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  • av Roger F. Harrington
    2 170,-

    First published in 1961, Roger Harrington's Time-Harmonic Electromagnetic Fields is one of the most significant works in electromagnetic theory and applications. Over the past forty years, it proved to be a key resource for students, professors, researchers, and engineers who require a comprehensive, in-depth treatment of the subject.

  • av Dragan Poljak
    1 536,-

    Help protect your network with this important reference work on cyber security Deterministic computational models are those for which all inputs are precisely known, whereas stochastic modeling reflects uncertainty or randomness in one or more of the data inputs. Many problems in computational engineering therefore require both deterministic and stochastic modeling to be used in parallel, allowing for different degrees of confidence and incorporating datasets of different kinds. In particular, non-intrusive stochastic methods can be easily combined with widely used deterministic approaches, enabling this more robust form of data analysis to be applied to a range of computational challenges. Deterministic and Stochastic Modeling in Computational Electromagnetics provides a rare treatment of parallel deterministic-stochastic computational modeling and its beneficial applications. Unlike other works of its kind, which generally treat deterministic and stochastic modeling in isolation from one another, it aims to demonstrate the usefulness of a combined approach and present particular use-cases in which such an approach is clearly required. It offers a non-intrusive stochastic approach which can be incorporated with minimal effort into virtually all existing computational models. Readers will also find: A range of specific examples demonstrating the efficiency of deterministic-stochastic modeling Computational examples of successful applications including ground penetrating radars (GPR), radiation from 5G systems, transcranial magnetic and electric stimulation (TMS and TES), and more Introduction to fundamental principles in field theory to ground the discussion of computational modeling Deterministic and Stochastic Modeling in Computational Electromagnetics is a valuable reference for researchers, including graduate and undergraduate students, in computational electromagnetics, as well as to multidisciplinary researchers, engineers, physicists, and mathematicians.

  • av Vladimir (University of Manitoba Okhmatovski
    1 616,-

    "This book provides a detailed, up-to-date and comprehensive overview of both the theory and the numerical methods to determine electromagnetic fields in layered media. It begins with an introduction to Maxwell Equations, fundamental relations of the electromagnetic theory, and Green's function concept and definitions. It then moves on to solving canonical problems of vertical and horizontal dipole radiation, describing Method of Moments (MoM) schemes and integral equations governing EM fields, and explaining Michalski-Zheng's theory of mixed-potential Green's function representation in multi-layered medium. The book also includes chapters on evaluation of Sommerfeld integrals, procedures for evaluation of the far field, theory and application of hierarchical matrices, and more."--

  • - Wave Phenomena and Engineering Applications
    av ZH Jiang
    1 786,-

    Discover the most recent advances in electromagnetic vorticesIn Electromagnetic Vortices: Wave Phenomena and Engineering Applications, a team of distinguished researchers delivers a cutting-edge treatment of electromagnetic vortex waves, including their theoretical foundation, related wave properties, and several potentially transformative applications.The book is divided into three parts. The editors first include resources that describe the generation, sorting, and manipulation of vortex waves, as well as descriptions of interesting wave behavior in the infrared and optical regimes with custom-designed nanostructures. They then discuss the generation, multiplexing, and propagation of vortex waves at the microwave and millimeter-wave frequencies. Finally, the selected contributions discuss several representative practical applications of vortex waves from a system perspective.With coverage that incorporates demonstration examples from a wide range of related sub-areas, this essential edited volume also offers:* Thorough introductions to the generation of optical vortex beams and transformation optical vortex wave synthesizers* Comprehensive explorations of millimeter-wave metasurfaces for high-capacity and broadband generation of vector vortex beams, as well as orbital angular momentum (OAM) detection and its observation in second harmonic generations* Practical discussions of microwave SPP circuits and coding metasurfaces for vortex beam generation and OAM-based structured radio beams and their applications* In-depth examinations and explorations of OAM multiplexing for wireless communications, wireless power transmission, as well as quantum communications and simulationsPerfect for students of wireless communications, antenna/RF design, optical communications, and nanophotonics, Electromagnetic Vortices: Wave Phenomena and Engineering Applications is also an indispensable resource for researchers in academia, at large defense contractors, and in government labs.

