On how to best introduce the concept of differential in Physics

[mcastillo356]

Hi, PF

Here is the text I've taken a look at

file:///C:/Users/usuario/Desktop/2001_JMT_Girep.pdf

And the article I'm looking for:

Artigue M. and Viennot L.
Some aspects of students' conceptions and difficulties about differentials,
Misconceptions and Edu. Strategies in Sci&Math. Cornell, Ithaca, USA (1987)

To further understand the text. Don't know where to start from.

Love.

 

[berkeman]

Hi, PF

Here is the text I've taken a look at

file:///C:/Users/usuario/Desktop/2001_JMT_Girep.pdf

And the article I'm looking for:

Artigue M. and Viennot L.
Some aspects of students' conceptions and difficulties about differentials,
Misconceptions and Edu. Strategies in Sci&Math. Cornell, Ithaca, USA (1987)

To further understand the text. Don't know where to start from.

Love.

The first link is to your computer's hard drive.

I'm able to find links to the PDF for the article you are asking about with a Google search. Are you not getting the same search links?

 

[mcastillo356]

Hi, @berkeman, how are you?
This page:
https://iopscience.iop.org/article/10.1088/0143-0807/11/5/002/pdf
Three options: access through my institution (I am not enroled now), purchase or rent.
I will purchase.
Best wishes!
PD I would like to write you on April. Would you allow me? Things on track, thanks God, but still have an important meeting with a specialized doctor.

 

[Vanadium 50]

Here is the text I've taken a look at

Which is on your computer. We can't see it.

 

[mcastillo356]

Which is on your computer. We can't see it.

Sorry, http://rua.ua.es/dspace/handle/10045/23593

 

[berkeman]

PD I would like to write you on April. Would you allow me? Things on track, thanks God, but still have an important meeting with a specialized doctor.

Of course, feel free to contact me anytime.

 

[vanhees71]

Sorry, http://rua.ua.es/dspace/handle/10045/23593

Are these people really serious that one should explain differentiation and differentials in this way? I'm sure that I'd have been utmost confused, if somebody had tried to explain it to me like this.

Often didacts make things much more difficult for the student in their confused attempts to "simplify" or "elementarize" a subject.

I think as a physicist you need both an intuitive understanding of expressions like $\mathrm{d} x$ as a difference in the limit of zero distance and in a rigorous sense of taking the appropriate well-defined limit (using the "$\epsilon$-$\delta$ description".

Another more modern approach is also that of differential forms (Cartan), but that's for sure too advanced at the high-school level.

 

[George Jones]

Are these people really serious that one should explain differentiation and differentials in this way?

The goal should be to have a non-infinitesimal transfer of knowledge about infinitesimals.

 

[robphy]

Possibly enlightening:
(Dray and Manogue) Using differentials to bridge the vector calculus gap
https://bridge.math.oregonstate.edu/papers/use.pdf
(Dray and Manogue) Using differentials to differentiate trigonometric and exponential functions
https://bridge.math.oregonstate.edu/papers/trig.pdf
from Tevian's site:
https://sites.science.oregonstate.edu/~tevian/onid/cv/pubs.html#vector
and https://bridge.math.oregonstate.edu/

UPDATE:
https://blogs.ams.org/matheducation/2016/05/31/thick-derivatives/

 

[DaveE]

https://sci-hub.hkvisa.net/10.1088/0143-0807/11/5/002

 

[Frabjous]

This might not be helpful, but there is the nonstandard analysis approach to calculus
https://www.amazon.com/gp/product/0486428869/?tag=pfamazon01-20
https://www.amazon.com/dp/0486484521/?tag=pfamazon01-20

 

[mcastillo356]

Hi, PF
@robphy, @DaveE, @caz , that's hard work! I've decided to turn back to the textbook Calculus. The links are very interesting, but too difficult for me at this moment. Anyhow, I will keep them on mind.
Greetings!