On how to best introduce the concept of differential in Physics

In summary, these people are trying to explain differentiation and differentials to someone who is not an expert in the field. Often didacts make things much more difficult for the student in their confused attempts to "simplify" or "elementarize" a subject. Another more modern approach is also that of differential forms (Cartan), but that's for sure too advanced at the high-school level.
  • #1
mcastillo356
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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.
 
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  • #2
mcastillo356 said:
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?
 
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  • #3
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.
 
  • #4
mcastillo356 said:
Here is the text I've taken a look at
Which is on your computer. We can't see it.
 
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  • #6
mcastillo356 said:
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. :smile:
 
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  • #7
mcastillo356 said:
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.
 
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  • #8
vanhees71 said:
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.
 
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  • #9
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/
 
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  • #12
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!
 

FAQ: On how to best introduce the concept of differential in Physics

What is differential in Physics?

Differential in Physics refers to the concept of infinitesimal changes in a physical quantity, such as position, velocity, or acceleration. It is a fundamental concept in calculus and is used to analyze and model the behavior of complex systems.

Why is differential important in Physics?

Differential is important in Physics because it allows us to understand and predict the behavior of physical systems. By analyzing infinitesimal changes, we can gain insight into how a system will respond to different conditions and make accurate predictions.

How is differential used in Physics?

Differential is used in Physics to describe the relationship between different variables and how they change over time. It is commonly used in equations and models to represent the rate of change of a physical quantity.

What are some real-world applications of differential in Physics?

Differential is used in various fields of Physics, including mechanics, electromagnetism, and thermodynamics. It is used to model the motion of objects, the behavior of electric and magnetic fields, and the flow of heat and energy in systems.

How can one best introduce the concept of differential in Physics?

The best way to introduce the concept of differential in Physics is to start with the basics of calculus, such as limits and derivatives. Then, show how these concepts can be applied to physical systems and how differential is used to analyze and predict their behavior. Hands-on demonstrations and real-world examples can also help students understand the importance and applications of differential in Physics.

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