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Realms question

  1. Oct 31, 2016 #1
    1. The problem statement, all variables and given/known data
    (See attachment: if it doesn't work, see below for poorer formatting)

    Theorem 6.1 (Centered Formula of Order O(h2)). Assume that f ∈ C^3[a, b] and that x − h, x, x + h ∈ [a, b]. Then (3) f (x) ≈ f (x + h) − f (x − h) 2h . Furthermore, there exists a number c = c(x) ∈ [a, b] such that (4) f (x) = f (x + h) − f (x − h) 2h + Etrunc( f, h), where Etrunc( f, h) = −h2 f (3) (c) 6 = O(h2).

    2. Relevant equations
    While reading Theroem 6.1, I have difficulty understanding (realms? "∈") in general, so I was wondering what is meant by C^3

    3. The attempt at a solution
     

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  2. jcsd
  3. Nov 1, 2016 #2

    haruspex

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  4. Nov 1, 2016 #3

    Mark44

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    This symbol, ∈, means "is an element of"
     
  5. Nov 1, 2016 #4

    Ray Vickson

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    What you wrote makes no sense, and is almost always wrong. You wrote f (x) ≈ f (x + h) − f (x − h) 2h, which is generally false. What IS true is that f'(x) ≈ [f(x+h) - f(x-h)]/(2h) for small |h|. Parentheses are important!
     
  6. Nov 1, 2016 #5
    Thank you for pointing me to relevant pages and explaining symbols.
     
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