This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical rigor. The text is accessible to students from a wide variety of backgrounds, including undergraduate students entering applied mathematics from non-mathematical fields and graduate students in the sciences and engineering who want to learn analysis. A basic background in calculus, linear algebra and ordinary differential equations, as well as some familiarity with functions and sets, should be sufficient.
This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.
This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical rigor.The text is accessible to students from a wide variety of backgrounds, including undergraduate students entering applied mathematics from non-mathematical fields and graduate students in the sciences and engineering who want to learn analysis. A basic background in calculus, linear algebra and ordinary differential equations, as well as some familiarity with functions and sets, should be sufficient.
This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.
This book combines soil science, earth science, and environmental geochemistry, providing comprehensive background information for specialists interested in chemical-induced changes in the soil-subsurface system. Readers are introduced to the chemistry of contaminants that often disturb the natural soil-subsurface equilibrium as a result of human activity. While the soil-subsurface system has in many cases been affected by human impact, the effects of chemical contaminants on the actual matrix and properties have been largely neglected. The major focus of the book is on changes to the soil-subsurface matrix and properties caused by chemical pollution. By integrating results available in the literature, we observe that chemical pollutants may lead to the irreversible formation of a new soil-subsurface regime characterized by a matrix and properties different than those of the natural regime. In contrast to the geological time scales dictating natural changes to the matrix and properties of the soil-subsurface system, the time scale associated with chemical pollutant-induced changes is far shorter and extends over a “human lifetime scale.” The numerous examples presented in the book confirm that chemical contamination should be considered as an additional factor in the formation of a contemporary soil-subsurface regime that is different than that of the pristine system.
PREFACE The increasing demand on high data rate and quality of service in wireless communication has to cope with limited bandwidth and energy resources. More than 50 years ago, Shannon has paved the way to optimal usage of bandwidth and energy resources by bounding the spectral efficiency vs. signal to noise ratio trade-off. However, as any information theorist, Shannon told us what is the best we can do but not how to do it [1]. In this view, turbo codes are like a dream come true: they allow approaching the theoretical Shannon capacity limit very closely. However, for the designer who wants to implement these codes, at first sight they appear to be a nightmare. We came a huge step closer in striving the theoretical limit, but see the historical axiom repeated on a different scale: we know we can achieve excellent performance with turbo codes, but not how to realize this in real devices.
What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of the spectral approach, a concise primer on spectral triples is given. Chapter 2 is designed to serve as a toolkit for computations. The third chapter offers an in-depth view into the subtle links between the asymptotic expansions of traces of heat operators and meromorphic extensions of the associated spectral zeta functions. Chapter 4 studies the behaviour of the spectral action under fluctuations by gauge potentials. A subjective list of open problems in the field is spelled out in the fifth Chapter. The book concludes with an appendix including some auxiliary tools from geometry and analysis, along with examples of spectral geometries. The book serves both as a compendium for researchers in the domain of noncommutative geometry and an invitation to mathematical physicists looking for new concepts.
This extensive and increasing use of embedded systems and their integration in everyday products mark a significant evolution in information science and technology. Nowadays embedded systems design is subject to seamless integration with the physical and electronic environment while meeting requirements like reliability, availability, robustness, power consumption, cost, and deadlines. Thus, embedded systems design raises challenging problems for research, such as security, reliable and mobile services, large-scale heterogeneous distributed systems, adaptation, component-based development, and validation and tool-based certification. This book results from the ARTIST FP5 project funded by the European Commision. By integration 28 leading European research institutions with many top researchers in the area, this book assesses and strategically advances the state of the art in embedded systems. The coherently written monograph-like book is a valuable source of reference for researchers active in the field and serves well as an introduction to scientists and professionals interested in learning about embedded systems design.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.