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Scot Gould

Scot Gould

747 Reputation

14 Badges

11 years, 171 days
Claremont McKenna, Pitzer, Scripps College
Professor of Physics
Upland, California, United States
Contact Scot Gould
Dr. Scot Gould is a professor of physics in the W.M. Keck Science Department of 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.

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These are answers submitted by Scot Gould

Another example of premature evaluation...

Scot Gould 747
March 20 2023
1 5

The magenta error of death tells us the equation in fsolve is being evaluated before it is ever used. Put a single quote around the equation in fsolve and it will work.

h := y -> fsolve( ' f(x__0) = y', x__0 = Range)

They will learn...

Scot Gould 747
March 08 2023
1 1

I can empathize. Students in my class last week struggled with the same issue.  

For them, it was applying the slope (Euler's) numerical method to solve an ordinary

differential equation. If the endpoints were exact, such as 0 and 2, the looping took

forever. However, if the endpoints were floating point approximations such as 0.0

and/or 2.0, the calculations were instantaneous.

Because of these struggles, it has become ingrained in their head they must enter

constants in numerical calculations as floating-point numbers. And maybe that is

the best one can hope for since I agree with others, there probably is no way to

force Maple to see all numbers as approximations.

Regarding integrals, there is no need to memorize evalf or the option numeric.

Simply set the endpoints to floating point numbers, and Maple will generate a

floating point outcome. For example:

 

Exact integral:

> 

int(exp(-x^2), x = 0 .. infinity)

(1/2)*Pi^(1/2)

 (1)

 

Using the floating-point approximation.

> 

int(exp(-x^2), x = 0. .. infinity)

.8862269255

 (2)

   ``

Download Forcing_floating_point_approximations.mw

Full precision...

Scot Gould 747
February 09 2023
1 0

It is my experience that full-precision equations usually lead to full-precision answers, if possible.  If you prefer a "floating point approximation", change one of the numbers from a whole number in your equation to a floating point value. For example, 4 to 4. or 4.0.  Maple will report a floating point result. 

If you don't obtain a floating point result after making the modification, as suggested, take the result and evaluate it to a floating point value using the evalf procedure. 

ODE or PDE....

Scot Gould 747
February 08 2023
1 1

It is late, so the experts probably are asleep. Here is a quick reply.

 

As I read what you uploaded, the PDE is not a PDE but a 2nd order ODE with a parameter k in the initial conditions.

 

> 

restart; interface(imaginaryunit = 'I')

Rewriting the PDE as an ODE for which the variable u is a function of time:

> 

ode := (10*I)*(diff(u(t), t))+diff(u(t), t, t)-16*u(t) = 0

And setting the initial conditions at t = 0

> 

ices := u(0) = sqrt((1/2)*Pi)*csch((1/2)*Pi*k), (D(u))(0) = -(1/4)*sqrt(2)*Pi^(3/2)*csch((1/2)*Pi*k)*coth((1/2)*Pi*k)

Solve numerically, but let k be a floating parameter one can adjust on the fly:

 

> 

sols := dsolve({ices, ode}, numeric, output = listprocedure, parameters = [k])

Extracting out the variables:

> 

u := eval(u(t), sols); u_dot := eval(diff(u(t), t), sols)

 

Since k can be anything but appears to be somewhere between 0 and 100, make a plotting procedure that plots the magnitude of u and the u-dot for "t = 0 to 1." (Both variables are complex, so adjust to suit your interest.)

 

> 

"PlotVariables := proc(k::float) global sols, u, u_dot; sols(parameters = [k]); plot([|u(t)|, |u_dot(t)|], t= 0..1, legend = ['u', '(u)']); end proc: "

Now explore:

> 

Explore(PlotVariables(k), parameters = [k = 0 .. 100.0], initialvalues = [k = 50.0])

Play with the slider and satisfy the other conditions.

 


 

Download ODE_or_PDE_solution.mw

initialization file...

Scot Gould 747
January 09 2023
1 0

Try this help page to load the suggested commands:

https://www.maplesoft.com/support/help/maple/view.aspx?path=worksheet%2Freference%2Finitialization

error...

Scot Gould 747
January 04 2023
1 2

See if the procedure error() works for you.

For fun...

Scot Gould 747
December 31 2022
0 0

@zenterix For fun, I was playing around with the plots package.  It almost mimics your first plot.  However, to see it properly, download it. 

> 

restart; with(plots); symbolsize := 12
> 

display(pointplot([seq(`<,>`(x, x-1), x = -1 .. 5)], 'symbolsize' = symbolsize, symbol = circle, color = blue), plot(floor(x), x = -2 .. 5, color = blue, thickness = 4), pointplot([seq(`<,>`(x, x), x = -2 .. 4)], 'symbolsize' = symbolsize, symbol = solidcircle, color = blue), scaling = constrained, tickmarks = [8, 0], view = [-3 .. 6.5, -3 .. 5], arrow(`<,>`(-3, 0), `<,>`(9.5, 0), color = green, width = 1/100, head_width = 1/8, head_length = 1/7), arrow(`<,>`(0, -3), `<,>`(0, 8), color = green, width = 1/100, head_width = 1/8, head_length = 1/7), labels = [" ", " "], textplot([5.4, 4, "g", font = ["times", 20]], color = blue), size = [600, 600])

 
> 

``
> 

NULL

Download Plot_Floor.mw

Multiple options for Restore Backup...

