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Fourier Series and Numerical Methods for Partial Differential Equations
by Richard BernatzThe importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an introduction to the analytical and numerical methods that are essential for working with partial differential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations (ODEs), the book strengthens and extends readers' knowledge of the power of linear spaces and linear transformations for purposes of understanding and solving a wide range of PDEs. The book begins with an introduction to the general terminology and topics related to PDEs, including the notion of initial and boundary value problems and also various solution techniques. Subsequent chapters explore: The solution process for Sturm-Liouville boundary value ODE problems and a Fourier series representation of the solution of initial boundary value problems in PDEs The concept of completeness, which introduces readers to Hilbert spaces The application of Laplace transforms and Duhamel's theorem to solve time-dependent boundary conditions The finite element method, using finite dimensional subspaces The finite analytic method with applications of the Fourier series methodology to linear version of non-linear PDEs Throughout the book, the author incorporates his own class-tested material, ensuring an accessible and easy-to-follow presentation that helps readers connect presented objectives with relevant applications to their own work. Maple is used throughout to solve many exercises, and a related Web site features Maple worksheets for readers to use when working with the book's one- and multi-dimensional problems. Fourier Series and Numerical Methods for Partial Differential Equations is an ideal book for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It is also a reliable resource for researchers and practitioners in the fields of mathematics, science, and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.
Fourier Series and Orthogonal Polynomials: The Carus Mathematical Monographs, No. 6
by Dunham JacksonThis text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followed by chapters on orthogonal, Jacobi, Hermite, and Laguerre polynomials, and the text concludes with a chapter on convergence. 1941 edition.
Fourier Series and Transforms
by R.D HardingThis book helps in giving a qualitative feel for the properties of Fourier series and Fourier transforms by using the illustrative powers of computer graphics. It is useful for wide variety of students as it focuses on qualitative aspects and the flexibility with regard to program modification.
Fourier Series and Transforms
by R.D HardingThis book helps in giving a qualitative feel for the properties of Fourier series and Fourier transforms by using the illustrative powers of computer graphics. It is useful for wide variety of students as it focuses on qualitative aspects and the flexibility with regard to program modification.
Fourier Series, Fourier Transform and Their Applications to Mathematical Physics (Applied Mathematical Sciences #197)
by Valery SerovThis text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory of partial differential equations. Complete with nearly 250 exercises throughout, this text is intended for graduate level students and researchers in the mathematical sciences and engineering.
Fourier Series in Control Theory (Springer Monographs in Mathematics)
by Vilmos Komornik Paola LoretiThis book is the first serious attempt to gather all of the available theory of "nonharmonic Fourier series" in one place, combining published results with new results by the authors.
Fourier Techniques and Applications
by John F. PriceThe first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua non of Fourier analysis and synthesis, has led to the routine use of the methods originating with Fourier in a great diversity of areas - astrophysics, computing, economics, electrical engineering, geophysics, information theory, medical engineering, optics, petroleum and mineral exploration, quan tum physics and spectroscopy, to name a few.
Fourier Theory in Optics and Optical Information Processing (Multidisciplinary and Applied Optics)
by Toyohiko YatagaiFourier analysis is one of the most important concepts when you apply physical ideas to engineering issues. This book provides a comprehensive understanding of Fourier transform and spectral analysis in optics, image processing, and signal processing. Written by a world renowned author, this book looks to unify the readers understanding of principles of optics, information processing and measurement. This book describes optical imaging systems through a linear system theory. The book also provides an easy understanding of Fourier transform and system theory in optics. It also provides background of optical measurement and signal processing. Finally, the author also provides a systematic approach to learning many signal processing techniques in optics. The book is intended for researchers, industry professionals, and graduate level students in optics and information processing.
Fourier Theory in Optics and Optical Information Processing (Multidisciplinary and Applied Optics)
by Toyohiko YatagaiFourier analysis is one of the most important concepts when you apply physical ideas to engineering issues. This book provides a comprehensive understanding of Fourier transform and spectral analysis in optics, image processing, and signal processing. Written by a world renowned author, this book looks to unify the readers understanding of principles of optics, information processing and measurement. This book describes optical imaging systems through a linear system theory. The book also provides an easy understanding of Fourier transform and system theory in optics. It also provides background of optical measurement and signal processing. Finally, the author also provides a systematic approach to learning many signal processing techniques in optics. The book is intended for researchers, industry professionals, and graduate level students in optics and information processing.
