A Handbook Of Fourier Theorems
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A Handbook Of Fourier Theorems
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Author : D. C. Champeney
language : en
Publisher: Cambridge University Press
Release Date : 1989-01-27
A Handbook Of Fourier Theorems written by D. C. Champeney and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-27 with Mathematics categories.
This book is concerned with the well-established mathematical technique known as Fourier analysis (or alternatively as harmonic or spectral analysis). It is a handbook comprising a collection of the most important theorems in Fourier analysis, presented without proof in a form that is accurate but also accessible to a reader who is not a specialist mathematician. The technique of Fourier analysis has long been of fundamental importance in the physical sciences, engineering and applied mathematics, and is today of particular importance in communications theory and signal analysis. Existing books on the subject are either rigorous treatments, intended for mathematicians, or are intended for non-mathematicians, and avoid the finer points of the theory. This book bridges the gap between the two types. The text is self-contained in that it includes examples of the use of the various theorems, and any mathematical concepts not usually included in degree courses in physical sciences and engineering are explained. This handbook will be of value to postgraduates and research workers in the physical sciences and in engineering subjects, particularly communications and electronic engineering.
Fourier Transforms In Nmr Optical And Mass Spectrometry
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Author : A.G. Marshall
language : en
Publisher: Elsevier
Release Date : 2016-02-25
Fourier Transforms In Nmr Optical And Mass Spectrometry written by A.G. Marshall and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-25 with Science categories.
Written by spectroscopists for spectroscopists, here is a book which is not only a valuable handbook and reference work, but also an ideal teaching text for Fourier transform methods as they are applied in spectroscopy. It offers the first unified treatment of the three most popular types of FT/spectroscopy, with uniform notation and complete indexing of specialized terms. All mathematics is self-contained, and requires only a knowledge of simple calculus. The main emphasis is on pictures and physical analogs rather than detailed algebra. Instructive problems, presented at the end of each chapter, offer extensions of the basic treatment. Solutions are given or outlined for all problems.The book offers a wealth of practical information to spectroscopists. Non-ideal effects are treated in detail: noise (source- and detector-limited); non-linear response; limits to spectrometer performance based on finite detection period, finite data size, mis-phasing, etc. Common puzzles and paradoxes are explained: e.g. use of mathematically complex variables to represent physically real quantities; interpretation of negative frequency signals; on-resonance vs. off-resonance response; interpolation (when it helps and when it doesn't); ultimate accuracy of the data; differences between linearly- and circularly-polarized radiation; multiplex advantage or disadvantage, etc.Chapter 1 introduces the fundamental line shapes encountered in spectroscopy, from a simple classical mass-on-a-spring model. The Fourier transform relationship between the time-domain response to a sudden impulse and the steady-state frequency-domain response (absorption and dispersion spectra) to a continuous oscillation is established and illustrated. Chapters 2 and 3 summarize the basic mathematics (definitions, formulas, theorems, and examples) for continuous (analog) and discrete (digital) Fourier transforms, and their practical implications. Experimental aspects which are common to the signal (Chapter 4) and noise (Chapter 5) in all forms of Fourier transform spectrometry are followed by separate chapters for treatment of those features which are unique to FT/MS, FT/optical, FT/NMR, and other types of FT/spectroscopy.The list of references includes both historical and comprehensive reviews and monographs, along with articles describing several key developments. The appendices provide instant access to FT integrals and fast algorithms as well as a pictorial library of common Fourier transform function pairs. The comprehensive index is designed to enable the reader to locate particular key words, including those with more than one name.
A Handbook Of Terms Used In Algebra And Analysis
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Author : A. G. Howson
language : en
Publisher: Cambridge University Press
Release Date : 1972-09-07
A Handbook Of Terms Used In Algebra And Analysis written by A. G. Howson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-09-07 with Mathematics categories.
