Scot Gould

Scot Gould

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11 years, 266 days
Claremont McKenna, Pitzer, Scripps College
Professor of Physics
Upland, California, United States
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 answers submitted by Scot Gould

You might want to play with

interface(rtablesize = [n_rows, n_cols])

However, if you have a vector with 1 row, it appears that the number of entries shown is n_rows*n_cols. 

One can add a modification to the maple.ini file. 

While plotting an Array of plots works, I have never liked the fact that the plots are not centered in the region. For a quick solution, along with having the plots centered and the size controlled, consider DocumentTools:-Tabulate. 

display_vs_Tabulate_an_array_of_plots.mw

 

This is a completely different approach for a present - DocumentTools:-Tabulate.  It won't align the numbers with the precision of the print procedure. However, it is pretty. I wanted to look more at Tabulate, and you provided me with a good opportunity to play with it. (And this problem allows me to reinforce the simplicity and flexibility of using the option: output = listprocedure. 😁😉 )  

 

MaplePrimes_SIR_Model_with_Table.mw

@frankmath@Ronan

1) Create a worksheet with the styles that you want. The one I use is attached. 

2) Select Format -> Set Style Management to open a window.

3) In Style Set Operations, select "Export Style Set" and put it in a directory that you like. I have made a separate directory for the different styles that I use. I do not use the Maple default directory. 

4) In "Current Style Set," highlight "User-defined Style Set," and then browse to the appropriate directory and highlight this file. 

If you open another worksheet, the user-defined style set should be applied. 

Gould_Style_Template.mw

@paulmcquad This video shows an alternative way to put characters above other characters using the Maple interface. It is for making a vector sign over a variable, but a bar is just a vector sign without the > character. 

However, be careful.  Maple does not view a defined variable with a bar over it as the complex conjugate of the variable unless you tell it. 

You might also find this video on complex numbers useful. There is an associated document

I needed to test some other parts of Maple, and your problem came up as a good example. It doesn't go any further than what @rcorless wrote, but if you find the work useful, here it is. 

ODE_with_non-integer_component.mw

Your previous question was deleted even though I believe you responded to my suggestion. Posting again. MaplePrimes_question_visualization_of_animation.mw

I would try Explore the animation. 

Run the Explore and click on the animation to run.

 visualization.mw

I agree with Carl. Your pizza will be burned if you try to have it reach 300 F. Here are some common temperatures used. Turkey = 165, eye of round = 145 F.

Two basic recommendations:

1) Make a function with the parameters that could be modified. 

2) Make an Explore app to help aid in visualization. 

That is my experience. This is how I would cover Newton's model for cooling. 

MaplePrimes_Newton_Cooling.mw

See the video and example maple.ini file in the video description :

https://youtu.be/e4HR_Wmmr1E?si=NduEEQOGiz7e9IvT

I include a similar option in my maple.ini file. 

@lemelinm

Hmm, I appear to have missed your question. When a question is posted to one of my videos, I am (usually) notified immediately. Sorry to miss yours. 

Text version of the answer - there is no trick. Use the shortcut keys. Maple Help

See "Overscript" operation. 

Or watch this short video

Showing folks how to add the vector sign may be the most frequent request I receive.

Not that I know of, but you can always convert an expression to one with sines using:

   convert(expression, sin)

Since you did not mention which version of Maple you are using, it was noted by the Maplesoft folks that in version 2024, the procedure simplify would output tan and cot. 

Your problem, using an inert version of integral and sum so it does not try to execute either. (Note, this is not an equation because there is no equal sign in the expression.)

restart; yourInt := Int(-(Sum(B[i]*beta[i]*exp(-beta[i]*(t-tau)), i = 1 .. n)), tau = 0 .. t)

Int(-(Sum(B[i]*beta[i]*exp(-beta[i]*(t-tau)), i = 1 .. n)), tau = 0 .. t)

(1)

However, an integral of a summation can be converted to a sum of integrals. For example:

 

int(sum(a__i*x^i, i = 1 .. 3), x) = int(a__3*x^3+a__2*x^2+a__1*x, x) and int(a__3*x^3+a__2*x^2+a__1*x, x) = int(a__1*x, x)+int(a__2*x^2, x)+int(a__3*x^3, x) and int(a__1*x, x)+int(a__2*x^2, x)+int(a__3*x^3, x) = sum(int(a__i*x^i, x), i = 1 .. 3)

 

Does this make sense?

Consequently, we swap the summation sign with the integral sign (and pull out the negative sign for convenience.)

 

newInt := -(Sum(Int(B[i]*beta[i]*exp(-beta[i]*(t-tau)), tau = 0 .. t), i = 1 .. n))

-(Sum(Int(B[i]*beta[i]*exp(-beta[i]*(t-tau)), tau = 0 .. t), i = 1 .. n))

(2)


Now, we can evaluate what is possible. Maple will evaluate the integrals since those are doable.

newIntValue := value(newInt)

-(sum(-B[i]*exp(-beta[i]*t)+B[i], i = 1 .. n))

(3)

 

To match the result by dharr, let's simplify

newIntValue := simplify(newIntValue)

sum(B[i]*(-1+exp(-beta[i]*t)), i = 1 .. n)

(4)

 

To test this result let's look at one example with 3 terms. Let's evaluate both your expression and the generic solution assuming there are 4 terms, i.e., n = 4

yourInt4 := value(eval(yourInt, n = 4))

B[1]*exp(-beta[1]*t)+B[2]*exp(-beta[2]*t)+B[3]*exp(-beta[3]*t)+B[4]*exp(-beta[4]*t)-B[1]-B[2]-B[3]-B[4]

(5)

 

And the generic solution

newIntValue4 := simplify(eval(newIntValue, n = 4))

B[1]*exp(-beta[1]*t)+B[2]*exp(-beta[2]*t)+B[3]*exp(-beta[3]*t)+B[4]*exp(-beta[4]*t)-B[1]-B[2]-B[3]-B[4]

(6)

 

The results are the same. You can check this using the "is" procedure.

is(yourInt4 = newIntValue4)

true

(7)

Download MaplePrimes_Int_Sum_problem.mw

I agree with @Rouben Rostamian , I'm not exactly sure what you are trying to plot given that you appear to have 'a' on the horizontal axis. But here is another option - plot the function for a given value of 'a' that you can control with a slider. 

MaplePrimes_ODE_Explore.mw

If your intent is to have the x-axis to scale from 0 to 4*Pi rather than across the numerical numbers, the output=listprocedure provides the output necessary. 

restart; sols := dsolve({diff(y(t), t, t) = cos(t), y(0) = 1, (D(y))(0) = 0}, numeric, output = listprocedure)

y__sol := eval(y(t), sols); plot(y__sol(t), t = 0 .. 4*Pi, size = [400, 300])

 

Download MaplePrimes_x-axis_of_numeric_solution.mw

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