The Fourier Transform in Biomedical Engineering (Applied and Numerical Harmonic Analysis)
by Terry M. Peters Jacqueline C. WilliamsIn 1994, in my role as Technical Program Chair for the 17th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, I solicited proposals for mini-symposia to provide delegates with accessible summaries of important issues in research areas outside their particular specializations. Terry Peters and his colleagues submitted a proposal for a symposium on Fourier Trans forms and Biomedical Engineering whose goal was "to demystify the Fourier transform and describe its practical application in biomedi cal situations". This was to be achieved by presenting the concepts in straightforward, physical terms with examples drawn for the parti cipants work in physiological signal analysis and medical imaging. The mini-symposia proved to be a great success and drew a large and appreciative audience. The only complaint being that the time allocated, 90 minutes, was not adequate to allow the participants to elaborate their ideas adequately. I understand that this feedback helped the authors to develop this book.
Fourier Transformation for Pedestrians (Undergraduate Lecture Notes in Physics)
by Tilman ButzThis book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on window functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions.
Fourier Transformation for Pedestrians
by Tilman ButzCovers Fourier transformation and Fourier series with a particular emphasis on window functions. Written for students and practitioners who deal with Fourier transformation. Including many illustrations and easy-to-solve exercises Presents serious science in an amusing way
Fourier Transformation for Signal and System Description: Compact, Visual, Intuitively Understandable (essentials)
by Jörg Lange Tatjana LangeThe authors explain the Fourier transform and its technical applications, especially in signal and system theory. Based on their many years of teaching experience, they aim at helping especially STEM (science, technology, engineering, and mathematics) students as well as graduated professionals to better understand the subject. The authors also point out the importance of a deeper understanding, as all modern digital technologies such as sound and image recording and storage, radio and television, mobile telephony, signal transmission for the Internet, modern control techniques for vehicles or aircrafts – are largely based on the Fourier transform. The Authors Prof. Dr.-Ing. habil. Jörg Lange held a leading position in the development area of mobile communications in a large technology company. Prof. Dr.-Ing. Tatjana Lange taught control systems engineering at Merseburg University of Applied Sciences and is still active in research in the area of classification and cluster analysis.This Springer essential is a translation of the original German 1st edition essentials, Fourier-Transformation zur Signal- und Systembeschreibung by Jörg Lange and Tatjana Lange, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2019. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
Fourier-Transformation zur Signal- und Systembeschreibung: Kompakt, visuell, intuitiv verständlich (essentials)
by Jörg Lange Tatjana LangeDie Autoren erläutern die Fourier-Transformation und ihre technischen Anwendungen, insbesondere in der Signal- und Systemtheorie, dank ihrer langjährigen Erfahrungen sehr anschaulich. Sie möchten insbesondere MINT-Studenten und natürlich auch im Beruf stehenden Absolventen helfen, die Materie besser zu verstehen. Die Autoren zeigen zudem die Wichtigkeit eines vertieften Verständnisses auf, da alle modernen digitalen Techniken – wie Ton- und Bildaufzeichnung und Speicherung, Rundfunk und Fernsehen, Mobilfunk, Signalübertragung für das Internet, moderne Regelungstechniken für Fahrzeuge oder Flugzeuge – weitgehend auf den Erkenntnissen der Fourier-Transformation basieren.Die AutorenProf. Dr.-Ing. habil. Jörg Lange war in leitender Position im Entwicklungsbereich Mobilfunk in einem Technologiekonzern tätig, bevor er in Ruhestand ging.Prof. Dr.-Ing. Tatjana Lange lehrte vor ihrem Ruhestand Automatisierungstechnik an der Hochschule Merseburg und ist weiterhin in der Forschung aktiv.
Fourier Transforms: Principles and Applications
by Eric W. HansenFourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors—ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers. Class-tested at Dartmouth Provides the same solid background as classic texts in the field, but with an emphasis on digital and other contemporary applications to signal and image processing Modular coverage of material allows for topics to be covered by preference MATLAB files and Solutions Manual available to instructors Over 300 figures, 200 worked examples, and 432 homework problems
Fourier Transforms: Principles and Applications
by Eric W. HansenFourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors—ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers. Class-tested at Dartmouth Provides the same solid background as classic texts in the field, but with an emphasis on digital and other contemporary applications to signal and image processing Modular coverage of material allows for topics to be covered by preference MATLAB files and Solutions Manual available to instructors Over 300 figures, 200 worked examples, and 432 homework problems
Fourier Transforms. (AM-19), Volume 19
by Salomon Bochner Komaravolu ChandrasekharanThe description for this book, Fourier Transforms. (AM-19), Volume 19, will be forthcoming.
