Differential Equations, Bifurcations and Chaos

Erscheinungsjahr 2025
ISBN: 978-3-031-99542-2
Verlag: Springer

Buch, Englisch, 235 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 382 g

Reihe: Springer Undergraduate Mathematics Series

This book introduces qualitative methods for understanding differential equations, especially when analytical solutions are not possible. Aimed at second-year undergraduate students in mathematics or science, it assumes prior knowledge of calculus, linear algebra, and curve sketching. The book focuses on phase plane methods for second-order differential equations, supported by earlier sections on analytical techniques and phase lines for first-order equations. The later chapters explore bifurcation theory and chaos. Emphasizing application over theory, the book includes diagrams, worked examples, and exercises, with minimal use of formal proofs.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Matthews, Paul C.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Angewandte Informatik Bioinformatik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Naturwissenschaften Biowissenschaften Angewandte Biologie Bioinformatik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

Chapter 1. Introduction.- Chapter 2. Analytical Methods for Differential Equations.- Chapter 3. Qualitative Methods for First-Order Differential Equations.- Chapter 4. Second-Order Linear Systems.- Chapter 5. Second-Order Nonlinear Systems.- Chapter 6. Bifurcations.- Chapter 7. Difference Equations.- Chapter 8. Chaos.- Chapter 9. Solutions to Odd-Numbered Exercises.

Über Autor(innen)

Paul C. Matthews was on the faculty of the University of Nottingham for more than two decades. A specialist of dynamical systems and their numerical analysis, he is the author of the bestselling textbook (Springer, 1998).