# Partial Taylor Series Expansion

"Partial" Taylor Series Expansion

It has been awhile since I have had to use a Taylor series expansion (from scratch). I looked it up on wiki and the rules are easy enough, I am just a little confused as to how I apply it to a multivariable function, but only expand it about one variable.

For example, if I want to expand the function f(x,y) about x = a only, for let's say the first two terms of the expansion, how would I do that?

Would it just be:

$$f(x,y) = f(a,y) + \frac{f_x(a,y)}{1!}(x - a)$$ ?

I have a feeling it is not this simple...
Thoughts?

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Hurkyl
Staff Emeritus
Gold Member

That looks right. The function gy defined by
gy(x) = f(x,y)​
is an ordinary single-variable function, and the ordinary Taylor series formula works.

That looks right. The function gy defined by
gy(x) = f(x,y)​
is an ordinary single-variable function, and the ordinary Taylor series formula works.
Sweet! Thanks Hurkyl. 