Degree students of mathematics are often daunted by the mass of definitions and theorems with which they must familiarize themselves. In the fields algebra and analysis this burden will now be reduced because in A Handbook of Terms they will find sufficient explanations of the terms and the symbolism that they are likely to come across in their university courses. Rather than being like an alphabetical dictionary, the order and division of the sections correspond to the way in which mathematics can be developed. This arrangement, together with the numerous notes and examples that are interspersed with the text, will give students some feeling for the underlying mathematics. Many of the terms are explained in several sections of the book, and alternative definitions are given. Theorems, too, are frequently stated at alternative levels of generality. Where possible, attention is drawn to those occasions where various authors ascribe different meanings to the same term. The handbook will be extremely useful to students for revision purposes. It is also an excellent source of reference for professional mathematicians, lecturers and teachers.
Mathematical Handbook For Scientists And Engineers
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Author : Granino Arthur Korn
language : en
Publisher: Courier Corporation
Release Date : 2000-01-01
Mathematical Handbook For Scientists And Engineers written by Granino Arthur Korn and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
Convenient access to information from every area of mathematics: Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, game theory, much more.
A Guide To Distribution Theory And Fourier Transforms
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Author : Robert S. Strichartz
language : en
Publisher: World Scientific
Release Date : 2003
A Guide To Distribution Theory And Fourier Transforms written by Robert S. Strichartz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.
The Fourier Transform And Its Applications
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Author : Ronald Newbold Bracewell
language : en
Publisher:
Release Date : 1978
The Fourier Transform And Its Applications written by Ronald Newbold Bracewell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Fourier transformations categories.
A Student S Guide To Fourier Transforms
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Author : J. F. James
language : en
Publisher: Cambridge University Press
Release Date : 2002-09-19
A Student S Guide To Fourier Transforms written by J. F. James and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-19 with Mathematics categories.
Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science.
A Student S Guide To Fourier Transforms
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Author : J. F. James
language : en
Publisher: Cambridge University Press
Release Date : 2011-03-31
A Student S Guide To Fourier Transforms written by J. F. James and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-31 with Science categories.
Fourier transform theory is of central importance in a vast range of applications in physical science, engineering and applied mathematics. Providing a concise introduction to the theory and practice of Fourier transforms, this book is invaluable to students of physics, electrical and electronic engineering, and computer science. After a brief description of the basic ideas and theorems, the power of the technique is illustrated through applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of Computer Axial Tomography (CAT scanning). The book concludes by discussing digital methods, with particular attention to the Fast Fourier Transform and its implementation. This new edition has been revised to include new and interesting material, such as convolution with a sinusoid, coherence, the Michelson stellar interferometer and the van Cittert–Zernike theorem, Babinet's principle and dipole arrays.
Scattering Methods And Their Application In Colloid And Interface Science
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Author : Otto Glatter
language : en
Publisher: Elsevier
Release Date : 2018-01-08
Scattering Methods And Their Application In Colloid And Interface Science written by Otto Glatter and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-08 with Technology & Engineering categories.
Scattering Methods and their Application in Colloid and Interface Science offers an overview of small-angle X-ray and neutron scattering techniques (SAXS & SANS), as well as static and dynamic light scattering (SLS & DLS). These scattering techniques are central to the study of soft matter, such as colloidal dispersions and surfactant self-assembly. The theoretical concepts are followed by an overview of instrumentation and a detailed description of the evaluation techniques in the first part of the book. In the second part, several typical application examples are used to show the strength and limitations of these techniques. - Features the latest input from the world-leading expert with personal experience in all the fields covered (SAXS, SANS, SLS and DLS) - Includes unified notation throughout the book to enhance its readability - Provides—in a single source—scattering theory, evaluation of techniques and a variety of applications
Electromagnetic Anisotropy And Bianisotropy
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Author : Tom G. Mackay
language : en
Publisher: World Scientific
Release Date : 2010
Electromagnetic Anisotropy And Bianisotropy written by Tom G. Mackay and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
The topics of anisotropy and bianisotropy are fundamental to electromagnetics from both theoretical and experimental perspectives. These properties underpin a host of complex and exotic electromagnetic phenomenons in naturally occurring materials and in relativistic scenarios, as well as in artificially produced metamaterials. As a unique guide to this rapidly developing field, the book provides a unified presentation of key classic and recent results on the studies of constitutive relations, spacetime symmetries, planewave propagation, dyadic Green functions, and homogenization of composite materials. This book also offers an up-to-date extension to standard treatments of crystal optics with coverage on both linear and weakly nonlinear regimes.