## 2640 Reputation

16 years, 46 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.

## Imaginary unit, assignment operator, and...

The assignment operator in Maple is :=, not just =.

The imaginary unit is upper-case i, so it looks like I in this font.

The construct i(... needs to be changed to I*(

Generally, you want to apply the evalc command to a complex espression to break it into its real and imaginary parts. When I tried that with h1*h2, the resulting expression got very large, and it was evident that the sizes of a and lambda determined the form of the result. You will have to make appropriate assumptions on these parameters to achieve any kind of useful outcome.

## try this...

add in the command "with(plots)" so you get access to implicitplot3d, then change Kitonum's Explore command to

Explore(implicitplot3d(A=c,x=0.01..5,y=0.01..5,z=.01..5,axes=frame,grid=[15,15,15]),c=-1.2..0.)

You will get an animation of some of the level surfaces. You will have to modify the bounds and ranges to fit your needs.

## Calculate the correct Wronskians...

The "sub-Wronskians" cannot be calculated as 3x3 matrices with one column zero. Check the definitions of W1, W2, and W3. They are the determinants of appropirate 2x2 matrices formed by deleting the i-th row and column from the Wronskian matrix W, thereby defining W_i.

## Output of shilled fraction...

Both work-arounds eliminate the long fraction bar, but neither actually produces the "textbook" version (a+b)/c. But I guess the second uses the least horizontal space.

## Typesetting Assistant is in the View men...

Although the tool in question is called an Assistant, it has always been housed in the View menu, never with the other tools that are also called "Assistants."

Back in Maple 2015, the Typesetting Assistant required the user to manually set typesetting to "extended." In Maple 2019, the default for typesetting is already "extended" so the Typesetting Assistant works directly.

## Provision for the kerf must be made...

This solution is easy for the woodworker because all pieces can be cut "straight through." And it is an amazing piece of mathematics.

Unfortunately, provision for the saw kerf, at least 1/8", has not been made. Perhaps one should add the dimension of the kerf to all measurements, but there are pieces that would then end up oversized. Some woodworkers discount the squareness of 4x8 sheet goods and waste the factory edges as a matter of course. The stock-cutting problem is not easy!

## Subscripts as partial derivative operato...

Perhaps this post from December of 2010 is relevant.

https://www.mapleprimes.com/maplesoftblog/100265-Subscripts-As-Partial-Differentiation-Operators

It summarizes a Reporter article from July of 2010.

## MathType...

Because you say the equation in Word has to be editable, you can't just copy/paste - that results in an uneditable graphic.

Look into the program MathType that sets equations in an editable form in Word. I think the connection is that MathType understands LaTeX, and Maple can export the LaTeX form of its equations.

It's been about 20 years since I operated in that world, so forgive me if I'm in error on any of these points.

## Maximize is in Optimization package...

Since the Maximize command is part of the Optimization package, the usage in your check.mw worksheet should be

Optimization:-Maximize(...

If you first load the package via the with(Optimization) command, then the Maximize command will work as it appears in the check.mw worksheet.

## Is it executable math?...

We're just guessing here. Perhaps the last expression (x+4-2) lost it's "executable" tag. So, right-click on the expression and inspect the pop-up that results. There's a line "Executable Math" in the pop-up. If there's no check at the left of this line, then what was clicked on is not executable math. Also, executable math will be in a blue-tinged box but non-executable math will be in a gray-tinged box.

Next time you have a difficulty, post the worksheet in which the difficulty occurred. We'd all have a better chance of diagnosing an error if we could test the worksheet, not just an image of it. Use the green upwards-pointing arrow in the toolbar to upload a worksheet.

## Apparently, it's Draghilev, not Dragilev...

When I authored the Maple application just referenced, I was not aware that the correct usage is "Draghilev" and not "Dragilev." Shortly after my article was published, I was admonished about the spelling. I have since made it a point to use the correct spelling, but the original post in the Maplesoft Application Center unfortunately still retains the incorrect spelling. To correct this, I would have to revise the article and then induce Maplesoft to replace the original with an update. Not impossible, but tedious. I will put this on my to-do stack, which, in retirement, seems to grow faster than it can be diminished.

## pdsolve does return weak solutions...

If q is Laplace's equation, then the following pdsolve command returns a weak solution to a BVP that has discontinuous boundary data.

pdsolve([q,u(0,y)=0,u(x,0)=0,u(x,Pi)=0,u(Pi,y)=1]);

Whether this is by design or by accident, I don't know.

If the design is to catch all BVPs with discontinuous BCs, then this example points to a bug that I would hate to see fixed. I would not want Maple to stop returning a weak solution to such a problem. This issue of pdsolve and weak solutions really needs clarification. It appears that pdsolve presently solves some BVPs with discontinuous BCs, but not all. I would rather see it solve more such problems rather than fewer.

## Draghilev's method or DirectSearch packa...

Similar problems have been solved in this forum with Draghilev's method and with the DirectSearch package. This package is not built into Maple. It can be downloaded from the cloud.

Do a search on "Draghilev" in this forum and find examples that have been solved by both methods. Be advised that some posts in this forum have been saved with the tag "Dragilev".

If there is sufficient smoothness, etc., your particular example defines a curve parametrically. In principle, three equations in four unknowns can be solved for three of the unknowns in terms of the fourth. Hence, x=x(a), y=y(a), z=z(a). The nonlinearity in your equations might make the algebra of solving intractable, but a numeric solution should be possible. Note that for a given value of "a", there may be multiple points (x,y,z) that satisfy the equations. That would mean the curve so defined loops back over itself or has branches. The devil is always in the details.

## Graph might be right...

The evolute of the ellipse x^2+4*y^2=4 is given parametrically by x=3/2*cos(t)^3,y=-3*sin(t)^3. Call this evolute E. An involute of this evolute is given vectorially by E-s*T, where T is a unit tangent vector and s is arc length. In an upcoming webinar (A Tale of Two Involutes, prepared but not yet scheduled), I will show that the arc-length function must look essentiallylike the graph drawn by the OP. A strictly increasing s(t) will not yield any correct involute. I found that the indefinite integral rather than the definite integral worked. The evolute E does not have a continuous tangent vector, and the points of discontinuity are the cause of the anomalous behavior.

## fsolve or explicit Newton iteration?...

The Maple command for obtaining a numeric solution of an equation is fsolve. While there is an implementation of Newton's method in the Student Calculus1 package, it is there as a pedagogic tool. The command is NewtonsMethod, and there is a Tutor that implements it. But I imagine that you need the fsolve command for what you have seemed to describe.

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