The 9 best spherical harmonics in physics 2018
Finding the best spherical harmonics in physics suitable for your needs isnt easy. With hundreds of choices can distract you. Knowing whats bad and whats good can be something of a minefield. In this article, weve done the hard work for you.
1. An Elementary Treatise On Fourier's Series and Spherical, Cylindrical,: and Ellipsoidal Harmonics, With Applications To Problems In Mathematical Physics.
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An Elementary Treatise On Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics, With Applications To Problems In Mathematical Physics. By William Elwood Byerly, Ph.D., Professor Of Mathematics In Harvard University ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A Fourier series is a specific type of infinite mathematical series involving trigonometric functions. The series gets its name from a French mathematician and physicist named Jean Baptiste Joseph, Baron de Fourier, who lived during the 18th and 19th centuries. Fourier series are used in applied mathematics, and especially in physics and electronics, to express periodic functions such as those that comprise communications signal waveform Some waveforms are simple, such as the pure sine wave , but these are theoretical ideals. In the real world, most waveforms contain energy at harmonic frequencies (whole-number multiples of the lowest, or fundamental, frequency). The proportion of energy at harmonic frequencies, compared with the energy at the fundamental, depends on the waveform. Fourier series mathematically define such waveforms as functions of displacement (usually amplitude , frequency , or phase ) versus time . As the number of calculated terms in a Fourier series increases, the series more and more closely approximates the exact function that defines a complex signal waveform. Computers can calculate Fourier series out to hundreds, thousands, or millions of terms. About ten years ago I gave a course of lectures on Trigonometric Series. My course has been gradually modified and extended until it has become an introduction to Spherical Harmonics and Bessel's and Lame's Functions. Two years ago my lecture notes were lithographed by my class for their own use and were found so convenient that I have prepared them for publication, hoping that they may prove useful to others as well as to my own students. Meanwhile, Professor Peirce has published his lectures on The Newtonian Potential Function" (Boston, Ginn & Co.), and the two sets of lectures form a course given regularly at Harvard, and intended as a partial introduction to modern Mathematical Physics. Students taking this course are supposed to be familiar with so much of the infinitesimal calculus as is contained in my Differential Calculus" and my Integral Calculus", to which I refer in the present book as Dif. Cal." and Int. Cal." W. E. BYERLY.2. Fundamentals of Spherical Array Processing (Springer Topics in Signal Processing)
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Fundamentals of Spherical Array Processing Springer Topics in Signal ProcessingDescription
This book provides a comprehensive introduction to the theory and practice of spherical microphone arrays. It is written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications.
The first two chapters provide the reader with the necessary mathematical and physical background, including an introduction to the spherical Fourier transform and the formulation of plane-wave sound fields in the spherical harmonic domain.
The third chapter covers the theory of spatial sampling, employed when selecting the positions of microphones to sample sound pressure functions in space. Subsequent chapters present various spherical array configurations, including the popular rigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonics domain, including axis-symmetric beamforming, and the performance measures of directivity index and white noise gain are introduced, and a range of optimal beamformers for spherical arrays, including beamformers that achieve maximum directivity and maximum robustness, and the Dolph-Chebyshev beamformer are developed. The final chapter discusses more advanced beamformers, such as MVDR and LCMV, which are tailored to the measured sound field.
