What are the practical applications of the Taylor Series? I started learning about the Taylor Series in my calculus class, and although I understand the material well enough, I'm not really sure what actual applications there are for the series.

Question: What are the practical applications of the Taylor Series? Whether it's in a mathematical context, or in real world examples.


The applications of Taylor series is mainly to approximate ugly functions into nice ones(polynomials)!
Example: Take  $f(x) = \sin(x^2) + e^{x^4}$. This is not a nice function, but it can be approximated to a polynomial using Taylor series.
