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dexza666

Member

Registered: 2008-04-21

Posts: 5

local linearization

An unevenly heated plate has temperature T(x,y) in degrees celcius at the point (x,y). If T(2,1)=135, and Tx(2,1)=16 and Ty(2,1)= -15, estimate the temperature at the point (2.04, 0.97).

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: local linearization

I havn't covered this before, or heard of it, i can only assume that Tx and Ty are the partial derivitves of T with respect to x and y respectively.

in which case, im guessing you are meant to assume that it is linear, and calculate

T(2.04,0.97) ≈ 135 + (2.04-2)*16 + (0.97-1)*-15 = 136.09

or in general

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: local linearization

Essentially, am I right in saying that this is an extension of a first degree Taylor series expansion to muiltivariable functions?

since with 1 variable you would have

so you could make a local 'quadratic'isation of a function with

and in 2 variables

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The Beginning Of All Things To End.
The End Of All Things To Come.

dexza666

Member

Registered: 2008-04-21

Posts: 5

Re: local linearization

The first answer was the right way of doing it. im not sure about thia local quadraticisation