The Pantheon of Derivatives

  • #1
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  1. Derivatives in first year calculus
  2. Gateaux Derivatives
  3. Frechet Derivatives
  4. Covariant Derivatives
  5. Lie Derivatives
  6. Exterior Derivatives
  7. Material Derivatives

So, I learn about Gateaux and Frechet when studying calculus of variations
I learn about Covariant, Lie and Exterior when studying calculus on manifolds
I learn about Material derivatives when studying fluid mechanics

But I would have never thought there would be so many.

Is this about all there is?

May I ask if someone can categorize these?
When are they used? How are they used? Are there more?
Can you possibly create a table? Are there subsets of each other?
Are some a manifestation of only physics or engineering or math?

Can anyone bring order out of this chaos for me?
 
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Answers and Replies

  • #2
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I'm inclined to make an Insight out of it. Looks like an invitation to a small essay.
 
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  • #3
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I'm inclined to make an Insight out of it. Looks like an invitation to a small essay.
Please...
 
  • #4
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Please...
But this takes some time. Maybe someone is faster here. But I doubt there is a short answer, except perhaps: continuous generalizations.
 

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