Nonlinear Ordinary Differential Equations

4. Auflage 2007
ISBN: 978-0-19-920825-8
Verlag: ACADEMIC

Buch, Englisch, 544 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 1199 g

This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents.

Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007).

Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.

Autoren/Hrsg.

Jordan, Smith

Jordan, Dominic

Smith, Peter

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Technik Allgemein Physik, Chemie für Ingenieure
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Populärwissenschaftliche Werke
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie

Inhaltsverzeichnis

- Preface

- 1: Second-order differential equations in the phase plane

- 2: Plane autonomous systems and linearization

- 3: Geometrical aspects of plane autonomous systems

- 4: Periodic solutions; averaging methods

- 5: Perturbation methods

- 6: Singular perturbation methods

- 7: Forced oscillations: harmonic and subharmonic response, stability, and entrainment

- 8: Stability

- 9: Stability by solution perturbation: Mathieu's equation

- 10: Liapurnov methods for determining stability of the zero solution

- 11: The existence of periodic solutions

- 12: Bifurcations and manifolds

- 13: Poincaré sequences, homoclinic bifurcation, and chaos

- Answers to the exercises

- Appendices

- A: Existence and uniqueness theorems

- B: Topographic systems

- C: Norms for vectors and matrices

- D: A contour integral

- E: Useful identities

- References and further reading

- Index

Über Autor(innen)

Prior to his retirement, Dominic Jordan was a professor in the Mathematics Department at Keele University. His research interests include applications of applied mathematics to elasticity, asymptotic theory, wave and diffusion problems, as well as research on the development of applied mathematics in its close association with late 19th century engineering technologies.

Peter Smith is a professor in the Mathematics Department of Keele University. He has taught courses in mathematical methods, applied analysis, dynamics, stochastic processes, and nonlinear differential equations, and his research interests include fluid dynamics and applied analysis.