rlopez

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14 years, 344 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.

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These are replies submitted by rlopez

@Zeineb 

Tried nX=nY=4..7 and got solutions in each case. At 8, fsolve returns unevaluated. But at 7, the solution takes a bit of time. So, the issue seems to be in Maple's ability to solve the set of equations generated in the worksheet. The equations are nonlinear, so at some point fsolve probably needs some help determining where to look for solutions.

@tomleslie 

eliminate(newEqs,[U[1,1],U[2,1]]); reduces the system to two equations in two unknowns. Then, an implicitplot shows the curves defined by these two equations do not intersect. So you are probably right about there being something wrong with the original equations.

@MapleMathMatt 

I think your use of % gives the desired result, but that's not the & mentioned in your text. But your code seems to be the simplest way to obtain the desired result.

@mortezaghafoori 

As far as I can tell, you have a first order ODE but you are applying two boundary conditions.

Maple can provide a general solution to the ODE itself. It contains only one constant, so you can't apply both boundary conditions, unless what appears to be "A" on the right-hand side is a second parameter that can be adjusted. Unfortunately, my experiments with this approach seem to indicate that the problem (as I've interpreted it) has no solution.

By the way, it is not true that dsolve only handles initial-value problems. It will also solve boundary-value problems as well.

Finally, rather than post an image of your work, post a worksheet containing this work by using the green "up-arrow" in the MaplelPrimes toolbar.

 

 

I just installed the .3 update to Maple 2017 and noted that the glitch exhibited by vv persists in the updated version.

@NorwegianStudent 

I don't know if both packages can exist simultaneously in Maple. There may be clashes that lurk beneath the surface. These packages are not maintained by Maplesoft, so there's no guarantee that they are compatible. Perhaps someone with greater coding skills might be able to give a more definitive answer.

@NorwegianStudent 

If you define f(t) on [0,2*Pi], but integrate or call some Fourier Series command on [-Pi,Pi], you are bound to have discrepancies in the results. You need to use the domain over which f(t) is defined.

@NorwegianStudent 

If you use the plot command, add in the option "discont=true" so that Maple finds the discontinuity and does not connect the dots across the jump.

If you use the Plot Builder launched from the Context Menu, look for the Option "find discontinuities"

@NorwegianStudent 

I don't recall if the OrthogonalExpansions package provides code for creating the periodic extension of a function defined on an interval, but you can find it in Example 3 of the first worksheet in the series of 4 that I mentioned earlier.

https://www.maplesoft.com/applications/view.aspx?sid=4848

The extension can be defined in one line of code using the floor command as the greatest-integer function.

@vv Apparently, I didn't make myself clear. Let me try again: use the input style that is appropriate for the task at hand.

@max125 

All generalizations are false, including this one. Not all Maple experts use text (linear, 1d) input exclusively. It depends on what the expert is trying to do. Coders prefer textual input. Writers of Maple content, even experts within Maplesoft, will use typeset input that looks more natural mathematically, when appropriate.

Many opinions about this distinction can be found in past posts to MaplePrimes. Each style of Maple input has its advantages and disadvantages. It all depends on what the end-use for the resulting document might be.

@max125 

Apparently, you work in a Maple worksheet using red commands at red prompts. In that case, your only recourse is to use unapply. I'm not sure about how this is coded in Maple, but from experience I know that you cannot use as a rule to the right of the mapping arrow any reference, whether it be %, the named of a pre-defined expression, or an equation label.

However, if at the red prompt you would switch to math mode so that the line is typed in typeset math, then

f(x)=... will define a function if the Context Menu option "Assign Function" is selected, and the ellipsis is any form of the rule, whether it be %, the name of an existing expression, or an equation label.

If you do this, you will see the Maple code that executes, and it makes liberal use of the unapply command. Perhaps one of the Maple developers will weigh in on your question and give a more insightful answer as to why the mapping arrow cannot point to a "reference". I just know by experience that it can't.

A list, Matrix, or Array can be used to store the data in what mathematically can be thought of as a "vector." In Maple, at top-level (no packages installed) a Vector defined with the "Vector" command or with angle brackets (inequality symbols) is the same type object as the "Vector" defined in the LinearAlgebra or Student:-MultivariateCalculus packages. These vectors do not carry coordinate information. Vectors defined with the confines of the VectorCalculus packages carry a coordinate system as an attribute. This is the fundamental difference between working inside or outside a VectorCalculus package. The Physics:-Vectors package contains a completely different structure for representing vectors in 3-space.

As with any degree of flexibility, these additional forms and options present their own complexities, especially when some of these different structures are used together.

@vv I think that the first argument to IntOverDomain should be called fx, not f. Then, if Q=int(fx,x) were called f, the code would have been clearer. Then, instead of seeing int(Q*dy,...), one would have seen int(f*dy...), a more natural bit of notation.

Because y is a linear function along each segment of a polygonal line, dy is just the coefficient of x (or t, depending on the parametrization along the line) in the expression for the line.

The nodes defining a polygonal line must be listed in the order in which they are encountered as the line is traversed in the direction induced by the positive orientation of the SCROC. This direction is generally counterclockwise: walk the boundary with the left hand pointing into the interior of the region enclosed by the SCROC. If you do this with, say, a circle, you will see that the direction of motion is counterclockwise. If Maple's Flux command is used for the line integral, then simply list the nodes in the proper order. For segments defined parametrically, parametrize each segment so as to continue in the counterclockwise direction as the parameter advances in value.

I thank vv for having answered the questions posed. I saw them earlier today, but I was busy preparing for a week's vacation and didn't clear the agenda until hours later.

@vv -exp(3*Pi) raised to the power (1+I) does not equal 1. Similarly, for all solutions other than 1 and -exp(Pi).

The only way I can see that the given equation has an infinite number of solutions is by taking a different branch of the logarithm for each of these many solutions. If the principal branch of the log is used, then there are not an infinite number of solutions. That seems to be at the heart of the confusion here. Maple uses "ln" to mean both the principle logarithm and symbolically, to mean "true on some branch." I have always found this usage difficult in Maple.

Indeed, take the real and imaginary parts of (a+b*I)^(1+I)-1 and draw an implicit plot. Only two solutions of the resulting simultaneous equations appear to exist. These two solutions correspond to z=1 and z=-exp(Pi).

Does this example need further investigation or interpretation?

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