Higher Order Systems

This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization.

The book covers a large class of nonlinear systems with many practical engineering applications. The approach is based on the extension of linear systems theory using the Volterra series. In contrast to the few existing treatments, our approach highlights the algebraic structure underlying such systems and is based on Schwartz’s distributions (rather than functions). The use of distributions leads naturally to the convolution algebras of linear time-invariant systems and the ones suitable for weakly nonlinear systems emerge as simple extensions to higher order distributions, without having to resort to ad hoc operators.

This book serves as an easily accessible reference for wireless digital communication systems. Topics are presented with simple but non-trivial examples and then elaborated with their variations and sophistications. It includes numerous examples and exercises to illustrate key points. The book emphasizes both practical problem solving and a thorough understanding of fundamentals, aiming to realize the complementary relationship between practice and theory. Though the author emphasize wireless radio channels, the fundamentals that are covered are useful to different channels - digital subscriber line, coax, power lines, optical fibers, and even Gigabit serial interconnection.

This brief monograph is the first one to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit operator. Here we study with rates the approximation properties of the "right" sigmoidal and hyperbolic tangent artificial neural network positive linear operators. In particular we study the degree of approximation of these operators to the unit operator in the univariate and multivariate cases over bounded or unbounded domains. This is given via inequalities and with the use of modulus of continuity of the involved function or its higher order derivative. We examine the real and complex cases.

Pointwise announced the latest release of its Pointwise 2022.2 (hotfix 2) is one of Cadence Design Systems' premium software tools used for grid generation and preprocessing for computational fluid dynamics (CFD).