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Delta Functions
Author : R F Hoskins
Publisher : Horwood Publishing
Release Date : 2009-04-14
ISBN 10 : 9781904275398
Pages : 270 pages
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Delta Functions has now been updated, restructured and modernised into a second edition, to answer specific difficulties typically found by students encountering delta functions for the first time. In particular, the treatment of the Laplace transform has been revised with this in mind. The chapter on Schwartz distributions has been considerably extended and the book is supplemented by a fuller review of Nonstandard Analysis and a survey of alternative infinitesimal treatments of generalised functions. Dealing with a difficult subject in a simple and straightforward way, the text is readily accessible to a broad audience of scientists, mathematicians and engineers. It can be used as a working manual in its own right, and serves as a preparation for the study of more advanced treatises. Little more than a standard background in calculus is assumed, and attention is focused on techniques, with a liberal selection of worked examples and exercises. Second edition has been updated, restructured and modernised to answer specific difficulties typically found by students encountering delta functions for the first time Attention is focused on techniques, with a liberal selection of worked examples and exercises Readily accessible to a broad audience of scientists, mathematicians and engineers and can be used as a working manual in its own right

Delta Function Expansions, Complex Delta Functions and the Steepest-descent Method
Author : Ismo V. Lindell
Publisher : N.A
Release Date : 1992
ISBN 10 : 9789512209668
Pages : 10 pages
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An Introduction to Statistical Mechanics and Thermodynamics
Author : Robert Swendsen
Publisher : Oxford University Press, USA
Release Date : 2020-02-10
ISBN 10 : 0198853238
Pages : 448 pages
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An Introduction to Statistical Mechanics and Thermodynamics returns with a second edition which includes new chapters, further explorations, and updated information into the study of statistical mechanics and thermal dynamics. The first part of the book derives the entropy of the classical ideal gas, using only classical statistical mechanics and an analysis of multiple systems first suggested by Boltzmann. The properties of the entropy are then expressed as "postulates" of thermodynamics in the second part of the book. From these postulates, the formal structure of thermodynamics is developed. The third part of the book introduces the canonical and grand canonical ensembles, which are shown to facilitate calculations for many model systems. An explanation of irreversible phenomena that is consistent with time-reversal invariance in a closed system is presented. The fourth part of the book is devoted to quantum statistical mechanics, including black-body radiation, the harmonic solid, Bose-Einstein and Fermi-Dirac statistics, and an introduction to band theory, including metals, insulators, and semiconductors. The final chapter gives a brief introduction to the theory of phase transitions. Throughout the book, there is a strong emphasis on computational methods to make abstract concepts more concrete.

Signals and Systems Primer with MATLAB
Author : Alexander D. Poularikas
Publisher : CRC Press
Release Date : 2006-12-21
ISBN 10 : 9780849372674
Pages : 680 pages
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Signals and Systems Primer with MATLAB® equally emphasizes the fundamentals of both analog and digital signals and systems. To ensure insight into the basic concepts and methods, the text presents a variety of examples that illustrate a wide range of applications, from microelectromechanical to worldwide communication systems. It also provides MATLAB functions and procedures for practice and verification of these concepts. Taking a pedagogical approach, the author builds a solid foundation in signal processing as well as analog and digital systems. The book first introduces orthogonal signals, linear and time-invariant continuous-time systems, discrete-type systems, periodic signals represented by Fourier series, Gibbs's phenomenon, and the sampling theorem. After chapters on various transforms, the book discusses analog filter design, both finite and infinite impulse response digital filters, and the fundamentals of random digital signal processing, including the nonparametric spectral estimation. The final chapter presents different types of filtering and their uses for random digital signal processing, specifically, the use of Wiener filtering and least mean squares filtering. Balancing the study of signals with system modeling and interactions, this text will help readers accurately develop mathematical representations of systems.

NBS Technical Note
Author : N.A
Publisher : N.A
Release Date : 1966-10
ISBN 10 :
Pages : 329 pages
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A Survey of Some Empirical and Semi-empirical Interatomic and Intermolecular Potentials
Author : Benjamin Moses Axilrod
Publisher : N.A
Release Date : 1966
ISBN 10 :
Pages : 52 pages
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Delta Functions, Integration by Parts, and Calculus of Variations [microform]
Author : Martin Green
Publisher : National Library of Canada = Bibliothèque nationale du Canada
Release Date : 1992
ISBN 10 : 9780315779167
Pages : 62 pages
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Generalized Functions, Operator Theory, and Dynamical Systems
Author : I Antoniou,G Lumer
Publisher : CRC Press
Release Date : 1998-12-23
ISBN 10 : 9780849306198
Pages : 392 pages
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Nobel prize winner Ilya Prigogine writes in his preface: "Irreversibility is a challenge to mathematics...[which] leads to generalized functions and to an extension of spectral analysis beyond the conventional Hilbert space theory." Meeting this challenge required new mathematical formulations-obstacles met and largely overcome thanks primarily to the contributors to this volume." This compilation of works grew out of material presented at the "Hyperfunctions, Operator Theory and Dynamical Systems" symposium at the International Solvay Institutes for Physics and Chemistry in 1997. The result is a coherently organized collective work that moves from general, widely applicable mathematical methods to ever more specialized physical applications. Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems. The interplay between mathematics and physics is now more necessary than ever-and more difficult than ever, given the increasing complexity of theories and methods. Here the topics include:

An Introduction to Fourier Analysis and Generalised Functions
Author : M. J. Lighthill,Lighting Research Center,Lighthill M. J.
Publisher : Cambridge University Press
Release Date : 1958
ISBN 10 : 9780521091282
Pages : 79 pages
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"Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress

Theories of Generalised Functions
Author : R F Hoskins,J S Pinto
Publisher : Elsevier
Release Date : 2005-01-01
ISBN 10 : 0857099485
Pages : 306 pages
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Explaining and comparing the various standard types of generalised functions which have been developed during the 20th Century, this text also contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions. The book could readily be used as a main text on generalised functions for mathematical undergraduates in final year analysis courses, as it presupposes little more than a general mathematical background. It also makes a valuable reference text for non-specific applied mathematics students, such as physicists or electrical engineers, needing to gain expertise in the application of generalised functions to physical problems, without any prior acquaintance of the specialised subject matter. An ideal companion book to Delta Functions, also by Professor Hoskins. Explains and compares the various standard types of generalised functions that have been developed during the 20th Century Contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions

Geometrical Methods of Mathematical Physics
Author : Bernard F. Schutz,Director Bernard F Schutz
Publisher : Cambridge University Press
Release Date : 1980-01-28
ISBN 10 : 9780521298872
Pages : 250 pages
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For physicists and applied mathematicians working in the fields of relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This book provides an introduction to the concepts and techniques of modern differential theory, particularly Lie groups, Lie forms and differential forms.

Fourier Analysis and Imaging
Author : Ronald Bracewell
Publisher : Springer Science & Business Media
Release Date : 2004-01-31
ISBN 10 : 9780306481871
Pages : 689 pages
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As Lord Kelvin said, "Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics." This has remained durable knowledge for a century, and has extended its applicability to topics as diverse as medical imaging (CT scanning), the presentation of images on screens and their digital transmission, remote sensing, geophysical exploration, and many branches of engineering. Fourier Analysis and Imaging is based on years of teaching a course on the Fourier Transform at the senior or early graduate level, as well as on Prof. Bracewell's 1995 text Two-Dimensional Imaging. It is an excellent textbook and will also be a welcome addition to the reference library of those many professionals whose daily activities involve Fourier analysis in its many guises.