Distribution, Integral Transforms and Applications PDF Download

Author: W. Kierat
Publisher: CRC Press
ISBN: 1482264811
Category : Mathematics
Languages : en
Pages : 158

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Book Description
The theory of distributions is most often presented as L. Schwartz originally presented it: as a theory of the duality of topological vector spaces. Although this is a sound approach, it can be difficult, demanding deep prior knowledge of functional analysis. The more elementary treatments that are available often consider distributions as limits o

Author: Ram Shankar Pathak
Publisher: Routledge
ISBN: 135156269X
Category : History
Languages : en
Pages : 432

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Book Description
For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians and engineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of research and includes important results from other works.

Author: Kazumi Watanabe
Publisher: Springer
ISBN: 331917455X
Category : Technology & Engineering
Languages : en
Pages : 274

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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: Petre Teodorescu
Publisher: John Wiley & Sons
ISBN: 3527653635
Category : Science
Languages : en
Pages : 379

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Book Description
In this comprehensive monograph, the authors apply modern mathematical methods to the study of mechanical and physical phenomena or techniques in acoustics, optics, and electrostatics, where classical mathematical tools fail. They present a general method of approaching problems, pointing out different aspects and difficulties that may occur. With respect to the theory of distributions, only the results and the principle theorems are given as well as some mathematical results. The book also systematically deals with a large number of applications to problems of general Newtonian mechanics, as well as to problems pertaining to the mechanics of deformable solids and physics. Special attention is placed upon the introduction of corresponding mathematical models. Addressed to a wide circle of readers who use mathematical methods in their work: applied mathematicians, engineers in various branches, as well as physicists, while also benefiting students in various fields.

Author: Brychkov
Publisher: CRC Press
ISBN: 9782881247057
Category : Mathematics
Languages : en
Pages : 362

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Book Description
English translation (from revised and enlarged versions of the Russian editions of 1977 and 1984) of a reference work which makes available to engineers, physicists and applied mathematicians theoretical and tabular material pertaining to certain extensions of standard integral transform techniques. Diverse transforms are touched upon, but the emphasis (particularly in the tables) is on generalized Fourier and Laplace transforms. Some multi-dimensional results are presented. Expensive, but nicely produced, and redundant with nothing standard to the reference shelves of mathematical libraries. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Author: Hari Mohan Srivastava
Publisher: MDPI
ISBN: 3039368826
Category : Science
Languages : en
Pages : 220

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Book Description
This volume consists of a collection of 14 accepted submissions (including several invited feature articles) to the Special Issue of MDPI's journal Symmetry on the general subject area of integral transformations, operational calculus and their applications from many different parts around the world. The main objective of the Special Issue was to gather review, expository, and original research articles dealing with the state-of-the-art advances in integral transformations and operational calculus as well as their multidisciplinary applications, together with some relevance to the aspect of symmetry. Various families of fractional-order integrals and derivatives have been found to be remarkably important and fruitful, mainly due to their demonstrated applications in numerous diverse and widespread areas of mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional-order operators provide potentially useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations; fractional-calculus analogues and extensions of each of these equations; and various other problems involving special functions of mathematical physics and applied mathematics, as well as their extensions and generalizations in one or more variables.

Author: Lokenath Debnath
Publisher: CRC Press
ISBN: 1420010913
Category : Mathematics
Languages : en
Pages : 723

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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: Dr. B. B. Waphare
Publisher: Lulu Publication
ISBN: 1684742080
Category : Art
Languages : en
Pages : 16

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Book Description
1.1 Introduction In recent years, integral transforms have become essential working tools of every engineer and applied scientist. The Laplace transform, which undoubtedly is the most familiar example, is being suited to solving boundary value problems. The classical methods of solution of initial and boundary value problems in physics and engineering sciences have their roots in Fourier’s pioneering work. An alternative approach through integral transforms methods emerged primarily through Heaviside’s efforts on operational techniques. In addition to being of great theoretical interest to mathematicians, integral transform methods have been found to provide easy and effective ways of solving a variety of problems arising in engineering and physical science. The use of integral transforms is somewhat analogous to that of logarithms. That is, a problem involving multiplication or division can be reduced to one involving simple processes addition or subtraction by taking logarithms. For almost two centuries the method of function transformations has been used successfully in solving many problems in engineering, mathematical physics and applied mathematics. Function transformations include, but are not limited to the well-known technique of linear integral transformations. A function transformation simply means a mathematical operation through which a real or complex valued function f is transformed into an other F, or into a sequence of numbers, or more generally into a set of data. Since its birth in the 1780’s in the work of the great mathematician Laplace, on probability theory, the theory of function transformations has flourished and continues to do so. In the last few years, in particular, it has received a great impetus from the advent of wavelets. Not only is the wavelet transform an example of how practical function transformations can be, but it is also an example of a transformation that has gone beyond what it was designed to do as a technique. It has contributed to the development of modern mathematical analysis just as the Fourier transformation contributed to the advancement of classical analysis in the earliest years of the nineteenth century.

Author: Alexander D. Poularikas
Publisher: CRC Press
ISBN: 1420066536
Category : Mathematics
Languages : en
Pages : 911

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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: Robert S. Strichartz
Publisher: World Scientific
ISBN: 9789812384300
Category : Mathematics
Languages : en
Pages : 238

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Book Description
This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.