difference between local linearization/quadratic approx, Multivariable Taylor Approx?

Metronome

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Is there a difference between local linearization/quadratic approximations and multivariable taylor approximations? They appear to be identical (for first and second degree approximations, respectively), but go under different names, and in, i.e., the Khan Academy videos on local linearization and quadratic approximations, they seem to go almost out of their way to not call the subject multivariable taylor approximation.
 
Is there a difference between local linearization/quadratic approximations and multivariable taylor approximations?They appear to be identical (for first and second degree approximations, respectively), but go under different names, and in, i.e., the Khan Academy videos on local linearization and quadratic approximations, they seem to go almost out of their way to not call the subject multivariable taylor approximation.

Does it matter? Call it "Steve" if you like, so long as you can communicate it.

Are you saying quadratic is necessarily multivariable? That would not be the case.

In higher dimensions, one might "linearize" with a plane, or hyperplane. Still doesn't have to turn corners. That would be quadratic or higher order.
 
… [Khan Academy seems] to go almost out of their way to not call the subject multivariable taylor approximation.
If you'd like to discuss specific videos going forward, please also provide an example link.

My first thought was along the lines of tkhunny's comment. Perhaps, the reason Khan avoids using "multivariable taylor approximation" when discussing local linearization/quadratic approximation is because those methods are used with single-variable functions. :cool:
 
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Okay, will do.

As you extend the vector form of taylor approximation beyond second degree, does each new term involve a tensor of increasing order, or do you just keep using the Hessian in new configurations?

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