TITLE: Why isn't Fourier Series taught in calculus 2?
QUESTION [10 upvotes]: I am self taught and have read the book "Essential Calculus ETF" by Larson and Hosteller from cover to cover and have since been evaluating the more difficult problems in calculus. During my venture in solving difficult integrals using series expansions via the monotone convergence theorem, I noticed that some integrals were tackled easily with the Fourier series.
Now, why isn't this topic included in the same sections where power, taylor and maclaurin series are being discussed? 
Not that I'm complaining (though I
favor maclaurin and this is my hobby, so I'm learning something new), but shouldn't this series also be included in Calculus 2?

REPLY [4 votes]: Not that this is entirely new, but I'd like to put my $2-$cents in.
Like most of mathematics, you can learn the basics of any rich theory at any time. However, to truly understand something, and to see it's utility and purpose, you may need to understand other areas of mathematics.
Fourier series aren't discussed in Calculus II, because they would be unmotivated. Why exactly should $f(x)$ be representable as an infinite series of integrals, using sine and cosine? The answer lies in the fact that the integral is a useful way of defining an inner-product on a vector space of continuous functions. This is useful in that it allows you to define the  angle between two functions, and it allows you to associate a length to a function. The integrals you compute are giving you vector building blocks which approximate your function, but the why is because these variants of sine and cosine produce what is called an orthonormal basis (whatever that means). 
Fourier series is a powerful tool, which would be difficult to convey without the language of linear algebra, which typically taught after Calculus II and before Differential Equations.
At my institution, we teach Fourier series right after vector calculus. When students have a sufficient understanding of linear algebra to understand why Fourier series should work.