EACM is a comprehensive reference work covering the vast field of applied and computational mathematics. Applied mathematics itself accounts for at least 60 per cent of mathematics, and the emphasis on computation reflects the current and constantly growing importance of computational methods in all areas of applications. EACM emphasizes the strong links of applied mathematics with major areas of science, such as physics, chemistry, biology, and computer science, as well as specific fields like atmospheric ocean science. In addition, the mathematical input to modern engineering and technology form another core component of EACM.
This supplement to the authoritative series Encyclopedia of Fluid Mechanics steps back from the topical approach to fluid mechanics and embraces the overall subject from an entirely mathematical viewpoint-describing the properties and motion of fluids within the pure science of mathematics, and without the uncertainty that can accompany experimental investigations. It addresses the mathematical details of model formation and development which constitute the basis for numerical experimentation. In addition Supplement 1 contains the comprehensive index for the first ten volumes of the series.
Mathematics is one of the most basic -- and most ancient -- types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists. The two-volume Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences recovers this mathematical heritage, bringing together many of the world's leading historians of mathematics to examine the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times to the twentieth century. In 176 concise articles divided into twelve parts, contributors describe and analyze the variety of problems, theories, proofs, and techniques in all areas of pure and applied mathematics, including probability and statistics. This indispensable reference work demonstrates the continuing importance of mathematics and its use in physics, astronomy, engineering, computer science, philosophy, and the social sciences. Also addressed is the history of higher education in mathematics. Carefully illustrated, with annotated bibliographies of sources for each article, The Companion Encyclopedia is a valuable research tool for students and teachers in all branches of mathematics. Contents of Volume 1: Â•Ancient and Non-Western Traditions Â•The Western Middle Ages and the Renaissance Â•Calculus and Mathematical Analysis Â•Functions, Series, and Methods in Analysis Â•Logic, Set Theories, and the Foundations of Mathematics Â•Algebras and Number Theory Contents of Volume 2: Â•Geometries and Topology Â•Mechanics and Mechanical Engineering Â•Physics, Mathematical Physics, and Electrical Engineering Â•Probability, Statistics, and the Social Sciences Â•Higher Education and Institutions Â•Mathematics and Culture Â•Select Bibliography, Chronology, Biographical Notes, and Index
ECM2 is a completely updated and expanded Second Edition of the well-established Encyclopedia of Computational Mechanics. The project has once again been prepared under the guidance of three of the world’s foremost experts in the field: Erwin Stein, Professor Emeritus, Stein Institut für Baumechanik und Numerische Mechanik, Leibniz Universität, Hannover, Germany René de Borst, Centenary Professor of Civil Engineering, University of Sheffield, UK Thomas J. R. Hughes, Peter O'Donnell Jr. Chair in Computational and Applied Mathematics and Professor of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, TX USA Though following the same structure as the first edition, ECM2 has been expanded from three to six volumes with the subjects "Fundamentals" in Volumes 1 & 2, "Solids and Structures" in Volumes 3 & 4, and "Fluids" in Volumes 5 & 6. It is published both in print and on line. Volumes 1 & 2, Fundamentals , contain contributions related to mathematics, mechanics, and computer science, and are structured as discretization methods, treating approximations with finite differences, discrete variational forms, boundary integral equations and further problem-oriented techniques, and the generation and visualization of geometry; meshes and results; various direct and iterative solvers; and time-dependent problems. Volumes 3 & 4, Solids and Structures , are organized into five different parts, namely, structural behavior; constitutive theories and their implementation; materials and processing; interaction problems; and identification, stochastics, and optimization. Volumes 5 & 6, Fluids, builds on the fundamentals described in Volumes 1 & 2. The chapters in Volumes 5 & 6 fall within four main groupings. The first grouping includes chapters describing additional basic methodologies used in computational fluid dynamics. The second comprises chapters on various aspects of incompressible viscous flows. The third part focuses on compressible fluid dynamics. The fourth pertains to problems involving moving domains and free surfaces, and application areas. With contributions from more than 50 leading experts drawn from around the globe, this is an essential and comprehensive reference for any university engineering department or corporation, containing must-have, up-to-date content of huge value to researchers, students and practitioners alike.
With over forty chapters, written by leading scholars, this comprehensive volume represents the best work in America, Europe and Asia. Geographical diversity of the authors is reflected in the different perspectives devoted to the subject, and all major disciplinary developments are covered. There are also sections concerning the countries that have made the most significant contributions, the relationship between science and industry, the importance of instrumentation, and the cultural influence of scientific modes of thought. Students and professionals will come to appreciate how, and why, science has developed - as with any other human activity, it is subject to the dynamics of society and politics.
Entries cover statistical theory, methods, and applications. Includes the latest topics and advances made in statistical science over the past decade--in areas such as computer-intensive statistical methodology, genetics, medicine, the environment, and other applications.