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Differential equations, bifurcations and chaos

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Differential equations, bifurcations and chaos / by Paul C. Matthews.
作者:	Matthews, P. C.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xi, 235 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Differential equations. -
電子資源:	https://doi.org/10.1007/978-3-031-99543-9
ISBN:	9783031995439

Differential equations, bifurcations and chaos
Matthews, P. C.

Differential equations, bifurcations and chaos [electronic resource] /by Paul C. Matthews. - Cham :Springer Nature Switzerland :2025. - xi, 235 p. :ill., digital ;24 cm. - Springer undergraduate mathematics series,2197-4144. - Springer undergraduate mathematics series..

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.

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.

ISBN: 9783031995439

Standard No.: 10.1007/978-3-031-99543-9doiSubjects--Topical Terms:

517952
Differential equations.

LC Class. No.: QA371 / .M38 2025

Dewey Class. No.: 515.35

Differential equations, bifurcations and chaos
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505 0 $a 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.
520 $a 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.
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650 0 $a Bifurcation theory. $3 544229
650 0 $a Chaotic behavior in systems. $3 524350
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650 2 4 $a Applied Dynamical Systems. $3 3538870
650 2 4 $a Mathematical Physics. $3 1542352
650 2 4 $a Mathematical and Computational Biology. $3 1566274
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