Differential Equations, Bifurcations and Chaos
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Beschreibung
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.
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.
Suitable for undergraduate courses Deliberately concise and to the point Based on years of teaching experience
Autor*in
Paul C. Matthews
Themen in »Differential Equations, Bifurcations and Chaos«
Ordinary differential equations Undergraduate textbook on chaos Phase line Phase plane Non-autonomous equations Unstable fixed point Nullclines Nodes Saddles Spirals Applications of differential equations to modeling Bifurcations Hopf bifurcation Pitchfork bifurcation Saddle-node bifurcation
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“The book is mainly intended to undergraduate students in mathematics and sciences. The initial chapters give necessary facts about the differential equations: elementary integrable ODE’s, stable and unstable fixed points, second order linear and nonlinear systems, periodic orbits, bifurcations and difference equations. Written in UK applied mathematical style, a few theorems (without proofs), many examples, exercises and figures are given.” (Angel Zhivkov, zbMATH 1582.34001, 2026)
“If the goal is to help students understand differential equations through qualitative behavior, modeling, and geometry, this book does that very well. For anyone wanting a first serious encounter with this kind of mathematics at the undergraduate level, this is a very good place to start.” (Hyeeun Jang, MAA Reviews, maa.org, July 3, 2026)
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