# Methods for finding Zeros in Polynomials

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122 pages
Jazyk:
en
In this book you find the basic mathematics that is needed by engineers and university students .
Poslední vydání
O autorovi

Leif Mejlbro was educated as a mathematician at the University of Copenhagen, where he wrote his thesis on Linear Partial Differential Operators and Distributions. Shortly after he obtained a position at the Technical University of Denmark, where he remained until h

In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.

Polynomials are the first class of functions that the student meets. Therefore, one may think that they are easy to handle. They are not in general! Topics as e.g. finding roots in a polynomial and the winding number are illustrated. Some of the topics only require an elementary knowledge of Calculus in one variable. Others rely heavily on Complex Functions Theory.

1. Introduction
2. Complex polynomials in general
1. Polynomials in one variable
2. Transformations of real polynomials
3. The fundamental theorem of algebra
4. Vieti’s formulæ
5. Rolle’s theorems
3. Some solution formulæ of roots of polynomials
1. The binomial equation
2. The equation of second degree
3. Rational roots
4. The Euclidean algorithm
5. Roots of multiplicity > 1
4. Position of roots of polynomials in the complex plane
1. Complex roots of a real polynomial
2. Descartes’s theorem
3. Fourier-Budan’s theorem
4. Sturm’s theorem
5. Rouch´e’s theorem
6. Hurwitz polynomials
5. Approximation methods
1. Newton’s approximation formula
2. Graeffe’s root-squaring process
6. Appendix
1. The binomial formula
2. The identity theorem for convergent power series
3. Taylor’s formula
4. Weierstraß’s approximation theorem
7. Index
Excellent , I really learned new methods for finding the roots of polynomials.