This notebook contains an excerpt from the Python Programming and Numerical Methods - A Guide for Engineers and Scientists, the content is also available at Berkeley Python Numerical Methods.

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# Chapter 18. Series¶

## Motivation¶

Many functions such as $$\sin(x)$$ and $$\cos(x)$$ are useful for engineers and scientists, but they are impossible to compute explicitly. In practice, these functions can be approximated by sums of functions that are easy to compute, such as polynomials. In fact, most functions common to engineers and scientists cannot be computed without approximations of this kind. Since these functions are used so often, it is important to know how these approximations work and their limitations.

In this chapter, you will learn about Taylor series, which is one method of approximating complicated functions. This chapter in no way takes the place of a full course on functional analysis, but it does provide exposure that will be useful for subsequent chapters.