Download or read book An Introduction to the Method of Averaging written by and published by . This book was released on 1992 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of averaging is a powerful tool for the integration of systems of ordinary differential equations which have some rapidly oscillating variables and other slowly oscillating variables. This report bridges the gap from casual acquaintance with the underlying idea to technical reading and application. Three examples are worked in detail.
Download or read book An Introduction to the Method of Averaging written by Carl Edwin Crockett (Major, USAF) and published by . This book was released on 1992 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of averaging is a powerful tool for the integration of systems of ordinary differential equations which have some rapidly oscillating variables and other slowly oscillating variables. This report bridges the gap from casual acquaintance with the underlying idea to technical reading and application. Three examples are worked in detail.
Download or read book Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems written by William G. Gray and published by Springer Science & Business Media. This book was released on 2014-02-19 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thermodynamically constrained averaging theory provides a consistent method for upscaling conservation and thermodynamic equations for application in the study of porous medium systems. The method provides dynamic equations for phases, interfaces, and common curves that are closely based on insights from the entropy inequality. All larger scale variables in the equations are explicitly defined in terms of their microscale precursors, facilitating the determination of important parameters and macroscale state equations based on microscale experimental and computational analysis. The method requires that all assumptions that lead to a particular equation form be explicitly indicated, a restriction which is useful in ascertaining the range of applicability of a model as well as potential sources of error and opportunities to improve the analysis.
Download or read book Averaging Methods in Nonlinear Dynamical Systems written by Jan A. Sanders and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.
Download or read book An Introduction to Statistical Methods written by Horace Secrist and published by . This book was released on 1919 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multiscale Methods written by Grigoris Pavliotis and published by Springer Science & Business Media. This book was released on 2008-01-18 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to multiscale methods gives you a broad overview of the methods’ many uses and applications. The book begins by setting the theoretical foundations of the methods and then moves on to develop models and prove theorems. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable you to build your own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter.With the exception of Chapter One, all chapters are supplemented with exercises.
Download or read book An Introduction to the Methods of Economic Statistics written by William Leonard Crum and published by . This book was released on 1925 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spin Glass Theory And Beyond An Introduction To The Replica Method And Its Applications written by Marc Mezard and published by World Scientific Publishing Company. This book was released on 1987-11-01 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular attention to new applications in the study of optimization theory and neural networks. About two-thirds of the book are a collection of the most interesting and pedagogical articles on the subject.
Download or read book Introduction to Time Series Analysis written by Mark Pickup and published by SAGE Publications. This book was released on 2014-10-15 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing time series methods and their application in social science research, this practical guide to time series models is the first in the field written for a non-econometrics audience. Giving readers the tools they need to apply models to their own research, Introduction to Time Series Analysis, by Mark Pickup, demonstrates the use of—and the assumptions underlying—common models of time series data including finite distributed lag; autoregressive distributed lag; moving average; differenced data; and GARCH, ARMA, ARIMA, and error correction models. “This volume does an excellent job of introducing modern time series analysis to social scientists who are already familiar with basic statistics and the general linear model.” —William G. Jacoby, Michigan State University
Download or read book A Method of Averaging in the Theory of Orthogonal Series and Some Problems in the Theory of Bases written by Sergeĭ Viktorovich Bochkarev and published by American Mathematical Soc.. This book was released on 1980 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Investigate various forms of convergence of Fourier series in general orthonormal systems as well as certain problems in the theory of bases" -- Introduction.
Download or read book An Introduction to Laboratory Physics written by Lucius Tuttle and published by . This book was released on 1915 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Statistical Computing written by Jochen Voss and published by John Wiley & Sons. This book was released on 2013-08-28 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to sampling-based methods in statistical computing The use of computers in mathematics and statistics has opened up a wide range of techniques for studying otherwise intractable problems. Sampling-based simulation techniques are now an invaluable tool for exploring statistical models. This book gives a comprehensive introduction to the exciting area of sampling-based methods. An Introduction to Statistical Computing introduces the classical topics of random number generation and Monte Carlo methods. It also includes some advanced methods such as the reversible jump Markov chain Monte Carlo algorithm and modern methods such as approximate Bayesian computation and multilevel Monte Carlo techniques An Introduction to Statistical Computing: Fully covers the traditional topics of statistical computing. Discusses both practical aspects and the theoretical background. Includes a chapter about continuous-time models. Illustrates all methods using examples and exercises. Provides answers to the exercises (using the statistical computing environment R); the corresponding source code is available online. Includes an introduction to programming in R. This book is mostly self-contained; the only prerequisites are basic knowledge of probability up to the law of large numbers. Careful presentation and examples make this book accessible to a wide range of students and suitable for self-study or as the basis of a taught course.
Download or read book An Introduction to Toxicogenomics written by Michael E. Burczynski and published by CRC Press. This book was released on 2003-03-26 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the advent of cDNA microarrays, oligonucleotide array technology, and gene chip analysis, genomics has revolutionized the entire field of biomedical research. A byproduct of this revolution, toxicogenomics is a fast-rising star within toxicological analysis. Gathering together leading authors and scientists at the forefront of the field, An Introduction to Toxicogenomics provides a comprehensive overview of this new discipline. With a focus on toxicology, it introduces the basic principles of microarray/oligonucleotide array-based genomic analysis and explains how it fits into the field of biomedical research. These discussions provide an overview to the actual mechanics of the analyses themselves and offer insights on handling and quality control. Then the book features an important section on the basics of data analysis and clustering methods such as genetic algorithms. Finally, it covers the application of expression profiling in the field of toxicology and addresses the two fundamental types of analysis in detail, with sections dedicated to both mechanistic and predictive studies. Although toxicogenomics promises fast, efficient techniques and information-rich data, much of its potential remains untapped. An Introduction to Toxicogenomics consolidates the concepts underlying the field to provide a solid foundation from which to begin your research endeavors.
Download or read book The Control Handbook three volume set written by William S. Levine and published by CRC Press. This book was released on 2018-10-08 with total page 3526 pages. Available in PDF, EPUB and Kindle. Book excerpt: At publication, The Control Handbook immediately became the definitive resource that engineers working with modern control systems required. Among its many accolades, that first edition was cited by the AAP as the Best Engineering Handbook of 1996. Now, 15 years later, William Levine has once again compiled the most comprehensive and authoritative resource on control engineering. He has fully reorganized the text to reflect the technical advances achieved since the last edition and has expanded its contents to include the multidisciplinary perspective that is making control engineering a critical component in so many fields. Now expanded from one to three volumes, The Control Handbook, Second Edition brilliantly organizes cutting-edge contributions from more than 200 leading experts representing every corner of the globe. They cover everything from basic closed-loop systems to multi-agent adaptive systems and from the control of electric motors to the control of complex networks. Progressively organized, the three volume set includes: Control System Fundamentals Control System Applications Control System Advanced Methods Any practicing engineer, student, or researcher working in fields as diverse as electronics, aeronautics, or biomedicine will find this handbook to be a time-saving resource filled with invaluable formulas, models, methods, and innovative thinking. In fact, any physicist, biologist, mathematician, or researcher in any number of fields developing or improving products and systems will find the answers and ideas they need. As with the first edition, the new edition not only stands as a record of accomplishment in control engineering but provides researchers with the means to make further advances.
Download or read book An Introduction to Logic and Scientific Method written by Morris F. Cohen and published by Read Books Ltd. This book was released on 2011-03-23 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though formal logic has in recent times been the object of radical and spirited attacks from many and diverse quarters, it continues, and will probably long continue, to be one of the most frequently given courses in colleges and universities here and abroad. Nor need this be surprising when we reflect that the most serious of the charges against formal logic, those against the syllogism, are as old as Aristotle, who seems to have been fully aware of them. But while the realm of logic seems perfectly safe against the attacks from without, there is a good deal of unhappy confusion within. Though the content of almost all logic books follows (even in many of the illustrations) the standard set by Aristotle’s Organon—terms, propositions, syllogisms and allied forms of inference, scientific method, probability and fallacies—there is a bewildering Babel of tongues as to what logic is about. The different schools, the traditional, the linguistic, the psychological, the epistemological, and the mathematical, speak different languages, and each regards the other as not really dealing with logic at all. No task is perhaps so thankless, or invites so much abuse from all quarters, as that of the mediator between hostile points of view. Nor is the traditional distrust of the peacemaker in the intellectual realm difficult to appreciate, since he so often substitutes an unclear and inconsistent amalgam for points of view which at least have the merit of a certain clarity. And yet no task is so essential, especially for the beginner, when it is undertaken with the objective of adjusting and supplementing the claims of the contending parties, and when it is accompanied by a refusal to sacrifice clarity and rigor in thought. In so far as an elementary text permits such a thing, the present text seeks to bring some order into the confusion of tongues concerning the subject matter of logic. But the resolution of the conflicts between various schools which it effects appears in the selection and presentation of material, and not in extensive polemics against any school. The book has been written with the conviction that logic is the autonomous science of the objective though formal conditions of valid inference. At the same time, its authors believe that the aridity which is (not always unjustly) attributed to the study of logic testifies to the unimaginative way logical principles have been taught and misused. The present text aims to combine sound logical doctrine with sound pedagogy, and to provide illustrative material suggestive of the rôle of logic in every department of thought. A text that would find a place for the realistic formalism of Aristotle, the scientific penetration of Peirce, the pedagogical soundness of Dewey, and the mathematical rigor of Russell—this was the ideal constantly present to the authors of this book.
Download or read book An Introduction to Information Science written by Roger Flynn and published by CRC Press. This book was released on 2020-10-02 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises an introduction to information as an external commodity; a data base that can be manipulated, retrieved, transmitted, and used. It is useful at an introductory undergraduate level and also for anyone who is new to the field of Information Science.
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
