Algebra and Analysis for Engineers and Scientists - Softcover

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Panos J. Antsaklis received his Ph.D. in Electrical Engineering from Brown University, where he was a Fulbright Scholar. His main research interests are in the area of systems and control, particularly in linear feedback systems and intelligent autonomous control systems, with emphasis on hybrid and discrete event systems and reconfigurable control. He is currently Professor of Electrical Engineering at the University of Notre Dame. He has held regular and visiting teaching and research positions at Imperial College of the University of London, Brown University, Rice University, MIT, the National Technical University of Athens, and the Technical University of Crete, Greece. Dr. Antsaklis has been awarded a departmental outstanding teacher award and has been a keynote speaker at a number of conferences. He is also a Distinguished Lecturer of the IEEE Control Systems Society. Dr. Antsaklis has authored a number of publications in journals, conference proceedings, and books and has coedited five books as well. He has served on the editorial boards of several journals, including the IEEE Transactions on Automatic Control, IEEE Transactions on Neural Networks, and the Journal of Discrete Event Dynamic Systems, and he has been the guest editor of special issues in these and other journals. Dr. Ansaklis has served as program chair and general chair of major systems and control conferences, and he is an IEEE Fellow and the 1997 President of the IEEE Control Systems Society. Anthony N. Michel holds a Ph.D. in Electrical Engineering from Marquette University, as well as a D.Sc. in Applied Mathematics from the Technical University of Graz, Austria. He has extensive industrial and academic experience, and his main research interests are in control systems, circuit theory, neural networks, and applied mathematics. He is currently the Frank M. Freiman Professor of Electrical Engineering and Dean of theCollege of Engineering at the University of Notre Dame. Dr. Michel has coauthored five books as well as a number of journal articles, conference proceedings, and conference books. He is a former editor of the IEEE Transactions on Circuits and Systems, and he has held a variety of positions on the editorial boards of the IEEE Transactions on Automatic Control, IEEE Transactions on Neural Networks, Circuits, Systems and Signal Processing, and Neurocomputing, as well as other journals. He is a past president of the IEEE Circuits and Systems Society and has served on the executive committees of several professional organizations. Dr. Michel is also the recipient of numerous professional awards. He is a Fellow of the IEEE. In 1984 he received the IEEE Centennial Medal, and he also earned three IEEE paper prizes. He spent 1992 as a Fulbright Scholar at the Technical University of Vienna, and, most recently, he received the 1995 Technical Achievement Award of the IEEE Circuits and Systems Society.

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"This is an intermediate level text, with exercises, whose avowed purpose is to provide the science and engineering graduate student with an appropriate modern mathematical (analysis and algebra) background in a succinct, but nontrivial, manner.... [T]he book is quite thorough and can serve as a text, for self-study, or as a reference."  ―Mathematical Reviews

Written for graduate and advanced undergraduate students in engineering and science, this classic book focuses primarily on set theory, algebra, and analysis. Useful as a course textbook, for self-study, or as a reference, the work is intended to:

* provide readers with appropriate mathematical background for graduate study in engineering or science;

* allow students in engineering or science to become familiar with a great deal of pertinent mathematics in a rapid and efficient manner without sacrificing rigor;

* give readers a unified overview of applicable mathematics, enabling them to choose additional, advanced topical courses in mathematics more intelligently.

Whereas these objectives for writing this book were certainly pertinent over twenty years ago when the work was first published, they are even more compelling now. Today’s graduate students in engineering or science are expected to be more knowledgeable and sophisticated in mathematics than students in the past. Moreover, today’s graduate students in engineering or science are expected to be familiar with a great deal of ancillary material (primarily in the computer science area), acquired in courses that did not even exist a couple of decades ago.

The book is divided into three parts: set theory (Chapter 1), algebra (Chapters 2–4), and analysis (Chapters 5–7). The first two chapters deal with the fundamental concepts of sets, functions, relations and equivalence relations, and algebraic structures. Chapters 3 and 4 cover vectorspaces and linear transformations, and finite-dimensional vector spaces and matrices. The last three chapters investigate metric spaces, normed and inner product spaces, and linear operators. Because of its flexible structure, Algebra and Analysis for Engineers and Scientists may be used either in a one- or two-semester course by deleting appropriate sections, taking into account the students’ backgrounds and interests.

A generous number of exercises have been integrated into the text, and a section of references and notes is provided at the end of each chapter. Applications of algebra and analysis having a broad appeal are also featured, including topics dealing with ordinary differential equations, integral equations, applications of the contraction mapping principle, minimization of functionals, an example from optimal control, and estimation of random variables.

Supplementary material for students and instructors is available at http://Michel.Herget.net.