rlopez

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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.

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These are Posts that have been published by rlopez

A wealth of knowledge is on display in MaplePrimes as our contributors share their expertise and step up to answer others’ queries. This post picks out one such response and further elucidates the answers to the posted question. I hope these explanations appeal to those of our readers who might not be familiar with the techniques embedded in the original responses.

Before I begin, a quick note that the content below was primarily created by one of our summer interns, Pia, with guidance and advice from me.

The Question: Source Code of Math Apps

Eberch, a new Maple user, was interested in learning how to build his own Math Apps by looking at the source code of some of the already existing Math Apps that Maple offers.

Acer helpfully suggested that he look into the Startup Code of a Math App, in order to see definitions of procedures, modules, etc. He also recommended Eberch take a look at the “action code” that most of the Math Apps have which consist of function calls to procedures or modules defined in the Startup Code. The Startup Code can be accessed from the Edit menu. The function calls can be seen by right-clicking on the relevant component and selecting Edit Click Action.

Acer’s answer is correct and helpful. But for those just learning Maple, I wanted to provide some additional explanation.

Let’s talk more about building your own Math Apps

Building your own Math Apps can seem like something that involves complicated code and rare commands, but Daniel Skoog perfectly portrays an easy and straightforward method to do this in his latest webinar. He provides a clear definition of a Math App, a step-by-step approach to creating a Math App using the explore and quiz commands, and ways to share your applications with the Maple community. It is highly recommended that you watch the entire webinar if you would like to learn more about the core concepts of working with Maple, but you can find the Math App information starting at the 33:00 mark.

I hope that you find this useful. If there is a particular question on MaplePrimes that you would like further explained, please let me know. 

A wealth of knowledge is on display in MaplePrimes as our contributors share their expertise and step up to answer others’ queries. This post picks out one such response and further elucidates the answers to the posted question. I hope these explanations appeal to those of our readers who might not be familiar with the techniques embedded in the original responses.

Before I begin, a quick note that the content below was primarily created by one of our summer interns, Pia, with guidance and advice from me.

MaplePrimes member Thomas Dean wanted 1/2*x^(1/2) + 1/13*x^(1/3) + 1/26*x^(45/37)  to become  0.5*x^0.500000 + 0.07692307692*x^0.333333 + 0.03846153846*x^1.216216216  using the evalf command.

Here you can see the piece of code that Thomas Dean wrote in Maple:

eq:=1/2*x^(1/2) + 1/13*x^(1/3) + 1/26*x^(45/37);
evalf(eq);

Carl Love replied simply and effectively with a piece of code, using the evalindets command instead:

evalindets(eq, fraction, evalf);

As always, Love provided an accurate response, and it is absolutely correct. But for those just learning Maple, I wanted to provide some additional explanation.

The evalindets command, evalindets( expr, atype, transformer, rest ), is a particular combination of calls to eval and indets that allows you to efficiently transform all subexpressions of a given type by some algorithm. It encapsulates a common "pattern" used in expression manipulation and transformation.

Each subexpression of type atype is transformed by the supplied transformer procedure. Then, each subexpression is replaced in the original expression, using eval, with the corresponding transformed expression.

 

Note: the parameter restis an optional expression sequence of extra arguments to be passed to transformer. In this example it was not used.

I hope that you find this useful. If there is a particular question on MaplePrimes that you would like further explained, please let me know. 

A wealth of knowledge is on display in MaplePrimes as our contributors share their expertise and step up to answer others’ queries. This post picks out one such response and further elucidates the answers to the posted question. I hope these explanations appeal to those of our readers who might not be familiar with the techniques embedded in the original responses.

Before I begin, a quick note that the content below was primarily created by one of our summer interns, Pia, with guidance and advice from me.

The Question: why is 2*cos(x)^2-1 simpler than 1-2*sin(x)^2

The author, nm, asked why 2*cos(x)^2-1  was simpler than 1-2*sin(x)^2 according to Maple. nm wrote:

I looked at help trying to understand why Maple thinks 2*cos(x)^2-1 is simpler than 1-2*sin(x)^2 but did not see it. I was expecting to see cos(2*x) as a result.

Preben Alsholm answered nm’s question by recommending the use of the combine command to obtain the result he was expecting to see, as well as a further explanation on how the simplify command works. Alsholm wrote:

Use combine to obtain what you want:
combine(1-2*sin(x)^2);

simplify has a general preference for cos over sin. That doesn't mean however, that it turns sin into cos at all costs:

simplify(sin(x));
##Try also
simplify(1-2*sin(x)^2,size);

simplify doesn't necessarily get you the simplest result in the common sense of the word 'simplify'. Try as another example

expand((x+y)^3);
simplify(%);
factor(%);

As always, Alsholm provided an accurate, thoughtful response. But for those just learning Maple, I thought some additional explanation could be helpful.

Let’s talk more about the simplify command and combine function

The simplify command applies simplification rules to an expression. Its parameters can be any expression.

The combine function applies transformations which combine terms in sums, products, and powers into a single term. For many functions, the transformations applied by combine are the inverse of the transformations that are applied by expand. For example, consider the well-known identity:

sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

The combine function applies the identity from right to left, whereas the expand function does the reverse.

 

I hope that you find this useful. If there is a particular question on MaplePrimes that you would like further explained, please feel free to contact me.

 

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:

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.

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