ABSTRACT

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 me

part 1|2 pages

Averaging of Linear Differential Equations

chapter 2|10 pages

Bounded Solutions

chapter 3|14 pages

Lemmas on Regularity and Stability

chapter 4|10 pages

Parametric Resonance in Linear Systems

chapter 5|18 pages

Higher Approximations. The Shtokalo Method

chapter 7|12 pages

Asymptotic Integration

chapter 8|6 pages

Singularly Perturbed Equations

part 2|2 pages

Part II: Averaging of Nonlinear Systems

chapter 10|44 pages

Systems in the Standard Form. First Examples

chapter 11|26 pages

Pendulum Systems with an Oscillating Pivot

chapter 13|20 pages

Averaging and Stability

chapter 14|20 pages

Systems with a Rapidly Rotating Phase

chapter 16|16 pages

Systems with Slowly Varying Parameters

part 3|2 pages

Part III: Appendices