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A The Pantheon of Derivatives

  1. Feb 25, 2017 #1
    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?
     
    Last edited: Feb 25, 2017
  2. jcsd
  3. Feb 25, 2017 #2

    fresh_42

    Staff: Mentor

    I'm inclined to make an Insight out of it. Looks like an invitation to a small essay.
     
  4. Feb 25, 2017 #3
    Please...
     
  5. Feb 25, 2017 #4

    fresh_42

    Staff: Mentor

    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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