  • av Prabhakar H. Pathak
    2 086,-

    Electromagnetic Radiation, Scattering, and DiffractionDiscover a graduate-level text for students specializing in electromagnetic wave radiation, scattering, and diffraction for engineering applicationsIn Electromagnetic Radiation, Scattering and Diffraction, distinguished authors Drs. Prabhakar H. Pathak and Robert J. Burkholder deliver a thorough exploration of the behavior of electromagnetic fields in radiation, scattering, and guided wave environments. The book tackles its subject from first principles and includes coverage of low and high frequencies. It stresses physical interpretations of the electromagnetic wave phenomena along with their underlying mathematics.The authors emphasize fundamental principles and provide numerous examples to illustrate the concepts contained within. Students with a limited undergraduate electromagnetic background will rapidly and systematically advance their understanding of electromagnetic wave theory until they can complete useful and important graduate-level work on electromagnetic wave problems.Electromagnetic Radiation, Scattering and Diffraction also serves as a practical companion for students trying to simulate problems with commercial EM software and trying to better interpret their results. Readers will also benefit from the breadth and depth of topics, such as:* Basic equations governing all electromagnetic (EM) phenomena at macroscopic scales are presented systematically. Stationary and relativistic moving boundary conditions are developed. Waves in planar multilayered isotropic and anisotropic media are analyzed.* EM theorems are introduced and applied to a variety of useful antenna problems. Modal techniques are presented for analyzing guided wave and periodic structures. Potential theory and Green's function methods are developed to treat interior and exterior EM problems.* Asymptotic High Frequency methods are developed for evaluating radiation Integrals to extract ray fields. Edge and surface diffracted ray fields, as well as surface, leaky and lateral wave fields are obtained. A collective ray analysis for finite conformal antenna phased arrays is developed.* EM beams are introduced and provide useful basis functions. Integral equations and their numerical solutions via the method of moments are developed. The fast multipole method is presented. Low frequency breakdown is studied. Characteristic modes are discussed.Perfect for graduate students studying electromagnetic theory, Electromagnetic Radiation, Scattering, and Diffraction is an invaluable resource for professional electromagnetic engineers and researchers working in this area.

  • av ZN Chen
    1 516,-

    Substrate-Integrated Millimeter-Wave Antennas for Next-Generation Communication and Radar SystemsThe first and only comprehensive text on substrate-integrated mmW antenna technology, state-of-the-art antenna design, and emerging wireless applicationsSubstrate-Integrated Millimeter-Wave Antennas for Next-Generation Communication and Radar Systems elaborates the most important topics related to revolutionary millimeter-wave (mmW) technology. Following a clear description of fundamental concepts including substrate-­integrated waveguides and loss analysis, the text treats key design methods, prototyping techniques, and experimental setup and testing. The authors also highlight applications of mmW antennas in 5G wireless communication and next-generation radar systems. Readers are prepared to put techniques into practice through practical discussions of how to set up testing for impedance matching, radiation patterns, gain from 24GHz up to 325 GHz, and more.This book will bring readers state-of-the-art designs and recent progress in substrate-integrated mmW antennas for emerging wireless applications. Substrate-Integrated Millimeter-Wave Antennas for Next-Generation Communication and Radar Systems is the first comprehensive text on the topic, allowing readers to quickly master mmW technology. This book:* Introduces basic concepts such as metamaterials Huygens's surface, zero-index structures, and pattern synthesis* Describes prototyping in the form of fabrication based on printed-circuit-board, low-temperature-co-fired-ceramic and micromachining* Explores applications for next-generation radar and imaging systems such as 24-GHz and 77-GHz vehicular radar systems* Elaborates design methods including waveguide-based feeding network, three-dimensional feeding structure, dielectric loaded aperture antenna element, and low-sidelobe synthesisThe mmW is one of today's most important emerging technologies. This book provides graduate students, researchers, and engineers with the knowledge they need to deploy mmW systems and develop new antenna designs with low cost, low loss, and low complexity.

  • av Ismo V. (Helsinki University of Technology) Lindell
    1 726,-

    A comprehensive survey of boundary conditions as applied in antenna and microwave engineering, material physics, optics, and general electromagnetics research.Boundary conditions are essential for determining electromagnetic problems. Working with engineering problems, they provide analytic assistance in mathematical handling of electromagnetic structures, and offer synthetic help for designing new electromagnetic structures. Boundary Conditions in Electromagnetics describes the most-general boundary conditions restricted by linearity and locality, and analyzes basic plane-wave reflection and matching problems associated to a planar boundary in a simple-isotropic medium.This comprehensive text first introduces known special cases of particular familiar forms of boundary conditions -- perfect electromagnetic conductor, impedance, and DB boundaries -- and then examines various general forms of boundary conditions. Subsequent chapters discuss sesquilinear boundary conditions and practical computations on wave scattering by objects defined by various boundary conditions. The practical applications of less-common boundary conditions, such as for metamaterial and metasurface engineering, are referred to throughout the text. This book:* Describes the mathematical analysis of fields associated to given boundary conditions* Provides examples of how boundary conditions affect the scattering properties of a particle* Contains ample in-chapter exercises and solutions, complete references, and a detailed index* Includes appendices containing electromagnetic formulas, Gibbsian 3D dyadics, and four-dimensional formalismBoundary Conditions in Electromagnetics is an authoritative text for electrical engineers and physicists working in electromagnetics research, graduate or post-graduate students studying electromagnetics, and advanced readers interested in electromagnetic theory.

  • av Martin Stumpf
    1 566,-

    Describes applications of time-domain EM reciprocity and the Cagniard-deHoop technique to achieve solutions to fundamental antenna radiation and scattering problemsThis book offers an account of applications of the time-domain electromagnetic (TD EM) reciprocity theorem for solving selected problems of antenna theory. It focuses on the development of both TD numerical schemes and analytical methodologies suitable for analyzing TD EM wave fields associated with fundamental antenna topologies.Time-Domain Electromagnetic Reciprocity in Antenna Modeling begins by applying the reciprocity theorem to formulate a fundamentally new TD integral equation technique - the Cagniard-deHoop method of moments (CdH-MoM) - regarding the pulsed EM scattering and radiation from a thin-wire antenna. Subsequent chapters explore the use of TD EM reciprocity to evaluate the impact of a scatterer and a lumped load on the performance of wire antennas and propose a straightforward methodology for incorporating ohmic loss in the introduced solution methodology. Other topics covered in the book include the pulsed EM field coupling to transmission lines, formulation of the CdH-MoM concerning planar antennas, and more. In addition, the book is supplemented with simple MATLAB code implementations, so that readers can test EM reciprocity by conducting (numerical) experiments. In addition, this text:* Applies the thin-sheet boundary conditions to incorporate dielectric, conductive and plasmonic properties of planar antennas* Provides illustrative numerical examples that validates the described methodologies* Presents analyzed problems at a fundamental level so that readers can fully grasp the underlying principles of solution methodologies* Includes appendices to supplement material in the bookTime-Domain Electromagnetic Reciprocity in Antenna Modeling is an excellent book for researchers and professors in EM modeling and for applied researchers in the industry.

  • - How Electromagnetic Technologies Are Changing Our Lives
    av Rajeev Bansal
    556,-

    This book covers the study of electromagnetic wave theory and describes how electromagnetic technologies affect our daily lives.

  • - Analysis Methods and Applications
    av Hisamatsu (Hosei University Nakano
    1 540,-

    Presents recent progress in low-profile natural and metamaterial antennas This book presents the full range of low-profile antennas that use novel elements and take advantage of new concepts in antenna implementation, including metamaterials.

  • av Ismo V. (Helsinki University of Technology) Lindell
    1 816,-

    Applies the four-dimensional formalism with an extended toolbox of operation rules, allowing readers to define more general classes of electromagnetic media and to analyze EM waves that can exist in them. This book covers various properties of electromagnetic media in terms of which they can be set in different classes.

  • - From Fundamentals to Applications
    av Akira (University of Washington) Ishimaru
    1 800,-

    One of the most methodical treatments of electromagnetic wave propagation, radiation, and scattering including new applications and ideas Presented in two parts, this book takes an analytical approach on the subject and emphasizes new ideas and applications used today.

  • av Levent (Istanbul Technical University) Sevgi
    1 686,-

    Electromagnetic modeling is essential to the design and modeling of antenna, radar, satellite, medical imaging, and other applications. In Electromagnetic Modeling and Simulation, author Levent Sevgi explains techniques for solving real-time complex physical problems using MATLAB-based short scripts and comprehensive virtual tools.

