Scot Gould

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Name: Scot Gould

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Member for: 12 years, 246 days

Company/Institution: Claremont McKenna, Pitzer, Scripps College

Title: Professor of Physics

Location: Upland, California, United States

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Dr. Scot Gould is a professor of physics at Claremont McKenna, Pitzer, and Scripps Colleges - members of The Claremont Colleges in California. He was involved in the early development of the atomic force microscope. His research has included numerous studies and experiments using scanning probe microscopes, particularly those involving natural fibers such as spider silk. More recently, he was involved in developing and sustaining AISS. This full-year multi-unit, non-traditional, interdisciplinary undergraduate science education course integrated topics from biology, chemistry, physics, mathematics, and computer science. His current interest is integrating computational topics into the physics curriculum. He teaches the use of Maple's computer algebraic and numerical systems to assist students in modeling and visualizing physical and biological systems. His Dirac-notation-based quantum mechanics course is taught solely through Maple.

MaplePrimes Activity

These are replies submitted by Scot Gould

Not in my opinion...

Answered: Scot Gould 1059

November 13 2024

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@Christopher2222 As someone who also uploads videos to YouTube, I appreciate you bringing up this question. I pay for my account through my Google YouTube Music subscription. Consequently, I am unaware of what is free and what is not.

My guess is that Maplesoft is also unaware that one can no longer download the videos for offline viewing. I bet, like my videos, theirs are stored on a computer within their system. An email to Maplesoft might be sufficient to get them to list the links to the videos on their website.

Physical filter...

Answered: Scot Gould 1059

November 13 2024

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Have you considered a physical solution instead of looking for a programable solution? There are blue-light-reducing filters for computer screens. There are also blue-light-reducing spectacles.

Ctrl delete...

Answered: Scot Gould 1059

November 11 2024

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@Alfred_

Windows and Unix; ctrl-delete

Mac; command-delete

The two keys are struck simultaneously.

Also. Look for "shortcut keys" in either Help or the Maple Portal under help for other keystrokes of interest.

for new users...

Answered: Scot Gould 1059

November 11 2024

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For the basics, I recommend the thin book "How to get started in Maple" by Doug Meade. I have my own video series based on the book, which is at YouTube/@MapleProf called Learning Maple. You might like Fundamentals 8.

Another maple.ini file?...

Answered: Scot Gould 1059

October 29 2024

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@acer Seriously, another maple.ini file? Couldn't they have named it something else?

That said, it doesn't look like one could simply add a call to the interface procedure in the Maple initialization file to change the interface. Or am I missing something?

If not, I might request one. I like the scrollable matrices. The only time I need it to not scroll is when I generate a PDF.

Thank you for your expertise....

Answered: Scot Gould 1059

October 23 2024

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@Rouben Rostamian, I have never needed to solve a PDE beyond the more common cases of boundary conditions, so I appreciate your confirmation that there is a mathematical solution but that Maple cannot obtain it. Both @nm and I had looked at other full Robin condition examples and also had come up with wrong answers.

As for solving the problem by hand, I leave it to the person who approached me about it. LOL!

Yep - the minus sign did the trick...

Answered: Scot Gould 1059

October 23 2024

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@dharr Thanks for your work. nm, whose posts have disappeared, gave me a recommendation from the Wikipedia page.

which allowed me to solve the problem and reproduce the initial state of the system, and the steady-state outcome.

However, I very much appreciate your solution because your use of the selectremove procedure is far more elegant than my kludgy use of the op procedure, multiple times. What I had hoped to do was to use either eval or sub to somehow not have to do what we both ended up doing - using a loop. (I used add, which worked, but was not as readable as a sum. ) I've tagged your work as a favorite since I rarely use selectremove.

That is weird...

Answered: Scot Gould 1059

October 21 2024

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@nm All your work is gone. I have seen it, fortunately. Working on the directions of the BCs.

Thanks, yet again, nm...

Answered: Scot Gould 1059

October 21 2024

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@nm I wondered about my formulation of the boundary conditions. Neither of my two sources on Robin BC made the point you found on the Wiki page.

I find the potential solution to my problem ironic. As a physics instructor, I often am telling a student that it is not Maple failing to solve their problem; it is their equations that are physically impossible. Clearly, more research is required on my part.

