Method of Averaging for Differential Equations on an Infinite Interval
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A01=Vladimir Burd
Action Angle Variables
almost
asymptotic analysis applications
Asymptotically Stable
asymptotics
Author_Vladimir Burd
Category=PBKJ
Cosnt
D? Dt
Db Dt
differential equations
differential equations theory
dY1 Dt
Dη Dt
Dθ Dt
Entire Real Axis
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Fourier Series
function
Fundamental Matrix
Green's Function
Green’s Function
infinite interval
infinite interval averaging for researchers
matrix
Matrix A0
negative
Negative Real Parts
Non-zero Real Parts
nonlinear dynamical systems
nonlinear systems
parameter
Parametric Resonance
parametric resonance study
Period 2?
Period 2π
periodic
Periodic Function
periodic functions
Periodic Solution
Periodic Vector Function
polynomial
Positive Real Parts
Quasi-periodic Function
Shtokalo averaging technique
Shtokalo's method
Sin ?t
Sin Νt
small
Small Parameter
solution
stability analysis methods
trigonometric
Trigonometric Polynomial
Trivial Solution
Vladimir Burd
Product details
- ISBN 9781584888741
- Weight: 498g
- Dimensions: 156 x 234mm
- Publication Date: 19 Mar 2007
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Paperback
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In recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications. Encompassing these novel aspects, Method of Averaging of the Infinite Interval: Theory and Applications rigorously explains the modern theory of the method of averaging and provides a solid understanding of the results obtained when applying this theory.
The book starts with the less complicated theory of averaging linear differential equations (LDEs), focusing on almost periodic functions. It describes stability theory and Shtokalo's method, and examines various applications, including parametric resonance and the construction of asymptotics. After establishing this foundation, the author goes on to explore nonlinear equations. He studies standard form systems in which the right-hand side of a system is proportional to a small parameter and proves theorems similar to Banfi's theorem. The final chapters are devoted to systems with a rapidly rotating phase.
Covering an important asymptotic method of differential equations, this book provides a thorough understanding of the method of averaging theory and its resulting applications.
Yaroslavl State University, Yaroslavl, Russia
