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Author: Naum Il_ich Akhiezer Publisher: American Mathematical Soc. ISBN: 0821845241 Category : Mathematics Languages : en Pages : 118
Book Description
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
Author: Naum Il_ich Akhiezer Publisher: American Mathematical Soc. ISBN: 0821845241 Category : Mathematics Languages : en Pages : 118
Book Description
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
Author: Kazumi Watanabe Publisher: Springer ISBN: 331917455X Category : Technology & Engineering Languages : en Pages : 274
Book Description
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.
Author: B. Davies Publisher: Springer Science & Business Media ISBN: 1475755120 Category : Mathematics Languages : en Pages : 427
Book Description
This book is intended to serve as introductory and reference material for the application of integral transforms to a range of common mathematical problems. It has its im mediate origin in lecture notes prepared for senior level courses at the Australian National University, although I owe a great deal to my colleague Barry Ninham, a matter to which I refer below. In preparing the notes for publication as a book, I have added a considerable amount of material ad- tional to the lecture notes, with the intention of making the book more useful, particularly to the graduate student - volved in the solution of mathematical problems in the physi cal, chemical, engineering and related sciences. Any book is necessarily a statement of the author's viewpoint, and involves a number of compromises. My prime consideration has been to produce a work whose scope is selective rather than encyclopedic; consequently there are many facets of the subject which have been omitted--in not a few cases after a preliminary draft was written--because I v believe that their inclusion would make the book too long.
Author: Lokenath Debnath Publisher: CRC Press ISBN: 1420010913 Category : Mathematics Languages : en Pages : 723
Book Description
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.
Author: Lokenath Debnath Publisher: CRC Press ISBN: 1482223570 Category : Mathematics Languages : en Pages : 820
Book Description
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 development of the underlying theory as well as a modern approach to Fourier, Laplace, Hankel, Mellin, Radon, Gabor, wavelet, and Z transforms and their applications. New to the Third Edition New material on the historical development of classical and modern integral transforms New sections on Fourier transforms of generalized functions, the Poisson summation formula, the Gibbs phenomenon, and the Heisenberg uncertainty principle Revised material on Laplace transforms and double Laplace transforms and their applications New examples of applications in mechanical vibrations, electrical networks, quantum mechanics, integral and functional equations, fluid mechanics, mathematical statistics, special functions, and more New figures that facilitate a clear understanding of physical explanations Updated exercises with solutions, tables of integral transforms, and bibliography Through numerous examples and end-of-chapter exercises, this book develops readers’ analytical and computational skills in the theory and applications of transform methods. It provides accessible working knowledge of the analytical methods and proofs required in pure and applied mathematics, physics, and engineering, preparing readers for subsequent advanced courses and research in these areas.
Author: Brian Davies Publisher: Springer Science & Business Media ISBN: 1468492837 Category : Mathematics Languages : en Pages : 380
Book Description
This is a substantially updated, extended and reorganized third edition of an introductory text on the use of integral transforms. Chapter I is largely new, covering introductory aspects of complex variable theory. Emphasis is on the development of techniques and the connection between properties of transforms and the kind of problems for which they provide tools. Around 400 problems are accompanied in the text. It will be useful for graduate students and researchers working in mathematics and physics.
Author: Brad G. Osgood Publisher: American Mathematical Soc. ISBN: 1470441918 Category : Mathematics Languages : en Pages : 713
Book Description
This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques—all of which are important in many areas of engineering and science—the author's goal is to help engineering and science students cultivate more advanced mathematical know-how and increase confidence in learning and using mathematics, as well as appreciate the coherence of the subject. He promises the readers a little magic on every page. The section headings are all recognizable to mathematicians, but the arrangement and emphasis are directed toward students from other disciplines. The material also serves as a foundation for advanced courses in signal processing and imaging. There are over 200 problems, many of which are oriented to applications, and a number use standard software. An unusual feature for courses meant for engineers is a more detailed and accessible treatment of distributions and the generalized Fourier transform. There is also more coverage of higher-dimensional phenomena than is found in most books at this level.
Author: Ian Naismith Sneddon Publisher: ISBN: Category : Elastic solids Languages : en Pages : 130
Book Description
Contents: The Stress Intensity Factor for a Griffith Crack in an Elastic Body in which Body Forces are acting; The Stress Intensity Factor for a Penny-Shaped Crack in an Elastic Body under the Action of Symmetric Body Forces -- The Effect of Two Point Forces Symmetrically Placed; Inversion Formulae for Integral Transform Pairs of General Kinds -- Properties of the Mellin Transform, Y - Transforms, Integral equations of Abel type, Transforms whose kernels are Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated Legendre functions, and Hypergeometric functions; The Inversion of Hankel Transforms of Order Zero and Unity; and Lectures on Kontorovich-Lebedev Transforms and Some of their Applications -- Solutions of Bessel's Modified Equation, The Macdonald Function, Table of Kontorovich-Lebedev Transforms, Parseval Relation for Kontorovich-Lebedev Transforms, Functions which are Harmonic in an Infinite Wedge, in a Semi-Infinite Wedge, in a Wedge of Finite Thickness, and Applications in the Theory of Elasticity.
Author: Naum Il_ich Akhiezer
Author: Naum Il_ich Akhiezer
Author: Kazumi Watanabe
Author: B. Davies
Author: Lokenath Debnath
Author: Naum Ilʹich Akhiezer
Author: Lokenath Debnath
Author: Matthew C. M. Wright
Author: Brian Davies
Author: Brad G. Osgood
Author: Ian Naismith Sneddon