Principles of Fourier Analysis, Second Edition

Author: Kenneth B. Howell

Publisher: CRC Press

ISBN: 1498734138

Category: Mathematics

Page: 792

View: 5174

Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas. Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author's development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based on the use of Gaussian test functions that yields an even more general -yet simpler -theory than usually presented. Principles of Fourier Analysis stimulates the appreciation and understanding of the fundamental concepts and serves both beginning students who have seen little or no Fourier analysis as well as the more advanced students who need a deeper understanding. Insightful, non-rigorous derivations motivate much of the material, and thought-provoking examples illustrate what can go wrong when formulas are misused. With clear, engaging exposition, readers develop the ability to intelligently handle the more sophisticated mathematics that Fourier analysis ultimately requires.
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Mathematical Principles of Signal Processing

Fourier and Wavelet Analysis

Author: Pierre Bremaud

Publisher: Springer Science & Business Media

ISBN: 147573669X

Category: Mathematics

Page: 270

View: 4154

From the reviews: "[...] the interested reader will find in Bremaud’s book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier and wavelet basics." Mathematical Reviews
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Principles of Harmonic Analysis

Author: Anton Deitmar,Siegfried Echterhoff

Publisher: Springer

ISBN: 3319057928

Category: Mathematics

Page: 332

View: 647

This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.
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Fourier Analysis in Several Complex Variables

Author: Leon Ehrenpreis

Publisher: Courier Corporation

ISBN: 0486153037

Category: Mathematics

Page: 528

View: 5557

Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.
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A First Course in Harmonic Analysis

Author: Anton Deitmar

Publisher: Springer Science & Business Media

ISBN: 9780387228372

Category: Mathematics

Page: 192

View: 8780

Affordable softcover second edition of bestselling title (over 1000 copies sold of previous edition) A primer in harmonic analysis on the undergraduate level Gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory. Entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology. Almost all proofs are given in full and all central concepts are presented clearly. Provides an introduction to Fourier analysis, leading up to the Poisson Summation Formula. Make the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. Introduces the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.
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A Radical Approach to Real Analysis

Author: David M. Bressoud

Publisher: MAA

ISBN: 9780883857472

Category: Mathematics

Page: 323

View: 5279

Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.
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Mathematical Methods for Engineers and Scientists 3

Fourier Analysis, Partial Differential Equations and Variational Methods

Author: Kwong-Tin Tang

Publisher: Springer Science & Business Media

ISBN: 3540446958

Category: Science

Page: 440

View: 4177

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous examples, completely worked out, together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable in using advanced mathematical tools in junior, senior, and beginning graduate courses.
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Reelle und Komplexe Analysis

Author: Walter Rudin

Publisher: Walter de Gruyter

ISBN: 9783486591866

Category: Analysis - Lehrbuch

Page: 499

View: 7319

Besonderen Wert legt Rudin darauf, dem Leser die Zusammenhänge unterschiedlicher Bereiche der Analysis zu vermitteln und so die Grundlage für ein umfassenderes Verständnis zu schaffen. Das Werk zeichnet sich durch seine wissenschaftliche Prägnanz und Genauigkeit aus und hat damit die Entwicklung der modernen Analysis in nachhaltiger Art und Weise beeinflusst. Der "Baby-Rudin" gehört weltweit zu den beliebtesten Lehrbüchern der Analysis und ist in 13 Sprachen übersetzt. 1993 wurde es mit dem renommierten Steele Prize for Mathematical Exposition der American Mathematical Society ausgezeichnet. Übersetzt von Uwe Krieg.
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Trigonometric Series

Author: A. Zygmund

Publisher: Cambridge University Press

ISBN: 9780521890533

Category: Mathematics

Page: 747

View: 2324

Both volumes of classic text on trigonometric series, with a foreword by Robert Fefferman.
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Introductory Fourier Transform Spectroscopy

Author: Robert Bell

Publisher: Elsevier

ISBN: 0323152104

Category: Science

Page: 400

View: 6109

Introductory Fourier Transform Spectroscopy discusses the subject of Fourier transform spectroscopy from a level that requires knowledge of only introductory optics and mathematics. The subject is approached through optical principles, not through abstract mathematics. The book approaches the subject matter in two ways. The first is through simple optics and physical intuition, and the second is through Fourier analysis and the concepts of convolution and autocorrelation. This dual treatment bridges the gap between the introductory material in the book and the advanced material in the journals. The book also discusses information theory, Fourier analysis, and mathematical theorems to complete derivations or to give alternate views of an individual subject. The text presents the development of optical theory and equations to the extent required by the advanced student or researcher. The book is intended as a guide for students taking advanced research programs in spectroscopy. Material is included for the physicists, chemists, astronomers, and others who are interested in spectroscopy.
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Fourier Analysis on Finite Groups and Applications

