Partial Taylor Series Expansion

[Saladsamurai]

"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?

 

[Hurkyl]

That looks right. The function g_y defined by

g_y(x) = f(x,y)​

is an ordinary single-variable function, and the ordinary Taylor series formula works.

 

[Saladsamurai]

That looks right. The function g_y defined by

g_y(x) = f(x,y)​

is an ordinary single-variable function, and the ordinary Taylor series formula works.

Sweet! Thanks Hurkyl.