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