Hopefully, you receive this reply. I am no longer receiving notifications in the little flag in the upper lefthand corner. Is anyone else?

I like the last integral for multiple re...

Answered: Scot Gould 1059

October 19 2024

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Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/mapleprimes_integral.mw .

Download MaplePrimes_Integral.mw

☹️ Contents won't load.

Upvote...

Answered: Scot Gould 1059

October 19 2024

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@Rouben Rostamian Appreciated. A check of the integral of the terms inside the double summation appears to confirm your belief in the lack of assumption in deriving the anti-derivatives.

Heat Equation in 2D

restart; interface(imaginaryunit = I); heat_equation := diff(T(x, y, t), t) = k*(diff(T(x, y, t), x, x)+diff(T(x, y, t), y, y))

Solving without defining the state of the system at .

>	$sols := `assuming`([pdsolve({bces, ice, heat_equation}, T(x, y, t))], [k > 0, L > 0])$

T(x, y, t) = Sum(Sum(4*sin(n*Pi*x/L)*sin(n1*Pi*y/L)*exp(-Pi^2*k*t*(n^2+n1^2)/L^2)*(Int(sin(n1*Pi*y/L)*(Int(sin(n*Pi*x/L)*T__0(x, y), x = 0 .. L, AllSolutions)), y = 0 .. L, AllSolutions))/L^2, n = 1 .. infinity), n1 = 1 .. infinity)

(1)

Extracting out the term within the double summation

4*sin(n*Pi*x/L)*sin(n1*Pi*y/L)*exp(-Pi^2*k*t*(n^2+n1^2)/L^2)*(Int(sin(n1*Pi*y/L)*(Int(sin(n*Pi*x/L)*T__0(x, y), x = 0 .. L, AllSolutions)), y = 0 .. L, AllSolutions))/L^2

(2)

Calculate the value of the integrals

1) No assumption about the integrals

"`T__0`(x,y) :=1/(4)*sin((2 Pi*x)/(L) )^(2)*sin((3 Pi*y)/(L)): value(s)"

4*sin(n*Pi*x/L)*sin(n1*Pi*y/L)*exp(-Pi^2*k*t*(n^2+n1^2)/L^2)*(-1+cos(n*Pi))*piecewise(n1 = -3, -1, n1 = 3, 1, -6*sin(n1*Pi)/(Pi*(n1^2-9)))/(Pi*n*(n^2-16))

(3)

This term fails at .

2) With with the assumption about the values of .

4*sin(n*Pi*x/L)*sin(n1*Pi*y/L)*exp(-Pi^2*k*t*(n^2+n1^2)/L^2)*piecewise(n = 4, 0, piecewise(n1 = 3, L^2*(-1+(-1)^n)/(Pi*n*(n^2-16)), 0))/L^2

(4)

Here, all is good. And a solution can be rebuilt

"s := MakeFunction(s, (x, y, t, n, n1)): `T__sol`(x, y, t, N) := (∑)((∑)s(x, y, t, n, n1))"

proc (x, y, t, N) options operator, arrow, function_assign; sum(sum(s(x, y, t, n, n1), n1 = 1 .. N), n = 1 .. N) end proc

(5)

L := 1; k := 0.5e-1; plot3d(T__sol(x, y, 0, 20), x = 0 .. L, y = 0 .. L, scaling = constrained, size = [500, 500])

H := .25; plots:-animate(plot3d, [T__sol(x, y, t, 20), x = 0 .. L, y = 0 .. L], t = 0 .. .25, scaling = constrained, view = [0 .. L, 0 .. L, 0-H .. H], size = [600, 600], paraminfo = false, frames = 40)

Download Heat_Eq_2D.mw

In 1D input only...

Answered: Scot Gould 1059

October 12 2024

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In 2D input, it catches the error, reporting a missing operation. IMO, this is preferable to a FORTRAN-like outcome.

If you prefer 2d...

Answered: Scot Gould 1059

September 28 2024

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@smart2718 I was working on testing something else when I decided to use your problem with Acer's answer as a test case. If you can use it, it is yours. Sorry for not uploading it earlier. Click on the link to download the .mws file.

MaplePrimes_Reg_IV.mw