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PERTURBATION METHODS, INSTABILITY, CATASTROPHE AND CHAOS
by C F Chan Man Fong & D De Kee (Tulane University, USA)
This important book introduces perturbation and qualitative methods for differential equations in terms understandable to students with only a basic knowledge of calculus and ordinary linear differential equations. Theorems are stated clearly with their limitations and restrictions and are applied to solve examples from various disciplines. The writing style is informal and new ideas are introduced gradually via concepts already familiar to the reader.
Contents:
- Qualitative Theory: Two-Dimensional Linear
Systems
- Two-Dimensional Almost Linear Systems
- Existence and Non-Existence of Periodic Solutions
- Floquet's Theorem
- Perturbation Methods: Regular and Singular Perturbation
- Method of Multiple Scales
- Method of Averaging
- Matched Asymptotic Expansions
- Stability: Definitions
- Liapunov's Direct Method — Autonomous System
- Liapunov's Direct Method — Non-Autonomous System
- Hydrodynamic Stability
- Bifurcation and Catastrophe: Examples of Bifurcation in One Dimension
- Two-Dimensional Problems
- Discrete Systems
- Elementary Catastrophe
- Chaos: Criteria for Chaos
- Routes to Chaos
Readership: Undergraduates and graduates in applied mathematics,
biomedical engineering, chemical engineering, chaos and dynamical systems.
"... the accounts in the text and the illustrative examples are very clearly set out. The large format makes the book attractive to use."
| Mathematical Reviews, 2001 |
| 268pp |
Pub. date: Jun 1999 |
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