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Author: Alexander I. Saichev
Publisher: Birkhäuser
ISBN: 3319925865
Category : Mathematics
Languages : en
Pages : 413
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Book Description
Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences. Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts. Distributions in the Physical and Engineering Sciences is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas. The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed. An appendix also provides background material concerning the Dirac-delta and other distributions.
Author: Alexander I. Saichev
Publisher: Birkhäuser
ISBN: 3319925865
Category : Mathematics
Languages : en
Pages : 413
Get Book Here
Book Description
Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences. Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts. Distributions in the Physical and Engineering Sciences is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas. The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed. An appendix also provides background material concerning the Dirac-delta and other distributions.
Author: Alexander I. Saichev
Publisher: Springer Science & Business Media
ISBN: 0817646523
Category : Mathematics
Languages : en
Pages : 427
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Book Description
Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important for practitioners and researchers. The goal of the books is to give the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis. Volume 2: Linear and Nonlinear Dynamics of Continuous Media continues the multivolume project which endeavors to show how the theory of distributions, also called the theory of generalized functions, can be used by graduate students and researchers in applied mathematics, physical sciences, and engineering. It contains an analysis of the three basic types of linear partial differential equations--elliptic, parabolic, and hyperbolic--as well as chapters on first-order nonlinear partial differential equations and conservation laws, and generalized solutions of first-order nonlinear PDEs. Nonlinear wave, growing interface, and Burger’s equations, KdV equations, and the equations of gas dynamics and porous media are also covered. The careful explanations, accessible writing style, many illustrations/examples and solutions also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. Features · Application oriented exposition of distributional (Dirac delta) methods in the theory of partial differential equations. Abstract formalism is keep to a minimum. · Careful and rich selection of examples and problems arising in real-life situations. Complete solutions to all exercises appear at the end of the book. · Clear explanations, motivations, and illustration of all necessary mathematical concepts.
Author: Karl V. Bury
Publisher: Cambridge University Press
ISBN: 9780521635066
Category : Mathematics
Languages : en
Pages : 386
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Book Description
This 1999 book presents single-variable statistical distributions useful in solving practical problems in a wide range of engineering contexts.
Author: Petre Teodorescu
Publisher: John Wiley & Sons
ISBN: 3527653635
Category : Science
Languages : en
Pages : 379
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Book Description
In this comprehensive monograph, the authors apply modern mathematical methods to the study of mechanical and physical phenomena or techniques in acoustics, optics, and electrostatics, where classical mathematical tools fail. They present a general method of approaching problems, pointing out different aspects and difficulties that may occur. With respect to the theory of distributions, only the results and the principle theorems are given as well as some mathematical results. The book also systematically deals with a large number of applications to problems of general Newtonian mechanics, as well as to problems pertaining to the mechanics of deformable solids and physics. Special attention is placed upon the introduction of corresponding mathematical models. Addressed to a wide circle of readers who use mathematical methods in their work: applied mathematicians, engineers in various branches, as well as physicists, while also benefiting students in various fields.
Author: Gerlind Plonka
Publisher: Springer Nature
ISBN: 3031350057
Category : Mathematics
Languages : en
Pages : 676
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Book Description
New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.
Author: Dmitry Balandin
Publisher: Springer Nature
ISBN: 3031241452
Category : Computers
Languages : en
Pages : 319
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Book Description
This book constitutes selected and revised papers from the 22nd International Conference on Mathematical Modeling and Supercomputer Technologies, MMST 2022, held in Nizhny Novgorod, Russia, in November 2022. The 20 full papers and 5 short papers presented in the volume were thoroughly reviewed and selected from the 48 submissions. They are organized in topical secions on computational methods for mathematical models analysis; computation in optimization and optimal control; supercomputer simulation.
Author: Manfred Denker
Publisher: Birkhäuser
ISBN: 3319661523
Category : Computers
Languages : en
Pages : 521
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Book Description
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.
Author: J. H. Pollard
Publisher: CUP Archive
ISBN: 9780521297509
Category : Mathematics
Languages : en
Pages : 372
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Book Description
This handbook is designed for experimental scientists, particularly those in the life sciences. It is for the non-specialist, and although it assumes only a little knowledge of statistics and mathematics, those with a deeper understanding will also find it useful. The book is directed at the scientist who wishes to solve his numerical and statistical problems on a programmable calculator, mini-computer or interactive terminal. The volume is also useful for the user of full-scale computer systems in that it describes how the large computer solves numerical and statistical problems. The book is divided into three parts. Part I deals with numerical techniques and Part II with statistical techniques. Part III is devoted to the method of least squares which can be regarded as both a statistical and numerical method. The handbook shows clearly how each calculation is performed. Each technique is illustrated by at least one example and there are worked examples and exercises throughout the volume.
Author: C. Zuily
Publisher: Elsevier
ISBN: 0080872549
Category : Mathematics
Languages : en
Pages : 247
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Book Description
The aim of this book is to provide a comprehensive introduction to the theory of distributions, by the use of solved problems. Although written for mathematicians, it can also be used by a wider audience, including engineers and physicists.The first six chapters deal with the classical theory, with special emphasis on the concrete aspects. The reader will find many examples of distributions and learn how to work with them. At the beginning of each chapter the relevant theoretical material is briefly recalled. The last chapter is a short introduction to a very wide and important field in analysis which can be considered as the most natural application of distributions, namely the theory of partial differential equations. It includes exercises on the classical differential operators and on fundamental solutions, hypoellipticity, analytic hypoellipticity, Sobolev spaces, local solvability, the Cauchy problem, etc.
Author: Kenneth Franklin Riley
Publisher:
ISBN:
Category :
Languages : en
Pages : 1008
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Book Description
