rlopez

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15 years, 222 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 answers submitted by rlopez

q:=arctan(1/(5^(1/2)-1)*(10+2*5^(1/2))^(1/2));

map(rationalize,q) => arctan((1/4)*(10+2*5^(1/2))^(1/2)*(5^(1/2)+1))

Now, if that argument could be factored to the form (1/4)*2^(1/2)*(5+5^(1/2))^(1/2)*(5^(1/2)+1), that is, if  sqrt(10+2*sqrt(5)) could be written as sqrt(2)*sqrt(5+sqrt(5)), then arctan of the resulting expression immediately evaluates to 2*Pi/5.

I have not been able to figure out a transformation of the key radical. That's probably why Maple needs the various tricks being reported here. What seems to be missing is a "simplification" of the radical to the form that arctan then recognizes.

RJL Maplesoft

 If I understand your question correctly, you are asking if it is possible to build a new embedded component in Maple. If that is the question, the answer is "no." The embedded components in Maple are what are available through the Components palette. New components are constructed by the Maple programmers as they see the need for same.

Also, I'm not sure of the distinction between "Big Time" and "small things" but I think that you could answer your own question by looking at the task templates that contain embedded components. Some of the early task templates are command-based, and did not make significant use of components. Many of the newer ones added later make use of embedded components. Whether the usage is "Big Time" or "small things" is something observers will have to answer for themselves.

RJL Maplesoft

 The Maple help system contains a pdf version of the programming guides, and a getting-started guide. Under Help, see Manuals, Resources and more,,,/Manuals

These should be enough to get  you started converting your code to Maple.

RJL Maplesoft

 The "white paper" http://www.maplesoft.com/applications/view.aspx?SID=33840 in the Applications Center might provide a streamlined introduction to using the DifferentialGeometry package for tensor calculus.

RJL Maplesoft

 The red code in the AEM ebook captures the calculations that have been off-loaded to Maple. Getting rid of the red code would remove that which makes the book interactive. Changing the text-form of the input (what Maplesoft calls 1D math) to typeset math input (2D math) would change the color from red to black, but the same issue prevails. The code shows how to capture in Maple the math under discussion. Maple then implements the calculations. The code can be modified as the text is read, allowing experiments, and what-if scenarios to be be explored. Much of the red code can also be converted to use in solving the exercises included with the ebook.

So, getting rid of the red code isn't the thing that caught my eye. It's the second part, converting it to something more meaningful. Well, what would be more meaningful? The intent of the ebook was to provide a mechanism for capturing the math in a format that was live, computable, and adaptable. It is its own meaning.

The alternative would be to have a completely discoursive text with no math, and no live calculations. I don't think that's what I set out to do when I wrote the text.

But I would welcome additional comment on just what it is that the questioner would like the ebook to be.

RJL

RJL Maplesoft

 If the equations are interpreted as they were by longrob, then the sum of squares of aa, bb, and cc is not 1. Hence, h cannot be 1 under this interpretation of the original expressions. Definitely, the original set of expressions are ambiguous as they stand.

RJL Maplesoft

 In the Slider Properties dialog, use a floating-point number for either "Value at Lowest Position" or "Value at Highest Position." This will convert the whole slider to floats.

RJL Maplesoft

 See the Blog post "Understanding the Question", which analyzes the implicit function at the heart of this question.

RJL Maplesoft

 Maple 14 has a problem with some forms of the PlotPositionVector command. However, it seems you are trying to do something that Maple has built-in commands for. For example, the following command will draw 5 TNB frames along the graph of the given curve.

Student[VectorCalculus][TNBFrame](<cos(t), sin(t), cos(2*t)>, t, 'output'=plot, 'range'=0 .. 2*Pi, 'frames'=5,binormaloptions=[color=red],normaloptions=[color=blue],tangentoptions=[color=orange]);

The output option even takes the "animate" parameter to create an animation of one TNB frame moving along the curve.

Alternatively, use the Space Curves tutor accessible from Tools/Tutors/VectorCalculus. This will give the same results in an interactive environment.

RJL Maplesoft

 The Minimize command in Maple's Optimization package hits a complex number in its iteration, and throws an error message. I couldn't get this package to produce anything worth discussing.

But, the given equation, of the form f(x,y,z)=0, can be solved explicitly for x = x(y,z) by Maple. There are four branches to the solution, only two of which are real.

Hence, each of the two real branches can be plotted with plot3d on the square 0<=y,z<=1. From these two plots, it is easy to see that one branch has a minimum of approximately 0.123 at (y,z) = (0,1).

The other branch has a minimum on the face y=0. Substituting y=0 into this branch gives a function x=x(z) which can be graphed to observe that there is a minimum of approximately -0.236 at (y,z) = (0,0.4). This function can be differentiated, etc., and fsolve will produce the critical value z = 0.4567706470, from which the actual constrained minimum of x = -0.2363733816 can be found.

RJL Maplesoft

 Looks to me like you have a system of three second-order ODEs in three unknowns. However, your boundary conditions contain values of only two of the functions. Since you are looking for a numeric solution, the solver in Maple will issue various complaints about this calculation. You need to impose two conditions on each of the three unknown functions.

RJL Maplesoft

 Maple integrates 1/x to ln(x) and not ln(abs(x)) by design. It is correct, provided the logarithm is interpreted to be defined over the complex plane. This isn't necessarily satisfying in a beginning calculus course, so one way around the issue is the following kluge.

Suppose the ln(x) appears in an expression called q. The following command is one way to change ln(x) to ln(abs(x)).

eval(q,ln=ln@abs)

The "at" symbol @ is Maple's symbol for composition, so the eval command is evaluating the given expression and any "ln" that it finds will be replaced by ln composed with abs.

RJL Maplesoft

 Suppose the three vertices that "sit on the table" are A,B,C, and that the vertex not "on the table" is D. If you have the vectors from A to B and A to C, called respectively AB and AC, you can obtain their cross-product, giving a vector N that is "perpendicular to the table." The length of the component of the vector AD along the normal N is the height of the tetrahedron.

The geom3d package allows a definition of a general tetrahedron. Then, using the package's "volume" command, it should be possible to check your answer more directly.

RJL Maplesof

 If "q" has the value 2, your nested seq commands should produce a sequence of four equations. If "q" is not assigned, you should get an error message to the effect that Maple is unable to execute the seq command.

RJL Maplesoft

 You have two choices: You can either assign the expression to a name, or you can reference the expression via its equation label.

q:=x^2+1 is the way you assign the expression the name "q".

It's not clear what flavor of Maple you're working with, so the issue of equation labels may or may not be relevant. If  you see equation labels on the right edge of  your worksheet, you can use those to reference the item so labeled. Use Ctrl+L (in Windows) to bring up the Equation Label dialog, and here, enter the number of the label (do not type any parentheses).

RJL Maplesoft

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