Scot Gould 747
December 07 2022
1 0

Under Tools->Options (or Preferences on the Mac), at the bottom of the first page of the popup box is where you can control how often Maple saves a backup copy and if it keeps every copy of a backup file. I believe it the default is 3 minutes, but you can set it to any value. In addition, Maple  keeps every copy of the backup file. Personally, I turn off the "Keep files" so that the folder isn't filled with backup copies I don't need to use. If you safely close the file, it deletes the backup copy. But if you don't, the backup copy is still there. That makes it much easier to find the backup file of needed. 

However, when one uses File -> Restore Backup, one can ask to display the details of the files which allows you to sort by when the file was created. 

IMO, the system is much improved over the previous backup system. 

Readability with palettes...

Scot Gould 747
May 04 2022
3 0

Or, you can have fun with palettes and write out something that  non-Maple-coders can read:

NULL

"f(x,y) := {[[1,x = 0 and y=0],[(x^(2)+y^(2))^(x),otherwise]]: "

NULL

NULL

eval(`<,>`(diff(f(x, y), x), diff(f(x, y), y)), {x = 1, y = 1})

Vector[column](%id = 36893489998615880996)

 (1)

NULL

Download Partial_Diff_with_Palettes.mw

Not a shortcut, but looks like a matrix...

Scot Gould 747
April 21 2022
1 0

A search of shortcut keys shows no way to create a matrix. This is probably  understandable given the complexity of a matrix.  Also, I suspect there really isn't to much interest in one.  For me, when I want to explain how to create a Matrix without using the palette to new users, I mimic the matrix in the call of the Matrix function:

 

> 

M := Matrix([[1, 2, 3], [0, a, b], [3, 2, 1]])

Matrix(%id = 36893490805376578132)

 (1)

 

But later I offer the vectors in columns approach:

 

> 

M := `<|>`(`<,>`(1, 0, 3), `<,>`(2, a, 2), `<,>`(3, b, 1))

Matrix(%id = 36893490805376567764)

 (2)

 

At this point, it is a matter of personal preference.

Download Matrix_entry.mw

Keyboard shortcut : ++< " >...

Scot Gould 747
April 14 2022
3 0

IMO, using a keyboard shortcut is easy and quick for creating a vector sign above a variable name.
See help on "keyboard shortcuts".

 

Overscript:

Window: <ctrl>  + <shift> + < " >  

Mac:       <command> + <shift>+ <">

 

type varaible, then the keyboard shortcut combination, then add "-" ">" to create a vector:

 

   `#mover(mi("v"),mo("&rarr;"))`

 

It is very handy for writing non-executable mathematical statements in documents. For example:

 

    "&conint; B * d`&ell;` = &int;((&nabla;) * B ) * dA = `mu__0` `I__enclosed` = `mu__0` &int;J * dA "

 

And note, the vector `#mover(mi("v"),mo("&rarr;"))` does not equal the non-vector v.

 

> 

is(`#mover(mi("v"),mo("&rarr;"))` = v)

false

 (1)

which means you can define a vector with the same name variable:

> 

`#mover(mi("v"),mo("&rarr;"))` := `<,>`(v, 0, 0); `<,>`(1, 0, 0).`#mover(mi("v"),mo("&rarr;"))`

v

 (2)

 

From a readability standpoint, I find the vector sign more informative than making the variable bold because
I cannot always tell if a variable is bolded or not.

 

Download Creating_variables_with_vector_signs.mw

what worked for Maple...

Scot Gould 747
February 01 2022
0 0

Uninstall and reinstall to version 2021.1  Just a suggestion if possible.

Looking at Section 3.5 and 3.10 of Help...

Scot Gould 747
January 26 2022
1 8

One can control the number format given that the default is 3 values after the decimal, but it appears that changing the Digits does nothing. I have attempted to reproduce Figure 3.7 at the bottom of page 11. 

Regardless, I would hope the next version allows for one to change the interface

Alternative......

Scot Gould 747
January 13 2022
1 1

If you have several lines of code, you can insert a code-edit-region into your worksheet with the icon to the left of the "T" icon in the icon toolbar. Then, copy and paste the 2d-Math into the code-edit-region.  When you hit enter, it executes.

Error could not be reproduced, but resul...

Scot Gould 747
December 30 2021
0 3

I was not able to reproduce this error.

However, to work with complex numbers in MapleFlow, the expression is 1+2i, not 1+2*i. (Also, 1+2I is viewed as 1+2i). If one types 1+2*i, MapleFlow interprets the letter "i" as a variable. 

What I don't understand is given that the letter "I" is defined as sqrt(-1) in Maple, why the expression (1+2*I) in MapleFlow is not interpreted as a complex number. Instead, "I" is interpreted as a variable. 

(And I don't understand why my pasted response can't be unbolded.) 
 

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