Mathematical Analysis pp 145-186 | Cite as

# Polynomials, Rational Functions and Trigonometric Polynomials

## Abstract

In this chapter we want to illustrate the relevance of complex numbers in some elementary situations. After a brief discussion of the algebra of polynomials in Section 5.1, we prove the *fundamental theorem of algebra* and discuss solutions by radicals of algebraic equations in Section 5.2. In Section 5.3 we present *Hermite’s decomposition formulas* for rational functions, which are useful for the integration of rational functions, see Chapter 4 of [GM1]. Finally, in Section 5.4, we discuss some basic facts about *trigonometric polynomials* and, more generally, sums of sinusoidal signals. In particular we shall see that the *spectrum* of a signal completely identifies the signal itself, we shall prove the *energy identity* and present a *sampling formula*.

## Keywords

Rational Function Positive Root Fundamental Theorem Trigonometric Polynomial Sinusoidal Signal## Preview

Unable to display preview. Download preview PDF.