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Author: Alexander I. Saichev Publisher: Birkhäuser ISBN: 3319925865 Category : Mathematics Languages : en Pages : 413
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
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 ISBN: 3319979582 Category : Mathematics Languages : en Pages : 347
Book Description
Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems which is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practitioners and researchers. The goal of the book is to give the reader, specialist and non-specialist usable and modern mathematical tools in their research and analysis. This new text is intended for graduate students and researchers in applied mathematics, physical sciences and engineering. The careful explanations, accessible writing style, and many illustrations/examples 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. The present, softcover reprint is designed to make this classic textbook available to a wider audience.
Author: A. I. Saichev Publisher: ISBN: Category : Theory of distributions (Functional analysis) Languages : en Pages : 0
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. This new text is intended for graduate students and researchers in applied mathematics, physical sciences and engineering. The careful explanations, accessible writing style, and many illustrations/examples also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise.
Author: Alexander I. Saichev Publisher: Springer Science & Business Media ISBN: 0817646523 Category : Mathematics Languages : en Pages : 427
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: Frank T. Smith Publisher: Springer ISBN: 3030122328 Category : Technology & Engineering Languages : en Pages : 703
Book Description
This book presents several aspects of research on mathematics that have significant applications in engineering, modelling and social matters, discussing a number of current and future social issues and problems in which mathematical tools can be beneficial. Each chapter enhances our understanding of the research problems in a particular an area of study and highlights the latest advances made in that area. The self-contained contributions make the results and problems discussed accessible to readers, and provides references to enable those interested to follow subsequent studies in still developing fields. Presenting real-world applications, the book is a valuable resource for graduate students, researchers and educators. It appeals to general readers curious about the practical applications of mathematics in diverse scientific areas and social problems.
Author: Alexander I. Saichev Publisher: Birkhäuser ISBN: 9783030017927 Category : Mathematics Languages : en Pages :
Book Description
Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems which is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and researchers. The goal of the books is to give the reader, specialist and non-specialist usable and modern mathematical tools in their research and analysis. Volume 1 provides detailed coverage of asymptotic methods, including the stationary phase and steepest descent methods, for Fourier and other integral transforms from an application perspective. Other topics covered include fractional calculus, the uncertainty principle, wavelets, and multiresolution analysis. Volume 2 contains an analysis of the three basic types of linear PDEs - elliptic, parabolic, and hyperbolic - as well as chapters on first-order nonlinear PDEs and conservation laws. Nonlinear waves, Burger's equations, KdV equations, and the equations of gas dynamics and porous media are also covered. Volume 3 extends the scope 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 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.
Author: Vasily E. Tarasov Publisher: MDPI ISBN: 303936118X Category : Business & Economics Languages : en Pages : 278
Book Description
This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.
Author: Kyandoghere Kyamakya Publisher: Springer Science & Business Media ISBN: 3642042260 Category : Computers Languages : en Pages : 401
Book Description
The selected contributions of this book shed light on a series of interesting aspects related to nonlinear dynamics and synchronization with the aim of demonstrating some of their interesting applications in a series of selected disciplines. This book contains thirteenth chapters which are organized around five main parts. The first part (containing five chapters) does focus on theoretical aspects and recent trends of nonlinear dynamics and synchronization. The second part (two chapters) presents some modeling and simulation issues through concrete application examples. The third part (two chapters) is focused on the application of nonlinear dynamics and synchronization in transportation. The fourth part (two chapters) presents some applications of synchronization in security-related system concepts. The fifth part (two chapters) considers further applications areas, i.e. pattern recognition and communication engineering.
Author: Lutz Schimansky-Geier Publisher: SPIE-International Society for Optical Engineering ISBN: 9780819449740 Category : Mathematics Languages : en Pages : 564
Book Description
Proceedings of SPIE present the original research papers presented at SPIE conferences and other high-quality conferences in the broad-ranging fields of optics and photonics. These books provide prompt access to the latest innovations in research and technology in their respective fields. Proceedings of SPIE are among the most cited references in patent literature.
Author: Joseph Klafter Publisher: World Scientific ISBN: 981446080X Category : Mathematics Languages : en Pages : 530
Book Description
This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject.In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.
Author: Alexander I. Saichev
Author: Alexander I. Saichev
Author: Alexander I. Saichev
Author: A. I. Saichev
Author: Alexander I. Saichev
Author: Frank T. Smith
Author: Alexander I. Saichev
Author: Vasily E. Tarasov
Author: Kyandoghere Kyamakya
Author: Lutz Schimansky-Geier
Author: Joseph Klafter