3. An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics, pp. 1-283
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Leopold is delighted to publish this classic book as part of our extensive Classic Library collection. Many of the books in our collection have been out of print for decades, and therefore have not been accessible to the general public. The aim of our publishing program is to facilitate rapid access to this vast reservoir of literature, and our view is that this is a significant literary work, which deserves to be brought back into print after many decades. The contents of the vast majority of titles in the Classic Library have been scanned from the original works. To ensure a high quality product, each title has been meticulously hand curated by our staff. This means that we have checked every single page in every title, making it highly unlikely that any material imperfections such as poor picture quality, blurred or missing text - remain. When our staff observed such imperfections in the original work, these have either been repaired, or the title has been excluded from the Leopold Classic Library catalogue. As part of our on-going commitment to delivering value to the reader, within the book we have also provided you with a link to a website, where you may download a digital version of this work for free. Our philosophy has been guided by a desire to provide the reader with a book that is as close as possible to ownership of the original work. We hope that you will enjoy this wonderful classic work, and that for you it becomes an enriching experience. If you would like to learn more about the Leopold Classic Library collection please visit our website at www.leopoldclassiclibrary.com4. An Elementary Treatise on Fourier's Series and Spherical, Cylindric, and Ellipsoidal Harmonics: With Applications to Problems in Mathematical Physics
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First published in 1893, Byerly's classic treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics has been used in classrooms for well over a century. This practical exposition acts as a primer for fields such as wave mechanics, advanced engineering, and mathematical physics. Topics covered include: . development in trigonometric series . convergence on Fourier's series . solution of problems in physics by the aid of Fourier's integrals and Fourier's series . zonal harmonics . spherical harmonics . cylindrical harmonics (Bessel's functions) . and more. Containing 190 exercises and a helpful appendix, this reissue of Fourier's Series will be welcomed by students of higher mathematics everywhere. American mathematician WILLIAM ELWOOD BYERLY (1849-1935) also wrote Elements of Differential Calculus (1879) and Elements of Integral Calculus (1881).5. Spherical Harmonics and Approximations on the Unit Sphere: An Introduction (Lecture Notes in Mathematics)
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SpringerDescription
These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.6. The Theory of Spherical and Ellipsoidal Harmonics
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Ernest William Hobson (1856-1933) was a prominent English mathematician who held the position of Sadleirian Professor at the University of Cambridge from 1910 to 1931. In this volume, which was originally published in 1931, Hobson focuses on the forms and analytical properties of the functions which arise in connection with those solutions of Laplace's equation which are adapted to the case of particular boundary problems. The investigations take into account functions not, as was the case when they were originally introduced, confined to the cases where degree and order are integral. This is a highly informative book that will be of value to anyone with an interest in spherical and ellipsoidal harmonics.7. Fourier's Series and Spherical Harmonics
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Fourier's series in paperback An elementary trreatise on Fourier's Series and Spherical,Cylindrical and Ellisoidal Harmonics with Appliations to Problems in Mathematical Physics8. An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics, with applications to problems in mathematical physics
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This book was originally published prior to 1923, and represents a reproduction of an important historical work, maintaining the same format as the original work. While some publishers have opted to apply OCR (optical character recognition) technology to the process, we believe this leads to sub-optimal results (frequent typographical errors, strange characters and confusing formatting) and does not adequately preserve the historical character of the original artifact. We believe this work is culturally important in its original archival form. While we strive to adequately clean and digitally enhance the original work, there are occasionally instances where imperfections such as blurred or missing pages, poor pictures or errant marks may have been introduced due to either the quality of the original work or the scanning process itself. Despite these occasional imperfections, we have brought it back into print as part of our ongoing global book preservation commitment, providing customers with access to the best possible historical reprints. We appreciate your understanding of these occasional imperfections, and sincerely hope you enjoy seeing the book in a format as close as possible to that intended by the original publisher.9. Partial Differential Equations of Mathematical Physics (Dover Books on Physics)
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The classical partial differential equations of mathematical physics, formulated by the great mathematicians of the 19th century, remain today the basis of investigation into waves, heat conduction, hydrodynamics, and other physical problems.
In this comprehensive treatment by a well-known Soviet mathematician, the equations are presented and explained in a manner especially designed to be accessible to the novice in the field. The reader is assumed to have no previous knowledge other than elementary analysis. From there, more advanced concepts are developed in detail and with great precision; moreover, theorems are often approached through the study of special simpler cases, before being proved in their full generality, and are applied to many particular physical problems.
After deriving the fundamental equations, the author provides illuminating expositions of such topics as Riemann's method, Lebesgue integration of multiple integrals, the equation of heat conduction, Laplace's equation and Poisson's equation, the theory of integral equations, Green's function, Fourier's method, harmonic polynomials and spherical functions, and much more.
For this third edition, various improvements in style and clarifications of the presentations were made, including a simplification of the theory of multiple Lebesgue integrals and greater precision in the proof of the Fourier method. Finally, the translation is both idiomatic as well as accurate, making the vast amount of information in this book more readily accessible to the English reader.
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