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Quaternionic Integral Transforms
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Book Synopsis Quaternionic Integral Transforms by : Eckhard Hitzer
Download or read book Quaternionic Integral Transforms written by Eckhard Hitzer and published by Springer Nature. This book was released on 2023-09-09 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a machine-generated literature overview of quaternion integral transforms from select papers published by Springer Nature, which have been organized and introduced by the book’s editor. Each chapter presents summaries of predefined themes and provides the reader with a basis for further exploration of the topic. As one of the experimental projects initiated by Springer Nature for AI book content generation, this book shows the latest developments in the field. It will be a useful reference for students and researchers who are interested in exploring the latest developments in quaternion integral transforms.
Book Synopsis Rethinking Quaternions by : Ron Goldman
Download or read book Rethinking Quaternions written by Ron Goldman and published by Morgan & Claypool Publishers. This book was released on 2010-05-05 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quaternion multiplication can be used to rotate vectors in three-dimensions. Therefore, in computer graphics, quaternions have three principal applications: to increase speed and reduce storage for calculations involving rotations, to avoid distortions arising from numerical inaccuracies caused by floating point computations with rotations, and to interpolate between two rotations for key frame animation. Yet while the formal algebra of quaternions is well-known in the graphics community, the derivations of the formulas for this algebra and the geometric principles underlying this algebra are not well understood. The goals of this monograph are to provide a fresh, geometric interpretation for quaternions, appropriate for contemporary computer graphics, based on mass-points; to present better ways to visualize quaternions, and the effect of quaternion multiplication on points and vectors in three dimensions using insights from the algebra and geometry of multiplication in the complex plane; to derive the formula for quaternion multiplication from first principles; to develop simple, intuitive proofs of the sandwiching formulas for rotation and reflection; to show how to apply sandwiching to compute perspective projections. In addition to these theoretical issues, we also address some computational questions. We develop straightforward formulas for converting back and forth between quaternion and matrix representations for rotations, reflections, and perspective projections, and we discuss the relative advantages and disadvantages of the quaternion and matrix representations for these transformations. Moreover, we show how to avoid distortions due to floating point computations with rotations by using unit quaternions to represent rotations. We also derive the formula for spherical linear interpolation, and we explain how to apply this formula to interpolate between two rotations for key frame animation. Finally, we explain the role of quaternions in low-dimensional Clifford algebras, and we show how to apply the Clifford algebra for R3 to model rotations, reflections, and perspective projections. To help the reader understand the concepts and formulas presented here, we have incorporated many exercises in order to clarify and elaborate some of the key points in the text. Table of Contents: Preface / Theory / Computation / Rethinking Quaternions and Clif ford Algebras / References / Further Reading / Author Biography
Book Synopsis Quaternion and Clifford Fourier Transforms and Wavelets by : Eckhard Hitzer
Download or read book Quaternion and Clifford Fourier Transforms and Wavelets written by Eckhard Hitzer and published by Birkhäuser. This book was released on 2013-07-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.
Book Synopsis Integral Transforms and Their Applications by : Lokenath Debnath
Download or read book Integral Transforms and Their Applications written by Lokenath Debnath and published by CRC Press. This book was released on 2014-11-07 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic
Book Synopsis Utility of Quaternions in Physics by : Alexander McAulay
Download or read book Utility of Quaternions in Physics written by Alexander McAulay and published by . This book was released on 1893 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Quaternions by : Philip Kelland
Download or read book Introduction to Quaternions written by Philip Kelland and published by . This book was released on 1882 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Integral Transforms by : Naum Il_ich Akhiezer
Download or read book Lectures on Integral Transforms written by Naum Il_ich Akhiezer and published by American Mathematical Soc.. This book was released on 1988-12-31 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on classical integral transforms, principally the Fourier transform, and their applications. This book develops the general theory of the Fourier transform for the space $L DEGREES1(E_n)$ of integrable functions of $n$ var
Book Synopsis Integral Transforms and Their Applications, Second Edition by : Lokenath Debnath
Download or read book Integral Transforms and Their Applications, Second Edition written by Lokenath Debnath and published by CRC Press. This book was released on 2006-10-11 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keeping the style, content, and focus that made the first edition a bestseller, Integral Transforms and their Applications, Second Edition stresses the development of analytical skills rather than the importance of more abstract formulation. The authors provide a working knowledge of the analytical methods required in pure and applied mathematics, physics, and engineering. The second edition includes many new applications, exercises, comments, and observations with some sections entirely rewritten. It contains more than 500 worked examples and exercises with answers as well as hints to selected exercises. The most significant changes in the second edition include: New chapters on fractional calculus and its applications to ordinary and partial differential equations, wavelets and wavelet transformations, and Radon transform Revised chapter on Fourier transforms, including new sections on Fourier transforms of generalized functions, Poissons summation formula, Gibbs phenomenon, and Heisenbergs uncertainty principle A wide variety of applications has been selected from areas of ordinary and partial differential equations, integral equations, fluid mechanics and elasticity, mathematical statistics, fractional ordinary and partial differential equations, and special functions A broad spectrum of exercises at the end of each chapter further develops analytical skills in the theory and applications of transform methods and a deeper insight into the subject A systematic mathematical treatment of the theory and method of integral transforms, the book provides a clear understanding of the subject and its varied applications in mathematics, applied mathematics, physical sciences, and engineering.
Book Synopsis Integral Transforms and Operational Calculus by : H. M. Srivastava
Download or read book Integral Transforms and Operational Calculus written by H. M. Srivastava and published by MDPI. This book was released on 2019-11-20 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their multidisciplinary applications
Book Synopsis Integral Transforms, Reproducing Kernels and Their Applications by : Saburou Saitoh
Download or read book Integral Transforms, Reproducing Kernels and Their Applications written by Saburou Saitoh and published by CRC Press. This book was released on 2020-11-26 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.
Book Synopsis Integral Transforms in Science and Engineering by : K. Wolf
Download or read book Integral Transforms in Science and Engineering written by K. Wolf and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral transforms are among the main mathematical methods for the solution of equations describing physical systems, because, quite generally, the coupling between the elements which constitute such a system-these can be the mass points in a finite spring lattice or the continuum of a diffusive or elastic medium-prevents a straightforward "single-particle" solution. By describing the same system in an appropriate reference frame, one can often bring about a mathematical uncoupling of the equations in such a way that the solution becomes that of noninteracting constituents. The "tilt" in the reference frame is a finite or integral transform, according to whether the system has a finite or infinite number of elements. The types of coupling which yield to the integral transform method include diffusive and elastic interactions in "classical" systems as well as the more common quantum-mechanical potentials. The purpose of this volume is to present an orderly exposition of the theory and some of the applications of the finite and integral transforms associated with the names of Fourier, Bessel, Laplace, Hankel, Gauss, Bargmann, and several others in the same vein. The volume is divided into four parts dealing, respectively, with finite, series, integral, and canonical transforms. They are intended to serve as independent units. The reader is assumed to have greater mathematical sophistication in the later parts, though.
Book Synopsis A Manual of Quaternions by : Charles Jasper Joly
Download or read book A Manual of Quaternions written by Charles Jasper Joly and published by . This book was released on 1905 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elements of Quaternions by : Arthur Sherburne Hardy
Download or read book Elements of Quaternions written by Arthur Sherburne Hardy and published by . This book was released on 1881 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Transforms and their Applications by : B. Davies
Download or read book Integral Transforms and their Applications written by B. Davies and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: In preparing this second edition I have restricted myself to making small corrections and changes to the first edition. Two chapters have had extensive changes made. First, the material of Sections 14.1 and 14.2 has been rewritten to make explicit reference to the book of Bleistein and Handelsman, which appeared after the original Chapter 14 had been written. Second, Chapter 21, on numerical methods, has been rewritten to take account of comparative work which was done by the author and Brian Martin, and published as a review paper. The material for all of these chapters was in fact, prepared for a transla tion of the book. Considerable thought has been given to a much more com prehensive revision and expansion of the book. In particular, there have been spectacular advances in the solution of some non-linear problems using isospectra1 methods, which may be re garded as a generalization of the Fourier transform. However, the subject is a large one, and even a modest introduction would have added substantially to the book. Moreover, the recent book by Dodd et al. is at a similar level to the present volume. Similarly, I have refrained from expanding the chapter on num erical methods into a complete new part of the book, since a specialized monograph on numerical methods is in preparation in collaboration with a colleague.
Book Synopsis Partial Differential and Integral Equations by : Heinrich Begehr
Download or read book Partial Differential and Integral Equations written by Heinrich Begehr and published by Springer Science & Business Media. This book was released on 1999 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent results on partial differential equations as well as with complex analytic methods on singular integral equations and on related subjects are presented. Many of the contributions are survey articles. Topics ranging from elliptic, parabolic, hyperbolic, and mixed-type equations and systems to hyper-complex and quatern ionic analysis, M-analytic, bianalytic, polyharmonic and functions of several complex variables are covered. Applications to mathematical physics are also included. Audience: Specialists in partial differential equations and related topics, with an interest in real and complex methods and in applications to mathematical physics will find this book very useful.
Book Synopsis Integral Expansions Related to Mehler-Fock Type Transforms by : B N Mandal
Download or read book Integral Expansions Related to Mehler-Fock Type Transforms written by B N Mandal and published by CRC Press. This book was released on 2020-11-25 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important class of integral expansions generated by Sturm-Liouville theory involving spherical harmonics is commonly known as Mehler-Fock integral transforms. In this book, a number of integral expansions of such type have been established rigorously. As applications, integral expansions of some simple function are also obtained.
Book Synopsis Integral Transform Techniques for Green's Function by : Kazumi Watanabe
Download or read book Integral Transform Techniques for Green's Function written by Kazumi Watanabe and published by Springer. This book was released on 2015-04-20 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes mathematical techniques for integral transforms in a detailed but concise manner. The techniques are subsequently applied to the standard partial differential equations, such as the Laplace equation, the wave equation and elasticity equations. Green’s functions for beams, plates and acoustic media are also shown, along with their mathematical derivations. The Cagniard-de Hoop method for double inversion is described in detail and 2D and 3D elastodynamic problems are treated in full. This new edition explains in detail how to introduce the branch cut for the multi-valued square root function. Further, an exact closed form Green’s function for torsional waves is presented, as well as an application technique of the complex integral, which includes the square root function and an application technique of the complex integral.
