How is Taylor expansion used in physics?

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Discussion Overview

The discussion centers around the application of Taylor expansion in physics, particularly in the context of a specific problem involving small perturbations in a variable denoted as delta-r2. Participants seek clarification on the steps involved in the expansion and its implications.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the steps following a Taylor expansion mentioned in a photo, indicating a need for clarification.
  • Another participant suggests treating (r_2 - r_1) as a single quantity and introduces the approximation (1 + Δ)^p ≈ 1 + pΔ for small values of Δ, noting that multiple approximations are involved.
  • A further participant requests hints for understanding subsequent steps, indicating ongoing uncertainty.
  • One participant encourages the use of TeX for clearer communication of equations, suggesting that it would facilitate understanding for those providing help.
  • A later reply indicates that the participant has gained clarity on the topic, describing the concept as simple after further consideration.

Areas of Agreement / Disagreement

The discussion reflects a lack of consensus on the specific steps of the Taylor expansion, with participants expressing varying levels of understanding and confusion. Multiple viewpoints on the approach to the problem are present.

Contextual Notes

Some assumptions about the smallness of terms in the Taylor expansion are made, but these are not explicitly stated. The discussion also highlights the potential difficulty in communicating mathematical concepts without proper notation.

spaghetti3451
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I wasn't sure where to put this, so I put this here!

In the photo, you see there's written 'Taylor expanding for small delta-r2, we find' ...

I really don't get the two steps in the next line.

Any help would be greatly appreciated.
 

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he skips some steps. consider [itex](r_2-r_1)[/itex] as a single quantity and [itex]\Delta r[/itex] as another quantity. ignore the [itex](\Delta r)^2[/itex] term in the expansion as being super small. then use:[tex](1 + \Delta)^p \approx 1 + p \Delta[/tex]

for small [itex]|\Delta|[/itex].

so multiple approximations are going on here.
 
I see! But i still don't get the step after that. Any hints?
 
failexam said:
I see! But i still don't get the step after that. Any hints?

what? the [itex]\Delta d[/itex] thing?

i have a suggestion, do you know how to use TeX? try it out and spell out the equations right here. a jpg of a projected image is easy for you, but hard for me. since you're the person seeking help, it might behoove you to not make it unnecessarily difficult for whoever helps you.

but, after that approximation, it's all just algebra.
 
I see how it all works out, now! It's quite simple, really! But, anyway, thanks for trying to make a dumbass like me understand such a difficult concept.
 

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