When new ideas like chaos first move into the mathematical limelight, the early textbooks tend to be very difficult. The concepts are new and it takes time to find ways to present them in a form digestible to the average student. This process may take a generation, but eventually, what originally seemed far too advanced for all but the most mathematically sophisticated becomes accessible to a much wider readership. This book takes some major steps along that path of generational change. It presents ideas about chaos in discrete time dynamics in a form where they should be accessible to anyone who has taken a first course in undergraduate calculus. More remarkably, it manages to do so without discarding a commitment to mathematical substance and rigour. The book evolved from a very popular one-semester middle level undergraduate course over a period of several years and has therefore been well class-tested.
Rezensionen / Stimmen
'The tone, pace and level of the book are nicely judged for middle level undergraduates studying mathematics. The authors' friendly style, and the fact that the material has been developed from taught courses make the book ideal for self-study, and as a prelude to reading extensive treatments of chaos theory.' The Mathematical Gazette '... presented in such a form that it is accessible to anyone who has taken an undergraduate calculus course ... This textbook is highly recommended for a one semester undergraduate introduction to chaos theory.' Acta Sci. Math.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Produkt-Hinweis
Illustrationen
Worked examples or Exercises; 154 Line drawings, unspecified
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 18 mm
Gewicht
ISBN-13
978-0-521-53104-7 (9780521531047)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
La Trobe University, Victoria
La Trobe University, Victoria
La Trobe University, Victoria
Preface; 1. Making predictions; 2. Mappings and orbits; 3. Periodic orbits; 4. Asymptotic orbits I: linear and affine mappings; 5. Asymptotic orbits II: differentiable mappings; 6. Families of mappings and bifurcations; 7. Graphical composition, wiggly iterates and zeros; 8. Sensitive dependence; 9. Ingredients of chaos; 10. Schwarzian derivatives and 'woggles'; 11. Changing coordinates; 12. Conjugacy; 13. Wiggly iterates, Cantor sets and chaos; Index.
