rlopez

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16 years, 136 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

@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.

@Carl Love 

I believe this works if you first select the section. Use Control+Alt+Shift+S to select the section from anywhere within the section. Then press Enter or Return as appropriate.

@acer 

Isn't about time that dsolve acquired an option equivalent to the "free=..." option in LinearAlgebra's LeastSquares command? The _C1 of dsolve is ugly and tedious to deal with when working further with a solution containing same.

@janhardo 

Invoke the Plot Builder on x^2+y^2+z^2=1 and you get an empty frame because the defaults are -10 to 10 on all three variables. The default grid is too coarse to capture enough points on the sphere. Change the ranges to something smaller, like -1 to 1 for each dimension.

@janhardo 

The eliminate command in the corrected worksheet I attached to my last reply returns a list of two sets. The first set contains an equation for the eliminated variable. The second set contains the expression that results from using the first equation. This expression is the left side of an equation whose right-side is an unwritten zero.

In my usage of the command, I appended [], open and close square brackets. This causes the list brackets from the equate command to be dropped, so that the return is now just a sequence of two sets.

I then wanted to solve for z in the second "equation" returned by "eliminate." To access this expression, I used q[2], the second set in the returned seqence. But this referenced the second set, so to get rid of the set braces around the desired expression, I used q[2][1], in other words, the first thing inside the second member of the sequence q.

The isolate command is like a weak solve command that returns an equation whose left-hand side is the variable solved for.

These are operations that become familiar to users of 1D math input, the linear form advocated by so many of the respondants to this forum. This is the kind of thing I had to teach my students back when Maple had only the worksheet interface. They didn't like having to learn a computer language just to implement their math. That's why I see so much utility and value in the Typeset (2D math) input mode. It eliminates the need to teach students the minutiae of Maple manipulations that are only in service of Maple itself, not of the math you're trying to get Maple to do.

I could have done all the steps in the Corrected Worksheet in a syntax-free mode, but that requires explanatory text to describe what I would have clicked on, etc. I chose not to do that because it is indeed faster to use 1D input. But given your confusion over the syntax used, I have to ask "Was it really faster for the learner to have used what was faster for me?"

@janhardo 

The green surface is defined parametrically with parameters x and z: x=x, y=2*x-2, z, with z=2*x+y^2 and y=2*x-2, so z=0..2*x+(2*x-2)^2 = 4*x^2-6*x+4.

These calculations have been added to your worksheet along with some corrections and the calculation of the path integral.

corrected_worksheet.mw

@janhardo 

If you are asking about the red and green surfaces in the worksheet I posted, then note that the line integral of the scalar function is equal to the surface area of the green surface. The red surface is just a graph of the scalar f(x,y). It's there to bound the green surface at the top. The green surface goes from the plane curve C up to the red surface f(x,y). There is no claim about the area of the red surface. That does not enter the discussion at all.

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