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Delta Functions

Delta Functions
  • Author : R F Hoskins
  • Publisher :Unknown
  • Release Date :2009-04-14
  • Total pages :270
  • ISBN : 1904275397
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Summary : 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

Delta Function Expansions, Complex Delta Functions and the Steepest-descent Method
  • Author : Ismo V. Lindell
  • Publisher :Unknown
  • Release Date :1992
  • Total pages :10
  • ISBN : 9512209667
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Summary :

An Introduction to Statistical Mechanics and Thermodynamics

An Introduction to Statistical Mechanics and Thermodynamics
  • Author : Robert Swendsen
  • Publisher :Unknown
  • Release Date :2020-02-10
  • Total pages :448
  • ISBN : 9780198853237
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Summary : 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

Signals and Systems Primer with MATLAB
  • Author : Alexander D. Poularikas
  • Publisher :Unknown
  • Release Date :2006-12-21
  • Total pages :680
  • ISBN : 0849372674
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Summary : 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.

A Survey of Some Empirical and Semi-empirical Interatomic and Intermolecular Potentials

A Survey of Some Empirical and Semi-empirical Interatomic and Intermolecular Potentials
  • Author : Benjamin Moses Axilrod
  • Publisher :Unknown
  • Release Date :1966
  • Total pages :52
  • ISBN : UIUC:30112106611962
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Summary :

Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics

Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics
  • Author : F. Farassat
  • Publisher :Unknown
  • Release Date :1994
  • Total pages :52
  • ISBN : NASA:31769000447469
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Summary :

Delta Functions, Integration by Parts, and Calculus of Variations [microform]

Delta Functions, Integration by Parts, and Calculus of Variations [microform]
  • Author : Martin Green
  • Publisher :Unknown
  • Release Date :1992
  • Total pages :62
  • ISBN : 0315779160
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Summary :

Generalized Functions, Operator Theory, and Dynamical Systems

Generalized Functions, Operator Theory, and Dynamical Systems
  • Author : I Antoniou,G Lumer
  • Publisher :Unknown
  • Release Date :1998-12-23
  • Total pages :392
  • ISBN : 0849306191
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Summary : 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

An Introduction to Fourier Analysis and Generalised Functions
  • Author : M. J. Lighthill,Lighting Research Center,Lighthill M. J.
  • Publisher :Unknown
  • Release Date :1958
  • Total pages :79
  • ISBN : 0521091284
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Summary : "Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress

Generalized Functions: Theory and Technique

Generalized Functions: Theory and Technique
  • Author : Kanwal
  • Publisher :Unknown
  • Release Date :1983-12-01
  • Total pages :427
  • ISBN : 9780080956763
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Summary : Generalized Functions: Theory and Technique

Theories of Generalised Functions

Theories of Generalised Functions
  • Author : R F Hoskins,J S Pinto
  • Publisher :Unknown
  • Release Date :2005-01-01
  • Total pages :306
  • ISBN : 9780857099488
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Summary : 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

Geometrical Methods of Mathematical Physics
  • Author : Bernard F. Schutz,Director Bernard F Schutz
  • Publisher :Unknown
  • Release Date :1980-01-28
  • Total pages :250
  • ISBN : 0521298873
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Summary : 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

Fourier Analysis and Imaging
  • Author : Ronald Bracewell
  • Publisher :Unknown
  • Release Date :2004-01-31
  • Total pages :689
  • ISBN : 0306481871
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Summary : 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.

Fourier Methods in Imaging

Fourier Methods in Imaging
  • Author : Roger L. Easton Jr.
  • Publisher :Unknown
  • Release Date :2010-11-18
  • Total pages :954
  • ISBN : 1119991862
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Summary : Fourier Methods in Imaging introduces the mathematical tools for modeling linear imaging systems to predict the action of the system or for solving for the input. The chapters are grouped into five sections, the first introduces the imaging “tasks” (direct, inverse, and system analysis), the basic concepts of linear algebra for vectors and functions, including complex-valued vectors, and inner products of vectors and functions. The second section defines "special" functions, mathematical operations, and transformations that are useful for describing imaging systems. Among these are the Fourier transforms of 1-D and 2-D function, and the Hankel and Radon transforms. This section also considers approximations of the Fourier transform. The third and fourth sections examine the discrete Fourier transform and the description of imaging systems as linear "filters", including the inverse, matched, Wiener and Wiener-Helstrom filters. The final section examines applications of linear system models to optical imaging systems, including holography. Provides a unified mathematical description of imaging systems. Develops a consistent mathematical formalism for characterizing imaging systems. Helps the reader develop an intuitive grasp of the most common mathematical methods, useful for describing the action of general linear systems on signals of one or more spatial dimensions. Offers parallel descriptions of continuous and discrete cases. Includes many graphical and pictorial examples to illustrate the concepts. This book helps students develop an understanding of mathematical tools for describing general one- and two-dimensional linear imaging systems, and will also serve as a reference for engineers and scientists

Signals and Systems with MATLAB Applications

Signals and Systems with MATLAB Applications
  • Author : Steven T. Karris
  • Publisher :Unknown
  • Release Date :2003
  • Total pages :598
  • ISBN : 0970951167
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Summary : This text contains a comprehensive discussion of continuous and discrete time signals and systems with many examples from MATLAB--software used to write efficient, compact programs to solve electrical and computer engineering problems of varying complexity. Intended for junior- and senior-level electrical engineering students and for self-study by working professionals, it discusses Laplace transformation and circuit analysis, impulse response, Fourier series, Z transform, and the Discrete Fourier transform and FFT. Solutions to all exercises are included in this revised edition.

Waveforms

Waveforms
  • Author : Homer B. Tilton
  • Publisher :Unknown
  • Release Date :1986
  • Total pages :245
  • ISBN : UOM:39015010491150
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Summary :

Introduction to Infrared and Electro-optical Systems

Introduction to Infrared and Electro-optical Systems
  • Author : Ronald G. Driggers,Paul Cox,Timothy Edwards
  • Publisher :Unknown
  • Release Date :1999
  • Total pages :407
  • ISBN : UOM:39015045976506
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Summary : A complete and up-to-date introduction to the analysis and design of infrared and electro-optical (EO) imaging systems. The text details the principles and components of the Linear Shift-Invariant (LSI) infrared and electro-optical systems and combines it with calculus and domain transformations to achieve a successful imaging system analysis. Ultimately, the steps in this book lead to results in quantitative characterizations of performance metrics such as modulation transfer functions, minimum resolvable temperature difference; minimum resolvable contrast, and probability of object discrimination.

SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :2009
  • Total pages :229
  • ISBN : UOM:39015085194986
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Summary :

A Distributional Approach to Asymptotics

A Distributional Approach to Asymptotics
  • Author : Ricardo Estrada,Ram P. Kanwal
  • Publisher :Unknown
  • Release Date :2012-09-08
  • