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Author: Kenneth B. Howell
Publisher: CRC Press
ISBN: 1498734081
Category : Mathematics
Languages : en
Pages : 805
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Book Description
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.
Author: Kenneth B. Howell
Publisher: CRC Press
ISBN: 1498734081
Category : Mathematics
Languages : en
Pages : 805
Get Book Here
Book Description
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.
Author: Palle Jorgensen
Publisher: World Scientific
ISBN: 9811269017
Category : Mathematics
Languages : en
Pages : 270
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Book Description
This book presents the mathematics of wavelet theory and its applications in a broader sense, comprising entropy encoding, lifting scheme, matrix factorization, and fractals. It also encompasses image compression examples using wavelet transform and includes the principal component analysis which is a hot topic on data dimension reduction in machine learning.Readers will find equal coverage on the following three themes:The book entails a varied choice of diverse interdisciplinary themes. While the topics can be found in various parts of the pure and applied literature, this book fulfills the need for an accessible presentation which cuts across the fields.As the target audience is wide-ranging, a detailed and systematic discussion of issues involving infinite dimensions and Hilbert space is presented in later chapters on wavelets, transform theory and, entropy encoding and probability. For the problems addressed there, the case of infinite dimension will be more natural, and well-motivated.
Author: Guntram Henrik Herb
Publisher: Rowman & Littlefield
ISBN: 9780847684670
Category : History
Languages : en
Pages : 356
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Book Description
This groundbreaking work explores the vital importance of territory and space to any genuine understanding of nationalism and identity. Too often, the contributors argue, national identity is analyzed apart from the lands that are integral to its formation, as territory is seen as a commodity to be brokered rather than as central to a group's self-definition. This volume combines theoretical insights with structured case studies on how national identity manifests itself in space and at different geographical scales.
Author: Palle E. T. Jorgensen
Publisher: Springer Science & Business Media
ISBN: 0387330828
Category : Mathematics
Languages : en
Pages : 320
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Book Description
Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature
Author: Alan McKane
Publisher: Springer Science & Business Media
ISBN: 1489914218
Category : Science
Languages : en
Pages : 344
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Book Description
The NATO Advanced Study Institute on "Scale Invariance, Interfaces and Non Equilibrium Dynamics" was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK from 20-30 June 1994. The topics discussed at the Institute were all concerned with the origin and nature of complex structures found far from equilibrium. Examples ranged from reaction diffusion systems and hydrodynamics through to surface growth due to deposition. A common theme was that of scale invariance due to the self-similarity of the underly ing structures. The topics that were covered can be broadly classified as pattern for mation (theoretical, computational and experimental aspects), the non-equilibrium dynamics of the growth of interfaces and other manifolds, coarsening phenomena, generic scale invariance in driven systems and the concept of self-organized critical ity. The main feature of the Institute was the four one-hour-Iong lectures given each day by invited speakers. In addition to thirty-seven of these lectures, two contributed lectures were also given. The many questions that were asked after the lectures attested to the excitement and interest that the lecturers succeeded in generating amongst the students. In addition to the discussions initiated by lectures, an im portant component of the meeting were the poster sessions, where participants were able to present their own work, which took place on three of the afternoons. The list of titles given at the end of these proceedings gives some idea of the range and scope of these posters.
Author: Guntram Henrik Herb
Publisher: Rowman & Littlefield Publishers
ISBN: 9781442264755
Category : Social Science
Languages : en
Pages : 294
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Book Description
This volume combines theoretical analysis with a rich set of case studies to understand how national identity is negotiated across spatial scales. As nationalism and identity have continued as critical global flashpoints, this book provides the only up-to-date, comprehensive treatment of the territorial and scalar dimensions of national identity.
Author: Ola Bratteli
Publisher: Springer Science & Business Media
ISBN: 0817642803
Category : Computers
Languages : en
Pages : 424
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Book Description
This book combining wavelets and the world of the spectrum focuses on recent developments in wavelet theory, emphasizing fundamental and relatively timeless techniques that have a geometric and spectral-theoretic flavor. The exposition is clearly motivated and unfolds systematically, aided by numerous graphics. This self-contained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory, and is aimed at a broad readership of graduate students, practitioners, and researchers in applied mathematics and engineering. The book is also useful for other mathematicians with an interest in the interface between mathematics and communication theory.
Author: Alexander D. Poularikas
Publisher: CRC Press
ISBN: 1420066536
Category : Mathematics
Languages : en
Pages : 914
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Book Description
Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.
Author: Jean-Michel Bismut
Publisher: Springer Nature
ISBN: 303127234X
Category : Mathematics
Languages : en
Pages : 181
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Book Description
This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian. Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource for many researchers in geometry, analysis, and mathematical physics.
Author: Kalle Åström
Publisher: Springer Science & Business Media
ISBN: 3642202365
Category : Mathematics
Languages : en
Pages : 355
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Book Description
This book project was initiated at The Tribute Workshop in Honour of Gunnar Sparr and the follow-up workshop Inequalities, Interpolation, Non-commutative, Analysis, Non-commutative Geometry and Applications INANGA08, held at the Centre for Mathematical Sciences, Lund University in May and November of 2008. The resulting book is dedicated in celebration of Gunnar Sparr's sixty-fifth anniversary and more than forty years of exceptional service to mathematics and its applications in engineering and technology, mathematics and engineering education, as well as interdisciplinary, industrial and international cooperation. This book presents new advances in several areas of mathematics and engineering mathematics including applications in modern technology, engineering and life sciences. Thirteen high-quality chapters put forward many new methods and results, reviews of up to date research and open directions and problems for future research. A special chapter by Gunnar Sparr and Georg Lindgren contains a historical account and important aspects of engineering mathematics research and education, and the implementation of the highly successful education programme in Engineering Mathematics at Lund Institute of Technology, where not only the mathematical sciences have played a role. This book will serve as a source of inspiration for a broad spectrum of researchers and research students.
