Singular Perturbations: Introduction to System Order Reduction Methods with Applications

✍ Scribed by Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell (auth.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 224
• Series: Lecture Notes in Mathematics 2114
• Edition: 1
• Category: Library

✦ Synopsis

These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level.

Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system.

Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate students for the later chapters.

✦ Table of Contents

Front Matter....Pages i-xiii
Introduction....Pages 1-23
Slow Integral Manifolds....Pages 25-42
The Book of Numbers....Pages 43-80
Representations of Slow Integral Manifolds....Pages 81-92
Singular Singularly Perturbed Systems....Pages 93-110
Reduction Methods for Chemical Systems....Pages 111-117
Specific Cases....Pages 119-139
Canards and Black Swans....Pages 141-182
Appendix: Proofs....Pages 183-198
Back Matter....Pages 199-214

✦ Subjects

Ordinary Differential Equations; Dynamical Systems and Ergodic Theory; Mathematical Applications in the Physical Sciences; Mathematical and Computational Biology; Appl.Mathematics/Computational Methods of Engineering; Engineering Thermod