Bücher der Reihe Mathematical Engineering

The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems.

This textbook provides a mathematical introduction to linear systems, with a focus on the continuous-time models that arise in engineering applications such as electrical circuits and signal processing. The book introduces linear systems via block diagrams and the theory of the Laplace transform, using basic complex analysis. The book mainly covers linear systems with finite-dimensional state spaces. Graphical methods such as Nyquist plots and Bode plots are presented alongside computational tools such as MATLAB. Multiple-input multiple-output (MIMO) systems, which arise in modern telecommunication devices, are discussed in detail. The book also introduces orthogonal polynomials with important examples in signal processing and wireless communication, such as Telatar¿s model for multiple antenna transmission. One of the later chapters introduces infinite-dimensional Hilbert space as a state space, with the canonical model of a linear system. The final chapter covers modern applications to signal processing, Whittaker¿s sampling theorem for band-limited functions, and Shannon¿s wavelet. Based on courses given for many years to upper undergraduate mathematics students, the book provides a systematic, mathematical account of linear systems theory, and as such will also be useful for students and researchers in engineering. The prerequisites are basic linear algebra and complex analysis.

This monograph investigates violations of statistical stability of physical events, variables, and processes and develops a new physical-mathematical theory taking into consideration such violations - the theory of hyper-random phenomena.

This book provides analytical solutions to a number of classical problems in transport processes, i.e. Furthermore, analytical solutions for transport processes provide a much deeper understanding of the physical phenomena involved in a given process than do corresponding numerical solutions.

This edited book aims at presenting current research activities in the field of robust variable-structure systems. The scope equally comprises highlighting novel methodological aspects as well as presenting the use of variable-structure techniques in industrial applications including their efficient implementation on hardware for real-time control.

This monograph presents a systematic analysis of bubble system mathematics, using the mechanics of two-phase systems in non-equilibrium as the scope of analysis.

The first part is devoted to the study of channel flows, in particularthe lateral flow of a viscous and viscous-plastic liquid in a ring channelformed by coaxial cylinders.

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side.

This book describes useful analytical methods by applying them to real-world problems rather than solving the usual over-simplified classroom problems.

Ideal for engineering students with some knowledge of matrix algebra, this text bridges the gap between tensor algebra and the treatment of linear transformations in classical linear algebra. This revised second edition has additional examples and exercises.

Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics. Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework.

This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems.

For example, bounded uncertainties can be described by intervals, affine forms or general polynomial enclosures such as Taylor models, whereas stochastic uncertainties can be characterized in the form of a distribution described, for example, by the mean value, the standard deviation and higher-order moments.

This monograph presents results of the analytical and numerical modeling of convective heat and mass transfer in different rotating flows caused by (i) system rotation, (ii) swirl flows due to swirl generators, and (iii) surface curvature in turns and bends.

Describing principles from a variety of disciplines, this volume provides an overview of electrical machines and drives. Special attention is given to the necessary formulae to calculate machines and drives, as well as simplifications.

This book surveys topological methods in signal processing which address uncertainty in deterministic fashion. The author offers an efficient treatment of cellular sheaves, showing how their use is decisive in treating difficult problems in signal processing.

The true steady state mean value of the heat transfer coefficient must be multiplied by a newly defined coupling factor, which is always smaller than one and depends on the coupling parameters Biot number, Fourier number as well as dimensionless geometry and oscillation parameters.

This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.

For example, bounded uncertainties can be described by intervals, affine forms or general polynomial enclosures such as Taylor models, whereas stochastic uncertainties can be characterized in the form of a distribution described, for example, by the mean value, the standard deviation and higher-order moments.

This monograph presents an introduction to the Ito calculus techniques used to handle stochastic differential equations. It covers a broad spectrum of techniques which are useful for working with stochastic equations.

This monograph presents an introduction to Harmonic Balance for nonlinear vibration problems, covering the theoretical basis, its application to mechanical systems, and its computational implementation. Harmonic Balance is an approximation method for the computation of periodic solutions of nonlinear ordinary and differential-algebraic equations. It outperforms numerical forward integration in terms of computational efficiency often by several orders of magnitude. The method is widely used in the analysis of nonlinear systems, including structures, fluids and electric circuits. The book includes solved exercises which illustrate the advantages of Harmonic Balance over alternative methods as well as its limitations. The target audience primarily comprises graduate and post-graduate students, but the book may also be beneficial for research experts and practitioners in industry.

This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equations. It uses a unique teaching method which explains the analysis using exercises and detailed solutions.

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

This book examines control of nonlinear systems. Coverage ranges from mathematical system theory to practical industrial control applications. The author offers web-based videos illustrating some dynamical aspects and case studies in simulation.

This book presents the various design methods of a state-feedback control law and of an observer. * Quadratic optimization methods: Linear Quadratic Control (LQC), optimal Kalman filtering, Linear Quadratic Gaussian (LQG) control;

This book provides an introduction to sensor data fusion, as an information technology as well as a branch of engineering science and informatics. It presents a coherent methodological framework and features advanced application examples.

This authored monograph covers a viability to approach to traffic management by advising to vehicles circulated on the network the velocity they should follow for satisfying global traffic conditions;.

This book presents hypergraph theory and covers traditional elements of the theory as well as original concepts such as entropy of hypergraph, similarities and kernels. It details applications in telecommunications and parallel data structure modeling.

The book provides a self-contained treatment of stochastic finite element methods. The book covers the basic topics of computational stochastic mechanics focusing on the stochastic analysis of structural systems in the framework of the finite element method.