  • - Near-Field Scanning Applications
    av Arthur D. Yaghjian & Thorkild B. Hansen
    2 966,-

    Electrical Engineering Plane-Wave Theory of Time-Domain Fields Near-Field Scanning Applications A volume in the IEEE Press Series on Electromagnetic Wave Theory Donald G. Dudley, Series Editor Plane-Wave Theory of Time-Domain Fields provides a comprehensive framework for the formulation and solution of numerous problems involving the radiation, reception, propagation, and scattering of electromagnetic and acoustic waves. Green's function and plane-wave spectrum representations in both the time and frequency domains are systematically derived and effectively applied to the decomposition and analysis of transient and time-harmonic fields. With the publication of this book, probe-corrected near-field measurement techniques, which have previously been confined to the frequency domain, have been extended to ultra-wideband, short-pulse antennas and transducers. Featured topics include: Fundamental theorems in electromagnetics and acoustics A rigorous development of time-domain and frequency-domain plane-wave representations Probe-corrected planar near-field scanning for time-domain and frequency-domain fields Sampling theorems and computation schemes for time-domain and frequency-domain fields The application of plane-wave theory to static electric and magnetic fields Analytic-signal formulas that simplify the formulation and analysis of transient fields Wave phenomena, such as "electromagnetic missiles" encountered only in the time domain Definitive force and power relations for electromagnetic and acoustic fields and sources By combining unencumbered straightforward derivations with in-depth expositions of prerequisite material, the authors have created an invaluable resource for research scientists and engineers in electromagnetics and acoustics, and a definitive reference on plane-wave expansions and near-field measurements. About the IEEE Press Series on Electromagnetic Wave Theory The IEEE Press Series on Electromagnetic Wave Theory offers outstanding coverage of the field. It consists of new titles of contemporary interest, as well as reprintings and revisions of recognized classics by established authors and researchers. Emphasis is on works of long-term archival significance in electromagnetic waves and applications. Designed specifically for graduate students, researchers and practicing engineers, the series provides affordable volumes that explore and explain electromagnetic waves beyond the undergraduate level.

  • av Donald G. Dudley
    2 256,-

    Electrical Engineering/Electromagnetics Mathematical Foundations for Electromagnetic Theory A volume in the IEEE/OUP Series on Electromagnetic Wave Theory Donald G. Dudley, Series Editor This volume in the series lays the mathematical foundations for the study of advanced topics in electromagnetic theory. Important subjects covered include linear spaces, Green's functions, spectral expansions, electromagnetic source representations, and electromagnetic boundary value problems. You will find these key features: Introduction to modern linear analysis and linear operators Solution to Sturm-Liouville problems using Green's functions and spectral expansions Natural transforms and series expansions specific to a wide range of differential operators and associated boundary conditions Useful alternative representations for canonical electromagnetic sources Applications to electromagnetic boundary value problems This book will be of interest to graduate-level students in engineering, electromagnetics, physics, and applied mathematics, as well as to research engineers, physicists, and scientists. Also in the series Radiation and Scattering of Waves An IEEE Press Classic Reissue Leopold B. Felsen and Nathan Marcuvitz 1994 Hardcover 928 pp Dyadic Green Functions in Electromagnetic Theory Second Edition Chen- To Tai, University of Michigan 1994 Hardcover 360 pp Field Theory of Guided Waves Second Edition Robert E. Collin, Case Western Reserve University 1991 Hardcover 864 pp About the series Formerly the IEEE Press Series on Electromagnetic Waves, this new joint series between IEEE Press and Oxford University Press offers even better coverage of the field with new titles as well as reprintings and revisions of recognized classics that maintain long-term archival significance in electromagnetic waves and applications. Designed specifically for graduate students, practicing engineers, and researchers, this series provides affordable volumes that explore electromagnetic waves and applications beyond the undergraduate level.

  • av Frederic R. Morgenthaler
    1 950,-

    * Includes both conventional electromagnetic theory, Maxwell-Poynting representation, and also Alternate representation theory which is more suitable for modern EM environments. Students and theorists can examine two separate theories and witness the same outcomes.

  • av M. Mithat Idemen
    1 570,-

    Filled with new approaches and basic results connected with the discontinuities of the electromagnetic field, this new book offers an important resource for graduate and undergraduate students.

