## not sure I get the Taylor Series....

Hello Everyone.

I understand that the taylor series approximate a function locally about a point, within the radius of convergence.
If we use the Taylor series it means that we do not know the function itself.

But to find the taylor series we need the derivatives of the function. and to have the derivatives we need the function itself......

where is the problem?

Also, we could represent a function is a certain interval of interest by using orthogonal functions (legendre, sines cosines, and any other orthogonal set). Why go with the Taylor series?
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 Quote by fisico30 If we use the Taylor series it means that we do not know the function itself.
Not true! The Taylor series is useful in simplifying a known, complex function in a local region.

 Quote by fisico30 Why go with the Taylor series?
An example: the Taylor series tells us that any function is approximately quadratic around a minimum or maximum. This has tremendous implications when analyzing energy landscapes. Since a spring's energy is also quadratic around its equilibrium point, we can apply a lot of existing mathematics (e.g., simple harmonic motion) to systems near equilibrium.

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