This book studies the geometric theory of polynomials and rational functions in the plane. Any theory in the plane should make full use of the complex numbers and thus the early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology and analysis.
Inhaltsverzeichnis
Preface; List of notation; 1. The algebra of polynomials; 2. The degree principle and the fundamental theorem of algebra; 3. The Jacobian problem; 4. Analytic and harmonic functions in the unit disc; 5. Circular regions and Grace's theorem; 6. The Ilieff-Sendov conjecture; 7. Self-inversive polynomials; 8. Duality and an extension of Grace's theorem to rational functions; 9. Real polynomials; 10. Level curves; 11. Miscellaneous topics; References; Index.
Klappentext
This book studies the geometric theory of polynomials and rational functions in the plane.
