Talk:Linear approximation

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[edit] Clarification needed

  • The crucial point of this approximation is that it is local around some chosen point. This does not become clear sufficienty.
  • More or less, linear approximation make sense only for functions that are differentiable at the point of consideration. This should be made clear explicitly.
  • The function f(x) = ax + b isn't linear in the sense of the reference "linear transformation".

Hottiger 16:29, 15 April 2006 (UTC)

I did some changes. Feel free to clarify more where you think is not clear. Oleg Alexandrov (talk) 20:35, 15 April 2006 (UTC)

[edit] Merging with linearization

I disagree with a merger. Linearization is about much more than a linear approximation, it is the study of the differential equation obtained after linearization, and how it relates to the original equation. As such, linear approximation is an elementary calculus property, while linearization ends up a rather involved topic in theory of PDEs, and while the subjects of the articles are definitely related, I think they better be kept separate. Comments? Oleg Alexandrov (talk) 02:21, 17 September 2006 (UTC)

I don't see the difference. Can you give an example where replacing one term with the other would lead to an error? —Keenan Pepper 02:42, 17 September 2006 (UTC)
You linearize a differential equation, while you do a linear approximation to a function, as far as I am aware.
Ideally, linearization (of a differential equation) should be much expanded with results from stability theory, and that would be overkill for the linear approximation article I think.
I must confess I don't know the topic of linearization in good detail however. If you are willing (and able) to do the merger, then I would be for it. Oleg Alexandrov (talk) 03:48, 17 September 2006 (UTC)
Note also the linerization article on PlanetMath. Oleg Alexandrov (talk) 03:48, 17 September 2006 (UTC)

[edit] functions of 2 variables????

someone needs to add local linear approximation for functions of multivariables (2 vars and up)

[edit] Another form of the equation

I was taught a different equation of linear approximation: f(x+h)≈f(x)+hf'(x). Is it worth adding this to the article as well?Baggers89 (talk) 08:48, 16 May 2008 (UTC)