really one component of a curl. If you give your vector field a fictitious third component of zero, then you can take the curl.

And how quickly those 50 years have gone by.

@acer 

Thanks for the clarification. It's fortunate that you have access to Maple 18, access that I didn't have when I tested Carl's recipe. Your analysis is therefore far more comprehensive and complete.

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