  • av John W. Arthur
    1 740,-

    Provides an easy to understand mathematical tool set for professionals an students in electromagnetic study Non-axiomatic, non-challenging, less formal tutorial approach on the subject Includes appendices with reference material that includes a helpful glossary of terms .

  • av Ismo V. (Helsinki University of Technology) Lindell
    1 926,-

    Electrical Engineering/Electromagnetics Methods for Electromagnetic Field Analysis A volume in the IEEE Series on Electromagnetic Wave Theory Donald G. Dudley, Series Editor a gigantic platter of formulae of the dyadic kind.'--Akhlesh Lakhtaki, Professor, The Pennsylvania State University This monograph discusses mathematical and conceptual methods applicable in the analysis of electromagnetic fields and waves. Dyadic algebra is reviewed and armed with new identities it is applied throughout the book. The power of dyadic operations is seen when working with boundary, sheet and interface conditions, medium equations, field transformations, Greens functions, plane wave problems, vector circuit theory, multipole and image sources. Dyadic algebra offers convenience in handling problems involving chiral and bianisotropic media, of recent interest because of their wide range of potential applications. The final chapter gives, for the first time in book form, a unified presentation of EIT, the exact image theory, introduced by this author and colleagues. EIT is a general method for solving problems involving layered media by replacing them through image sources located in complex space. The main emphasis of the monograph is not on specific results but methods of analysis. The contents should be of interest to scientists doing research work in various fields of electromagnetics, as well as to graduate students. The addition of problems and answers in this reprint will enhance the teaching value of this work. Also in the series Mathematical Foundations for Electromagnetic Theory Donald D. Dudley, University of Arizona, Tucson 1994 Hardcover 256 pp Methods for Electromagnetic Wave Propagation D. S. Jones, University of Dundee 1995 Hardcover 672 pp The Transmission Line Modeling Method: TLM Christos Christopoulos, University of Nottingham 1995 Hardcover 232 pp

  • av Jean G. Van Bladel
    2 156,-

    Electrical Engineering/Electromagnetics Singular Electromagnetic Fields and Sources A volume in the IEEE Series on Electromagnetic Wave Theory Donald D. Dudley, Series Editor 'I will cherish my copy of this gem.'--James R. Wait This is a companion volume to the many available graduate textbooks on electromagnetic theory. It is devoted to a study of the infinities in electromagnetic fields and in their sources. Three types of singularities are investigated: (1) Those associated with strongly concentrated sources of charge and current, the relevant densities are expressed in terms of delta-functions and derivatives. (2) Those associated with the fields resulting from strongly concentrated sources. (3) Those which occur at sharp edges and vertices of cones and sectors. The approach is both theoretical and numerical. The information presented, far from being purely formal, is of importance for practical work. It can be used, for example, to accelerate significantly the convergence of a numerical algorithm. The book is written for electrical engineers and applied physicists who have an interest in the general topic of 'Maxwell's equations' and more particularly for those who are engaged in the actual solution of electromagnetic problems. The mathematical level of the text is that of the 'applied' mathematician. An introductory chapter on 'Distribution Theory' has been written in that spirit. Also in the series Mathematical Foundations for Electromagnetic Theory Donald D. Dudley, University of Arizona, Tucson 1994 Hardcover 256 pp Methods for Electromagnetic Field Analysis Ismo V. Lindell, Helsinki University of Technology 1992 Hardcover 320 pp The Transmission Line Modeling Method: TLM Christos Christopoulos, University of Nottingham 1995 Hardcover 232 pp

  • av Weng Cho (University of Illinois Chew
    2 356,-

    This comprehensive text thoroughly covers fundamental wave propagation behaviors and computational techniques for waves in inhomogeneous media. The author describes powerful and sophisticated analytic and numerical methods to solve electromagnetic problems for complex media and geometry as well. Problems are presented as realistic models of actual situations which arise in the areas of optics, radio wave propagation, geophysical prospecting, nondestructive testing, biological sensing, and remote sensing. Key topics covered include: analytical methods for planarly, cylindrically, and spherically layered media; transient waves, including the Cagniard de Hoop method; variational methods for the scalar wave equation and the electromagnetic wave equation; mode-matching techniqes for inhomogeneous media; the Dyadic Green's function and its role in simplifying problem-solving in inhomogeneous media; integral equation formulations and inverse problems; and time domain techniques for inhomogeneous media. This book will be of interest to electromagnetics and remote sensing engineers, physicists, scientists, and geophysicists. This IEEE Press preprinting of the 1990 version published by Van Nostrand Reinhold incorporates corrections and minor updating.

