Kulish V.V. Hierarchical Methods. Volume 1: Hierarchy and Hierarchical Asymptotic Methods in Electrodynamics

Kluwer Academic Publishers, 2002. — 385 p. — ISBN: 0306480611.Everybody is current in a world surrounded by computer. Computers determine our professional activity and penetrate increasingly deeper into our everyday life. Therein we also need increasingly refined computer technology. Sometimes we think that the next generation of computer will satisfy all our dreams, giving us hope that most of our urgent problems will be solved very soon. However, the future comes and illusions dissipate. This phenomenon occurs and vanishes sporadically, and, possibly, is a fundamental law of our life. Experience shows that indeed ‘systematically remaining’ problems are mainly of a complex technological nature (the creation of new generation of especially perfect microschemes, elements of memory, etc.). But let us note that amongst these problems there are always ones solved by our purely intellectual efforts alone. Progress in this direction does not require the invention of any ‘superchip’ or other similar elements. It is important to note that the results obtained in this way very often turn out to be more significant than the ‘fruits’ of relevant technological progress.General Ideas, Concepts, Definitions, and Other Preliminary Information
Hierarchy and Hierarchical Systems
Hierarchical Asymptotic Methods. General Ideas
Hierarchical Systems with Fast Rotating Phases
Hierarchical Systems with Fast Rotating Phases. Examples of Practical Applications
Hierarchical Systems with Partial Derivatives. Method of Averaged Characteristics
Example: Application of The Method of Averaged Characteristics in Nonlinear Theory of The Two-Stream Instability
Hierarchical Systems with Partial Derivatives. Some Other Asymptotic Methods