Applied Asymptotic Methods in Nonlinear Oscillations

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A. Halanay, V. Răsvan

This volume, which coincides with the centennial anniversary of the publication of the celebrated monograph The General Problem of the Stability Motion by A.M. Liapunov, reviews the current state of the art of the theory and applications of the Liapunov methods. The book contains an Introduction and four chapters. Chapter 2 presents some general results in stability theory. The remaining chapters deal with applications in power engineering, chemical engineering, and in non-engineering fields such as economics and in the modelling of interacting species. The beauty of the results obtained, the diversity of mathematical tools employed, and the described approach to mathematical modelling provide stimulating considerations for applications in many other fields. For mathematicians and engineers whose work involves the study and applications of stability theory in systems.

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Günter Kirschling

It is in general not possible to produce technical products having precisely predefined measures. Systematic and random deviations from nominal size cannot be avoided, and it is therefore necessary to define measurement tolerances. This book offers a comprehensive presentation of tolerance problems and their solution by statistical methods. All calculated solutions are presented in clear figure or graphical form. It is particularly appropriate for those working in the field of development and construction or in production and quality control, especially in mechanical engineering and related fields.

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Alexandre Ern, Jean-Luc Guermond

This book presents the mathematical theory of finite elements, starting from basic results on approximation theory and finite element interpolation and building up to more recent research topics, such as and Discontinuous Galerkin, subgrid viscosity stabilization, and a posteriori error estimation. The body of the text is organized into three parts plus two appendices collecting the functional analysis results used in the book. The first part develops the theoretical basis for the finite element method and emphasizes the fundamental role of inf-sup conditions. The second party addresses various applications encompassing elliptic PDE's, mixed formulations, first-order PDEs, and the time-dependent versions of these problems. The third part covers implementation issues and should provide readers with most of the practical details needed to write or understand a finite element code. Written at the graduate level, the text contains numerous examples and exercises and is intended to serve as a graduate textbook. Depending on one's interests, several reading paths can be followed, emphasizing either theoretical results, numerical algorithms, code efficiency, or applications in the engineering sciences. The book will be useful to researchers and graduate students in mathematics, computer science and engineering.

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Mihajlo D. Mesarovic, Yasuhiko Takahara

This book reports on the new results in Abstract Systems Theory (AST). It shows the progress made so far in the effort launched in 1960 to develop a mathematical theory of systems based on the "top-down"-formalization-approach. The volume can be used as a supplementary reading in courses in systems theory and engineering. The material is organized in such a way that portions of the book relevant for the supplementary reading in different courses can be used independently from the rest of the text.