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Scot Gould

Scot Gould

517 Reputation

14 Badges

10 years, 154 days
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, 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 making us of scanning probe microscopes, particularly those which involved natural fibers such as spider silk. More recently, he was involved in developing and sustaining AISS, a full-year multi-unit non-traditional interdisciplinary undergraduate science education course which 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 the computer algebraic and numerical system Maple to assist students in modeling and visualizing physical, and biological, systems. His Dirac-notation based quantum mechanics course is taught solely through Maple. An avid baseball fan, during his spare time, Dr. Gould is traveling, particularly to locations where he can bicycle on smooth, traffic-free roads, visit beaches and/or mountains, and enjoy good food and drink.

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These are questions asked by Scot Gould

Vector vs. list. Evaluation issue....

Scot Gould 517 Maple 2019
vector evaluation list
September 25 2019
1 1

We often use the vector notation "< >" as in <x, y, z>.  However, when I use it with a function, it does not evaluate the same way as a simple list "[ , ]". 
 

> 

"restart; g(r):=k*r;"

proc (r) options operator, arrow, function_assign; k*r end proc

 (1)
> 

g1 := g([x, y]); g2 := g(`<,>`(x, y))

g1 := k*[x, y]

  

Vector[column](%id = 18446745825756564886)

 (2)
> 

k := 1; g1; g2

k := 1

  

[x, y]

  

Vector[column](%id = 18446745825756564886)

 (3)

 

The value of k is not applied in g2.  Can someone point me in the direction as to the difference between the two types of entities as interpreted by Maple?  

Plotting with mod...

Scot Gould 517 Maple
plot mod
September 03 2019
3 4

How do I write plot ceil(x) mod 2 properly?

If I write: 

plot(ceil(x) mod 2, x = 0 .. 4)

it produces a step pattern and not a square wave. (Only 0 and 1 should be plotted.) 

setoption3d size...

Scot Gould 517 Maple
setoptions
December 12 2018
1 2

Has there been a option included in the plots:-setoptions3d that is equivalent to the size option found in plots:-setoptions? I can't seem to find one.  I would really like to be able to set all my 3d plots to the same size. Or am I missing something?

Slick technique to select positive root ...

Scot Gould 517
polynomial assuming roots
January 18 2017
3 6

I want to solve for the roots of a polynomial, such as a x^2+b x + c = 0, for which the output is only the positive root. All coefficients/variables in the polynomial are positive. 

Recently, someone posted an answer to a question where at some point they performed this task and their solution was really slick. But I can't find it. The answer used either solve, or eval or something like that. (Yes, I did perform a search via the MaplePrimes search before asking this question.) 

 

Solve... well it depends...

Scot Gould 517 Maple 2016
solve fsolve cotangent
December 28 2016
0 1

Here is one that the students generated which caused confusion. 

a := 0.76;
eq1 := 2*cot(a*sqrt(2*E)) = (2*E-5.4)/(sqrt(E*(5.4-E));
solve(eq1, E)

And the results are: 0., 4.411954070, 2.423743792

The problem is with the second answer because it does not exist. If we plot the LHS and the RHS of eq1 vs E where E=0..5.4

plot([2*cot(0.76*sqrt(2*E)), (2*E-5.4)/sqrt(E*(5.4-E))], E=0..5.4, -3..3)

And it gets more interesting, if we calculate:

solve(evalf(eq1), E)

The answers are: 0., 2.423743793, 14.33807304+27.39159712*I

where the 3rd answer is again incorrect.

Finally, if a = 0.8 or larger, the incorrect answers disappear. 

Note - fsolve does handle this problem correctly. And despite my attempts to remind them to use fsolve, they see the solve command as the universal truth. Apparently this will be another teaching moment for next year.

So any thoughts about why this happens and why there is a difference in the outcomes between 0.76 and 0.8 for the value of a?

 

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