# Does Calculus 2, Series Stuff Help w/ CS?

1. Nov 14, 2015

### Fancypen

I am in calc2 now and I just can't get excited about this series stuff. We went over many methods of testing for convergence/divergence and finally moved on to polar coordinates. Is series important in any type of CS field besides, I would imagine, creating software to solve series problems?

2. Nov 14, 2015

### Krylov

If, for example, you like to understand what binary (or decimal, or octal, or hexadecimal, or...) notation really means, in particular in relation to floating point arithmetic, then the answer is: yes, it is useful, see here for some amusing considerations: https://www.physicsforums.com/insights/is-there-a-rigorous-proof-of-1-0-999/

EDIT: Also, infinite series in one way or the other are central to numerical analysis, although this field seems to be (unfortunately, in my opinion) no longer considered part of the core of CS nowadays.

3. Nov 14, 2015

### micromass

Staff Emeritus
Solving equations happens by employing the power of series a lot of times. So if you're required to make a program where you're required to approximate certain functions, or solve certain (differential) equations, you might want to need series.
For example, the sine function can be approximated by
$$\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + ...$$
So this is one cool application of series. (It is not however the way the sine function is approximated nowadays, they use CORDIC for that).
As another application, let's say you want to find a lot of digits of the number $\pi$. Finding digits of $\pi$ is often a good test for new computers. Series help you there.

Finally, there's the entire theory of Fourier series and Fourier transforms. This Fourier theory is useful in a lot of ways, from signal processing to giving the most efficient way known for multiplying large numbers.