The Sturmian Sequence for Isolating Zeros of Polynomials (UMAP)

This module analyzes Sturm's theorem about zeros of polynomials and describes a finite procedure for finding the numbers and approximate locations of the real zeros of polynomials that are used in mathematical physics and in the computer integration of functions.

Table of Contents:

1. INTRODUCTION

2. THE SETTING OF THE PROBLEM

3. THE STANDARD SEQUENCE

4. THE NUMBER OF ZEROS IN AN INTERVAL

5. SIMPLIFICATION

6. PROOF OF STURM'S THEOREM

7. APPLICATION TO THE STANDARD SEQUENCE

8. MODEL EXAM

9. DETAILED SOLUTIONS TO THE EXERCISES

10. ANSWERS TO THE MODEL EXAM