Question on §3 of Einstein's 1905 paper

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SUMMARY

The discussion centers on §3 of Einstein's 1905 paper "On the Electrodynamics of Moving Bodies," specifically addressing the mathematical transition between two statements involving infinitesimal quantities. A participant, having recently completed high school and studied Special Relativity, initially sought clarification on the calculus concepts necessary for understanding the derivation. Ultimately, the participant successfully derived the solution independently and offered to share their findings for the benefit of others.

PREREQUISITES
  • Understanding of Special Relativity principles
  • Basic knowledge of calculus, particularly limits and infinitesimals
  • Familiarity with Einstein's 1905 paper and its context
  • Ability to interpret mathematical notation used in physics
NEXT STEPS
  • Study the concept of infinitesimals in calculus
  • Learn about the mathematical foundations of Special Relativity
  • Explore derivations of Lorentz transformations
  • Review advanced calculus topics, such as limits and continuity
USEFUL FOR

Students of physics, particularly those interested in Special Relativity, as well as educators and anyone looking to deepen their understanding of the mathematical underpinnings of Einstein's theories.

Brett Oertel
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Hi guys,

This is my first time posting on PF!

I have a question on §3 of Einstein's paper "On the electrodynamics of moving bodies."My problem is with the following mathematical statements:

img22.gif


Hence, if x' is chosen to be infinitesimally small,

img23.gif


or

img24.gif
I have just finished high school, and whilst I have finished two other books which concerned Special Relativity (and understood them well) I think I do not know enough maths to understand what i pasted above. Could someone explain how he gets from step 1 to step 2 please?
Or, perhaps could someone tell me what topics in calculus I must learn in order to understand it myself?

Thanks!

EDIT: I found many other threads asking the exact same thing as me... Oops! I managed to derive it on my own so no answer is necessary :).
 
Last edited:
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Brett Oertel said:
Oops! I managed to derive it on my own so no answer is necessary :).

Mind posting the derivation so others can see how it was done?
 

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