rlopez

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12 years, 319 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

@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?

@ The worksheet in Maple 7 is constructed with software issued by a company that went out of business sometime after Maple 9 was released. Hence, there is no way to continue developing that form of the product.

From Maple 10 onwards, it is possible to save a file as a "Maple Classic Worksheet (.mws)."

So, which meaning do you attach to "classic"? Do you mean the format used prior to the introduction of the Java-based interface that arrived with Maple 10, or do you mean the "Maple Classic Worksheet (.mws)" that is available from Maple 10 onwards? If you mean the former, does that imply that the latter is not a satisfactory replacement? And if so, why? What are the shortcomings of the extant Maple Classic Worksheet (.mws)?

A final note: Until recently, my home computer was a desktop running Windows XP. The last version of Maple that would install under that OS was Maple 18. It does not surprise me that in a newer operating system, an older version of Maple will not work. However, it is the case that Maple 2017, installed under Windows10, saves a worksheet as a Maple Classic Worksheet (.mws).

 

RJL Maplesoft

I'm not sure that the statement "Maplesoft wants everyone to switch to clickable things" is exactly true. I devised the term "Clickable Calculus" as a banner for the ease-of-use features that were beginning to appear in Maple, from Maple 10 onwards. Maplesoft at first wrinkled it nose at the term, then embraced as when it saw that "clickability" worked with an appropriate audience. (Think of all the users and students who don't need to master Maple commands in order to get value from the product.)

I was never aware of a Maplesoft mindset to get all Maple users to surrender the worksheet with text input, modes that appear to serve coders and programmers best. If there really is such a hidden agenda at Maplesoft, I'm as troubled about that as the many users who consistently report such feelings here on MaplePrimes.

Couldn't stop thinking about this calculation. The line integral on the right in the Divergence form of Green's theorem is actually the line integral of the normal component of <f,g> along a curve. Hence, this is a flux calculation, for which Maple has a built-in tool. So, using Kitonum's structure, it is possible to implement the line integral on the bounding SCROC with the Flux command in the Student VectorCalculus package. Just to prove to myself that this works, I shortened the code to the following, and verified that it gives the same answer(s) as the earlier code. By no means does this detract from the original insight exhibited by Kitonum.

IntOverDomain := proc(f, L)
local n, i, j, m, yk, yb, xk, xb, Q, p, P, R, V;
use Student:-VectorCalculus in
n:=nops(L);
Q:=int(f,x);
V:=VectorField(<Q,0>); 
for i from 1 to n do
if type(L[i], listlist(algebraic)) then
R:=Vector~(L[i])[];
P[i]:=Flux(V,LineSegments(R));
else
P[i]:=Flux(V,Path(Vector(L[i,1]),L[i,2]));fi;
od;
add(P[i], i = 1 .. n);
end use:
end proc:
 

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