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Here is a lucid and comprehensive introduction to the differential geometric study of partial differential equations (PDE). The first book to present substantial results on local solvability of general and nonlinear PDE systems without using power series techniques, it describes a general approach to PDE systems based on ideas developed by Lie, Cartan and Vessiot. The central theme is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields.
The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry contains all of Whitehead's published work on differential geometry, along with some papers on algebras. Most of these were written in the period 1929-1937, but a few later articles are included. The book begins with a list of Whitehead's works, in chronological order of writing as well as a biographical note by M. H. A. Newman and Barbara Whitehead, and a mathematical appreciation by John Milnor. This is followed by separate chapters on topics such as linear connections; a method of obtaining normal representations for a projective connection; representation of projective spaces; convex regions in the geometry of paths; locally homogeneous spaces in differential geometry; and the decomposition of an infinitesimal group. Also included are chapters on locally homogeneous spaces in differential geometry; Maurer's equations; linear associative algebras; an expression of Hopf's invariant as an integral; and normalizators of transformation groups.
This book is intended for students, teachers, researchers, engineers and project managers wishing to understand and implement systems engineering into their work. Based on numerous bibliographical sources, it provides coherent and accessible information, complemented with numerous illustrations. Systems Engineering will enable the reader to not only understand but also master the development cycle of a system, as well as gain an in-depth understanding of the associated terminology. An introduction to systems theory is presented first, clarifying what is meant by a complex system. The book then outlines systems engineering and one of its components: requirements engineering. A detailed presentation of the downhill activities of the development cycle follows the definition of requirements and the design of systems. Finally, the book explores the upstream activities of the development cycle with the virtual and concrete integration of the system.
This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.
The International Astronautical Federation is the only professional society in the field of aerospace engineering and Sciences which brings together specialists of all countries interested in the exploration and peaceful exploitation of space. At its annual Congresses a large number of invited and/or carefully selected con tributed papers are presented which cover a wide variety of topics and are distributed over a number of sessions, each one being organized by two leading scientists who later chair the session itself. Each year the selection of specific topics to be dealt with. is dictated either by significant new progress achieved in some sectors or by new developments and trends which are liable to influence substantially the objectives toward which space research and/or application of space technology will be oriented in the immediate future. A second rigorous screening, performed with the help of the Session Chairmen and carried out according to the same criteria identifies finally the papers which are published in the Proceedings. The outcome of all this is reliable and authoritative information as to the actual status and future trends of space activities, both from the research point of view and from the point of view of u~ilization and/or application.
In April 1991 BusinessWeek ran a cover story entitled, "I Can't Work This ?#!!@ Thing," about the difficulties many people have with consumer products, such as cell phones and VCRs. More than 15 years later, the situation is much the same-but at a very different level of scale. The disconnect between people and technology has had society-wide consequences in the large-scale system accidents from major human error, such as those at Three Mile Island and in Chernobyl. To prevent both the individually annoying and nationally significant consequences, human capabilities and needs must be considered early and throughout system design and development. One challenge for such consideration has been providing the background and data needed for the seamless integration of humans into the design process from various perspectives: human factors engineering, manpower, personnel, training, safety and health, and, in the military, habitability and survivability. This collection of development activities has come to be called human-system integration (HSI). Human-System Integration in the System Development Process reviews in detail more than 20 categories of HSI methods to provide invaluable guidance and information for system designers and developers.