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Introduction to Asymptotic Methods

Jan Awrejcewicz and Vadim A. Krysko
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2006
Number of Pages: 
251
Format: 
Hardcover
Series: 
Modern Mechanics and Mathematics 5
Price: 
89.95
ISBN: 
1584886773
Category: 
Textbook
We do not plan to review this book.

 Introduction

ELEMENTS OF MATHEMATICAL MODELING
Structure of a Mathematical Model
Examples of Reducing Problems to a Dimensionless Form
Mathematical Model Adequacy and Properties. Regular and Singular Perturbations

EXPANSION OF FUNCTIONS AND MATHEMATICAL METHODS
Expansions of Elementary Functions into Power Series
Mathematical Methods of Perturbations
Exercises

REGULAR AND SINGULAR PERTURBATIONS
Introduction. Asymptotic Approximations with Respect to Parameter
Non-Uniformities of a Classical Perturbation Approach
Method of "Elongated" Parameters
Method of Deformed Variables
Method of Scaling and Full Approximation
Multiple Scale Methods
Variations of Arbitrary Constants
Averaging Methods
Matching Asymptotic Decompositions
On the Sources of Non-Uniformities
On the Influence of Initial Conditions
Analysis of Strongly Nonlinear Dynamical Problems
A Few Perturbation Parameters
Exercises

WAVE-IMPACT PROCESSES
Definition of a Cylinder-Piston Wave
One-Dimensional Non-Stationary Non-Linear Waves

PADÉ APPROXIMATIONS
Determination and Characteristics of Padé Approximations
Application of Padé Approximations
Exercises

AVERAGING OF RIBBED PLATES
Averaging in the Theory of Ribbed Plates
Kantorovich-Vlasov -Type Methods
Transverse Vibrations of Rectangular Plates
Deflections of Rectangular Plates

CHAOS FORESIGHT
The Analysed System
Melnikov-Gruendler's Approach
Melnikov-Gruendler Function
Numerical Results

CONTINUOUS APPROXIMATION OF DISCONTINUOUS SYSTEMS
An Illustrative Example
Higher Dimensional Systems

NONLINEAR DYNAMICS OF A SWINGING OSCILLATOR
Parametrical Form of Canonical Transformations
Function Derivative
Invariant Normalization of Hamiltonians
Algorithm of Invariant Normalization for Asymptotical Determination of the Poincaré Series
Examples of Asymptotical Solutions
Swinging Oscillator
Normal Form
Normal Form Integral

References
Bibliography

Dummy View - NOT TO BE DELETED