Author: Audrey Terras

Publisher: Cambridge University Press

ISBN: 9780521457187

Category: Mathematics

Page: 442

View: 5952

A friendly introduction to Fourier analysis on finite groups, accessible to undergraduates/graduates in mathematics, engineering and the physical sciences.
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Harmonic Analysis of Probability Measures on Hypergroups

Author: Walter R. Bloom,Herbert Heyer

Publisher: Walter de Gruyter

ISBN: 3110877597

Category: Mathematics

Page: 607

View: 9544

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
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Higher Engineering Mathematics

Author: John Bird

Publisher: Routledge

ISBN: 185617767X

Category: Technology & Engineering

Page: 679

View: 6448

Now in its sixth edition, Higher Engineering Mathematics is an established textbook that has helped many thousands of students to gain exam success. John Bird's approach is ideal for students from a wide range of academic backgrounds, and can be worked through at the student's own pace. Mathematical theories are examined in the simplest of terms, supported by practical examples and applications from a wide variety of engineering disciplines, to ensure that the reader can apply theory to practice. This extensive and thorough topic coverage makes this an ideal book for a range of university degree modules, foundation degrees, and HNC/D units. This new edition of Higher Engineering Mathematics has been further extended with topics specifically written to help first year engineering degree students and those following foundation degrees. New material has been added on logarithms and exponential functions, binary, octal and hexadecimal numbers, vectors and methods of adding alternating waveforms. This book caters specifically for the engineering mathematics units of the Higher National Engineering schemes from Edexcel, including the core unit Analytical methods for Engineers, and two optional units: Further Analytical Methods for Engineers and Engineering Mathematics, common to both the electrical/electronic engineering and mechanical engineering pathways. A mapping grid is included showing precisely which topics are required for the learning outcomes of each unit. Higher Engineering Mathematics contains examples, supported by 900 worked problems and 1760 further problems contained within exercises throughout the text. In addition, 19 revision tests, which are available to use as tests or as homework are included at regular intervals.
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Fourier series, transforms, and boundary value problems

Author: J. Ray Hanna,John H. Rowland

Publisher: Wiley-Interscience

ISBN: N.A

Category: Mathematics

Page: 354

View: 8030

Retains both the spirit and philosophy of the popular First Edition. The primary changes consist of the addition of new material on integral transforms, discrete and fast Fourier transforms, series solutions, harmonic analysis, spherical harmonics and a glance at some of the numerical techniques for the solution of boundary value problems. With more than enough material for a one-semester course, it offers a full presentation of basic principles, and advanced topics are covered in the largely self-contained closing chapters. The order of presentation of some of the material has been rearranged to provide more flexibility in arranging courses.
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Boundary Value Problems of Applied Mathematics

Second Edition

Author: John L. Troutman,Maurino P. Bautista

Publisher: Courier Dover Publications

ISBN: 0486812227

Category: Mathematics

Page: 528

View: 6759

This text is geared toward advanced undergraduates and graduate students in mathematics who have some familiarity with multidimensional calculus and ordinary differential equations. Includes a substantial number of answers to selected problems. 1994 edition.
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Fundamentals of Fourier Transform Infrared Spectroscopy

Author: Brian C. Smith

Publisher: CRC Press

ISBN: 9780849324611

Category: Science

Page: 224

View: 4113

Fundamentals of Fourier Transform Infrared Spectroscopy teaches the basics of FTIR spectroscopy to those new to the field and serves as an excellent reference for experienced users. This book explains difficult theoretical concepts using diagrams and easy-to-understand language with a minimum of complex mathematics. It contains a unique chapter on spectral data manipulation and a discussion of the 15 pitfalls of quantitative analysis. The comprehensive glossary provides quick and easy access to important FTIR terms.
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Applied Linear Algebra

The Decoupling Principle

Author: Lorenzo Adlai Sadun

Publisher: American Mathematical Soc.

ISBN: 0821844415

Category: Mathematics

Page: 371

View: 5378

Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.
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Harmonic Analysis in Phase Space

Author: G. B. Folland

Publisher: Princeton University Press

ISBN: 9780691085289

Category: Mathematics

Page: 277

View: 470

This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.
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