Fourier Transforms, Filtering, Probability and Random Processes: Introduction to Communication Systems (Synthesis Lectures on Communications)
by Jerry D. GibsonThis book provides backgrounds and the mathematical methods necessary to understand the basic transforms in signal processing and linear systems to prepare for in depth study of analog and digital communications systems.This tutorial presentation provides developments of Fourier series and other orthogonal series, including trigonometric and complex exponential Fourier series, least squares approximations and generalized Fourier series, and the spectral content of periodic signals. This text thoroughly covers Fourier transform pairs for continuous time signals, Fourier transform properties, and the magnitude and phase of Fourier transforms. The author includes discussions of techniques for the analysis of continuous time linear systems in the time and frequency domains with particular emphasis on the system transfer function, impulse response, system/filter bandwidth, power and energy calculations, and the time domain sampling theorem.
Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras (Lecture Notes in Mathematics #1859)
by Emmanuel LetellierThe Fourier transforms of invariant functions on finite reductive Lie algebras are due to T.A. Springer (1976) in connection with the geometry of nilpotent orbits. In this book the author studies Fourier transforms using Deligne-Lusztig induction and the Lie algebra version of Lusztig’s character sheaves theory. He conjectures a commutation formula between Deligne-Lusztig induction and Fourier transforms that he proves in many cases. As an application the computation of the values of the trigonometric sums (on reductive Lie algebras) is shown to reduce to the computation of the generalized Green functions and to the computation of some fourth roots of unity.
Fouriertranformation für Fußgänger
by Tilman ButzDieses Werk ist ein unterhaltsames Lehrbuch. Es wendet sich an alle, die in der Ausbildung und in ihrer beruflichen Praxis mit Fouriertransformationen zu tun haben. Dabei sind elementare Kenntnisse der Integralrechnung wünschenswert. Das Buch behandelt sowohl Fourierreihen als auch kontinuierliche und diskrete Fouriertransformationen. Zahlreiche Abbildungen und Beispiele, die vom Leser meist von Hand nachgerechnet werden können, machen den Stoff leicht verständlich.
Fouriertransformation für Fußgänger
by Tilman ButzDieses unterhaltsame Lehrbuch wendet sich an alle, die in der Ausbildung und in ihrer beruflichen Praxis mit Fouriertransformationen zu tun haben. Das Buch behandelt sowohl Fourierreihen als auch kontinuierliche und diskrete Fouriertransformationen. Außerdem werden Fensterfunktionen ausführlich diskutiert. Zahlreiche Abbildungen und Beispiele, die vom Leser meist von Hand nachgerechnet werden können, machen den Stoff leicht verständlich.
Fouriertransformation für Fußgänger
by Tilman ButzDieses Werk ist ein unterhaltsames Lehrbuch. Es wendet sich an alle, die in der Ausbildung und in ihrer beruflichen Praxis mit Fouriertransformationen zu tun haben: Studenten der Ingenieur- und Naturwissenschaften, aber auch Praktiker, die Spektralanalysen oder Fouriertransformationsmethoden benötigen. Dabei sind elementare Kenntnisse der Integralrechnung wünschenswert. Das Buch behandelt sowohl Fourierreihen als auch kontinuierliche und diskrete Fouriertransformationen. Zahlreiche Abbildungen und Beispiele, die vom Leser meist von Hand nachgerechnet werden können, machen den Stoff leicht verdaulich.
Fouriertransformation für Fußgänger
by Tilman ButzDieses unterhaltsame Lehrbuch wendet sich an alle, die in der Ausbildung und in ihrer beruflichen Praxis mit Fouriertransformationen zu tun haben. Das Buch behandelt sowohl Fourierreihen als auch kontinuierliche und diskrete Fouriertransformationen. Außerdem werden Fensterfunktionen ausführlich diskutiert. Zahlreiche Abbildungen und Beispiele, die vom Leser meist von Hand nachgerechnet werden können, machen den Stoff leicht verständlich.
Fouriertransformation für Fußgänger
by Tilman ButzDiese Schrift ist ein unterhaltsames Lehrbuch. Es wendet sich an alle, die in der Ausbildung und in ihrer beruflichen Praxis mit Fouriertransformationen zu tun haben. Das Buch behandelt sowohl Fourierreihen als auch kontinuierliche und diskrete Fouriertransformationen. Außerdem werden Fensterfunktionen ausführlich diskutiert. Zahlreiche Abbildungen und Beispiele, die vom Leser meist von Hand nachgerechnet werden können, machen den Stoff leicht verständlich. Die vierte Auflage enthält einige Verbesserungen und am Ende der jeweiligen Kapitel zahlreiche neue Aufgaben - genannt "Spielwiese" - mit Lösungen im Anhang.
