Differential Equations, Bifurcations and Chaos

Paul C. Matthews (Autor)

Buch | Softcover

XI, 235 Seiten

2025
Springer International Publishing (Verlag)
978-3-031-99542-2 (ISBN)

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This book introduces qualitative methods for understanding differential equations, especially when analytical solutions are not possible. 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.

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.

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 Vector Calculus (Springer, 1998).

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.

Erscheinungsdatum	24.07.2025
Reihe/Serie	Springer Undergraduate Mathematics Series
Zusatzinfo	XI, 235 p. 63 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Applications of differential equations to modeling • Bifurcations • Center Manifold • Chaos • Hopf Bifurcation • Lorenz Equations • Nodes • Non-autonomous equations • Nullclines • Ordinary differential equations • Phase line • phase plane • Pitchfork bifurcation • Saddle-node bifurcation • saddles • Spirals • Transcritical bifurcation • Undergraduate textbook on chaos • Unstable fixed point
ISBN-10	3-031-99542-2 / 3031995422
ISBN-13	978-3-031-99542-2 / 9783031995422
Zustand	Neuware