Random Phenomena

Author: Babatunde A. Ogunnaike
Publisher: CRC Press
ISBN: 1420044982
Size: 14.15 MB
Format: PDF
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Many of the problems that engineers face involve randomly varying phenomena of one sort or another. However, if characterized properly, even such randomness and the resulting uncertainty are subject to rigorous mathematical analysis. Taking into account the uniquely multidisciplinary demands of 21st-century science and engineering, Random Phenomena: Fundamentals of Probability and Statistics for Engineers provides students with a working knowledge of how to solve engineering problems that involve randomly varying phenomena. Basing his approach on the principle of theoretical foundations before application, Dr. Ogunnaike presents a classroom-tested course of study that explains how to master and use probability and statistics appropriately to deal with uncertainty in standard problems and those that are new and unfamiliar. Giving students the tools and confidence to formulate practical solutions to problems, this book offers many useful features, including: Unique case studies to illustrate the fundamentals and applications of probability and foster understanding of the random variable and its distribution Examples of development, selection, and analysis of probability models for specific random variables Presentation of core concepts and ideas behind statistics and design of experiments Selected "special topics," including reliability and life testing, quality assurance and control, and multivariate analysis As classic scientific boundaries continue to be restructured, the use of engineering is spilling over into more non-traditional areas, ranging from molecular biology to finance. This book emphasizes fundamentals and a "first principles" approach to deal with this evolution. It illustrates theory with practical examples and case studies, equipping readers to deal with a wide range of problems beyond those in the book. About the Author: Professor Ogunnaike is Interim Dean of Engineering at the University of Delaware. He is the recipient of the 2008 American Automatic Control Council's Control Engineering Practice Award, the ISA's Donald P. Eckman Education Award, the Slocomb Excellence in Teaching Award, and was elected into the US National Academy of Engineering in 2012.

Mathematical Analysis Of Random Phenomena

Author: Ana Bela Ferreira Cruzeiro
Publisher: World Scientific
ISBN: 9812770542
Size: 23.33 MB
Format: PDF, ePub, Docs
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This volume highlights recent developments of stochastic analysis with a wide spectrum of applications, including stochastic differential equations, stochastic geometry, and nonlinear partial differential equations. While modern stochastic analysis may appear to be an abstract mixture of classical analysis and probability theory, this book shows that, in fact, it can provide versatile tools useful in many areas of applied mathematics where the phenomena being described are random. The geometrical aspects of stochastic analysis, often regarded as the most promising for applications, are specially investigated by various contributors to the volume.

Introductory Statistics And Random Phenomena

Author: Manfred Denker
Publisher: Birkhäuser
ISBN: 3319661523
Size: 12.19 MB
Format: PDF, Docs
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This textbook integrates traditional statistical data analysis with new computational experimentation capabilities and concepts of algorithmic complexity and chaotic behavior in nonlinear dynamic systems. This was the first advanced text/reference to bring together such a comprehensive variety of tools for the study of random phenomena occurring in engineering and the natural, life, and social sciences. The crucial computer experiments are conducted using the readily available computer program Mathematica® Uncertain Virtual WorldsTM software packages which optimize and facilitate the simulation environment. Brief tutorials are included that explain how to use the Mathematica® programs for effective simulation and computer experiments. Large and original real-life data sets are introduced and analyzed as a model for independent study. This is an excellent classroom tool and self-study guide. The material is presented in a clear and accessible style providing numerous exercises and bibliographical notes suggesting further reading. Topics and Features Comprehensive and integrated treatment of uncertainty arising in engineering and scientific phenomena – algorithmic complexity, statistical independence, and nonlinear chaotic behavior Extensive exercise sets, examples, and Mathematica® computer experiments that reinforce concepts and algorithmic methods Thorough presentation of methods of data compression and representation Algorithmic approach to model selection and design of experiments Large data sets and 13 Mathematica®-based Uncertain Virtual WorldsTM programs and code This text is an excellent resource for all applied statisticians, engineers, and scientists who need to use modern statistical analysis methods to investigate and model their data. The present, softcover reprint is designed to make this classic textbook available to a wider audience.

Structural Acoustics

Author: Joshua E. Greenspon
Publisher: CRC Press
ISBN: 1439830940
Size: 65.19 MB
Format: PDF, ePub, Docs
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From jet engine noise that generates vibrations in the structure of an aircraft, to the sound radiation from the hull of a ship or submarine that makes it identifiable, an understanding of structural acoustics is key in the design process in maritime, automotive, aerospace, and architectural engineering. Building on classic works in the field, Structural Acoustics: Deterministic and Random Phenomena presents fundamental concepts, relations, and simplified methods for calculating complex problems associated with vibrations and noise issues of automobiles, ships, submarines, and aircraft. This practical reference studies the response of structures and media that are coupled with a fluid and are under static, dynamic, and random loading. Simplified solutions to complicated problems Starting with a review of the fundamentals of acoustics and structural acoustics, the book discusses the response of the beams, plates, and shells that compose most built-up structures before providing methods for solving problems of built-up systems, including a procedure for computing the response of an elastic or viscoelastic media without resorting to a large computer program. Building on this analysis, the second section develops the analysis for random loading, which can also be applied to geophysical phenomena and viscoelastic media. Proceeding from the fundamental aspects of simple structures to more complicated cases with more involved loading, the book presents formulas and applications for random loading. By providing a fundamental understanding of sound radiation in air and water, this book shows readers how to solve structural and acoustical problems. An important reference for those working in the area of acoustics and vibration analysis, it also includes computer programs for acoustical analysis available at www.crcpress.com.

Mathematics Of Random Phenomena

Author: P. Krée
Publisher: Springer Science & Business Media
ISBN: 9400947704
Size: 52.95 MB
Format: PDF, Mobi
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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.

Theory And Simulation Of Random Phenomena

Author: Ettore Vitali
Publisher: Springer
ISBN: 9783319905143
Size: 66.65 MB
Format: PDF, ePub, Mobi
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The purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.

Random Matrices High Dimensional Phenomena

Author: Gordon Blower
Publisher: Cambridge University Press
ISBN: 1139481959
Size: 37.65 MB
Format: PDF, ePub, Mobi
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This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.