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 answers submitted by rlopez

You really don't want to calculate all the determinants needed for Cramer's rule. Instead, obtain the LU decomposition with the LUDecomposition command in the LinearAlgebra package.

It would help to make the Marker column visible. Go to the View menu and select the option "Markers". A thin gray column will open at the left edge of the Maple workspace and yoiu will see in it pairs of opposing triangles. Each such pair delineates a document block in which you can enter typeset math if you are in math mode, or text, if you are in text mode. In math mode, 2D math will appear in a blue rectangle. If you right-click on this math, you will have the option of changing this executable math to non-executable math that will then be in a gray rectangle.

Somewhere in here is the reason why your 2D math is not executing.

There are integrals for which a general result is obtained, but  which are not valid for particular values of a parameter such as n. These coefficients have to be evaluated with a separate integral for the particular values of n at stake.

At least one of the packages that users have created for generating Fourier series gets this right - the code identifies the special cases and determines the appropriate integral to obtain those coefficients. In fact, a recent thread on this forum dealt with at least two of those add-on packages.

A valid link in a Maple worksheet exported to pdf does not seem to be preserved in the pdf. I did find that I could set the link in the pdf itself. Is this a pdf-thing, or is there a way to export links from Maple to pdf?

This would be a useful feature for Maple if the shortcoming is in Maple. If the shortcoming is in pdf itself, shame.

with(Student:-VectorCalculus):

FlowLine( VectorField( <-y -z, x + y/5, 1/5 + (x-5/2)*z>),[<1,1,1>], fieldoptions=[transparency=.3,fieldstrength=fixed,grid=[5,5,5],arrows=SLIM], flowlineoptions=[color=black,thickness=2], axes=frame,caption="");

The number of initial points can be more than one: Just add them to the list containing the initial point (1,1,1).

The arrows of the field and integral curves (flow lines) emanating from the initial points are drawn.

The ApplyLinearTransformPlot command in the Student LinearAlgebra package may give you what you want, provided you can express the linear transformation as a matrix. The command then applies this matrix to a plot data structure.

Additional discussion and examples can be found in the November 2013 Tips & Techniques article "Locus of Eigenvalues," available in the Application Center.

https://www.maplesoft.com/applications/view.aspx?sid=153463

To obtain a locus of continuity class C1 (continuously turning tangent), one often needs to change branches. This can be seen for characteristic equations that can be solved in closed form. Once the degree gets high enough, only a numeric solution for the eigenvalues is feasible. Maple's numeric solvers return a sorted list of eigenvalues. The article concludes with the observation "There is no user-control of this sort, but even if there were, what sorting rule could be invoked across an eigenvalue with algebraic multiplicity greater than 1? It would seem that the only way to define a unique locus of eigenvalues is to require that it be of class C1, that is, that it have a continuously turning tangent."

(Not sure if the links included here are effective.)

I assume the question means "how do I include a link to a URL in a Maple worksheet?"

If so, then here's howto Hyperlink a word to the URL. To do that, select the "hot" word (it has to be text, not typeset math), right-click and select Convert To/Hyperlink. In the Hyperlink dialog that opens, select URL in the "Type" dropdown box. Paste the complete URL in the "Target" box. Click OK.

An alternate path to the Hyperlink dialog is via the Format menu option Convert To/Hyperlink.

If this wasn't the question, please clarify.

The Euler-Lagrange equation can be displayed using typeset (2D) math and items from appropriate palettes. To write a semblance of the equation that actually executes, you will have to accept a compromise.

For display purposes, you only need the differentiation templates available in the Calculus palette, or for displaying the partial derivatives use the partial derivative "squiggle" (PartialD) found in the Operators palette. The overdot can be set with one of the templates in the Layout palette, or can be set from the keyboard by pressing Control Shift Quote to jump on top of q and pressing the period key.

The compromise you have to accept to make the equation executable is that the L cannot be in the numerator of the partial derivative operator. It must be to the right of the operator that is obtained from the Calculus palette.

The following two steps worked for me.

bb:=abs~(b);

min[index](bb);

The first command produces a list of real numbers; the second, returns the "location" of the minimum.

You could combine both into one step: min[inded](abs~(b))

The tilde maps the abs command onto each element of the list b. (The tilde is a newer construct than the older map command.)

In addition to the LinearSolveSteps command, there are other tools in Maple to help with solving such linear equations.

For example, bring up the Context Menu (right-click in Windows, etc., elsewhere) and select "Manipulate Equation." An interactive tool pops up. In this tool, you can apply the various transformations you see in the stepwise solution provided by the LinearSolveSteps command.

You can also select terms in the equation and wait for Maple to provide suggestions for transformations (i.e., a next step).

If you know what steps you want to apply, you can also implement them stepwise from the keyboard. For example, to add 3 to both sides of the equation x-3=7, write (x-3=7)+3 and Maple will return x=10.

If you want to start out knowing what the solution is (so that you can recognize it when you find it stepwise) bring up the Context Menu and select the Solve option.

If you executed plots:-implicitplot(y=x+c,x=-1..1,y=-1..1); you would have gotten an error message indicating that "c" needed a value. But  you report that you got empty axes. So, we are now guessing what it was that you actually tried.

My suggestion would be to try the Explore command:

Explore(plots:-implicitplot(y=x+c,x=-1..1,y=-1..1,view=[-2..2,-2..2]),c=-1..1.0);

This draws a line segment whose location is controlled by the value of c, and the value of c is controlled by a slider under the graph.

If you used any form of the plot command applied to the equation y=x+c, or an equation of that form with c given a value, you would have obtained an error message. (The plot command graphs expressions, not equations.) Again, you do not report that you got an error message. Hope some of this helps.
 

Bring up the Context Menu (right-click in Windows) and select the option Standard Operations->Determinant.

If you do such a calculation using 1d input at a red prompt in a worksheet, Maple will write the underlying code that gets executed. That would show the Determinant command is part of the LinearAlgebra package.

In four Tips & Techniques articles (Maple Reporter series) between December 2006 and April 2007, I compared how to create and explore Fourier series with built-in Maple commands, and with three different packages contributed by Maple users. The first package is the one referenced by the OP, the one by Khanshan. I always found the second package, the one written by Prof. Wilhelm Werner, to be the best of the three. I believe Prof. Werner has maintained his package over a longer period of time than did Khanshan. I would recommend that the OP consider Werner's package.

The following link is to the Maple Application Center where Werner's contribution can be found.

https://www.maplesoft.com/applications/author.aspx?mid=162

The link to my T&T article describing this package is also in the Application Center:

https://www.maplesoft.com/applications/view.aspx?sid=4885

Since I wrote that sequence of articles, the Maple OrthogonalExpandsions package has been written and made available for direct download and installation from the Cloud [or link in the Application Center, for Maple versions older than 2017]. This package generalizes to the extent that it can deal with expansions in terms of a basis of orthogonal functions, not just orthogonal polynomials.

It took only a minute to enter the coefficient matrix interactively. The determinant of that matrix is zero, so, since the equations are homogeneous, a nontrivial solution exists. It's easy enough to generate the equations from the coefficient matrix. The solve/solve option from the context menu then provides the solution w = 3*z*(1/2), x = -(1/2)*z, y = z, z = z. Check your worksheet for anything that might be causing your "solve" to come up empty.

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