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yash2651995

  • one year ago

i'm not able to understand this: (this is WRT ODE course.) Linear - When do we say that F(x; y; y1; : : : ; y(n)) = 0 linear? Write F(x; y; y1; : : : ; y(n)) = 0 as L(y)(x) = L(y; y1; : : : ; y(n)) = f(x); and now L is a linear transformation from Cn = the space of functions which are at least n-times dierentiable to F = the space of functions. If these functions are dened on an open set R, we say that the ODE is dened on . (Why do we take an open set?)

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  1. anonymous
    • one year ago
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    "dened" ?

  2. yash2651995
    • one year ago
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    defined* both places sorry about typo

  3. anonymous
    • one year ago
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    I believe the "open set" requirement is there for the same reason a function \(f:\mathbb{R}\to\mathbb{R}\) can only be differentiable over an open interval \((a,b)\subset\mathbb{R}\).

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