  • - Antennas, Microwave Circuits, and Scattering Applications
    av John L. (University of Michigan) Volakis, Arindam (Hewlett-Packard) Chatterjee & Leo C. (Mission Research Corp.) Kempel
    2 966,-

    Employed in a large number of commercial electromagnetic simulation packages, the finite element method is one of the most popular and well-established numerical techniques in engineering. This book covers the theory, development, implementation, and application of the finite element method and its hybrid versions to electromagnetics. FINITE ELEMENT METHOD FOR ELECTROMAGNETICS begins with a step-by-step textbook presentation of the finite method and its variations then goes on to provide up-to-date coverage of three dimensional formulations and modern applications to open and closed domain problems. Worked out examples are included to aid the reader with the fine features of the method and the implementation of its hybridization with other techniques for a robust simulation of large scale radiation and scattering. The crucial treatment of local boundary conditions is carefully worked out in several stages in the book. Sponsored by: IEEE Antennas and Propagation Society.

  • - Applied Mathematics in Field Theory
    av Chen-To (Emeritus Tai
    2 170,-

    Unmatched in its coverage of the topic, the first edition of GENERALIZED VECTOR AND DYADIC ANALYSIS helped revolutionize the treatment of boundary-value problems, establishing itself as a classic in the field. This expanded, revised edition is the most comprehensive book available on vector analysis founded upon the new method symbolic vector. GENERALIZED VECTOR AND DYADIC ANALYSIS presents a copious list of vector and dyadic identities, along with various forms of Green's theorems with derivations. In addition, this edition presents an historical study of the past mis-understandings and contradictions that have occurred in vector analysis presentations, furthering the reader's understanding of the subject. Sponsored by: IEEE Antennas and Propagation Society.

  • av Y Zhu
    1 856,-

    The first comprehensive monograph to present state of the art utilization of multigrid methods for enhancing the modelling versatility, numerical robustness and computational efficiency of one of the most popular classes of numerical EM field modeling methods --- the method of finite elements.

  • av Jean G. (University of Ghent Van Bladel
    2 670,-

    To complete the IEEE-Wiley offering in Electromagnetic Theory, this is an important and current revision in a field where our most current text was published in 1991. Responds to the increased interest of the electro-mechanical community in field problems by including numerous examples throughout the text.

  • av Julius Adams (Massachusetts Institute of Technology) Stratton
    1 816,-

    This book is an electromagnetics classic. Originally published in 1941, it has been used by many generations of students, teachers, and researchers ever since. Since it is classic electromagnetics, every chapter continues to be referenced to this day. This classic reissue contains the entire, original edition first published in 1941.

  • - Deterministic and Statistical Theories
    av David A. (Electromagnetics Division Hill
    2 000,-

    Presents a combination of solutions to Maxwell's equations with conservation of energy to solve for the statistics of many quantities of interest: penetration into cavities (and shielding effectiveness), field strengths far from and close to cavity walls, and power received by antennas within cavities.

  • av Lars (Ericsson Microwave Systems (Sweden)) Josefsson
    2 000,-

    This is the first comprehensive treatment of conformal antenna arrays from an engineering perspective. While providing a thorough foundation in theory, the authors of this publication provide a wealth of hands-on instruction for practical analysis and design of conformal antenna arrays.

  • av Roger F. (Syracuse University) Harrington
    2 286,-

    "An IEEE reprinting of this classic 1968 edition, FIELD COMPUTATION BY MOMENT METHODS is the first book to explore the computation of electromagnetic fields by the most popular method for the numerical solution to electromagnetic field problems. It presents a unified approach to moment methods by employing the concepts of linear spaces and functional analysis. Written especially for those who have a minimal amount of experience in electromagnetic theory, this book illustrates theoretical and mathematical concepts to prepare all readers with the skills they need to apply the method of moments to new, engineering-related problems. Written especially for those who have a minimal amount of experience in electromagnetic theory, theoretical and mathematical concepts are illustrated by examples that prepare all readers with the skills they need to apply the method of moments to new, engineering-related problems."

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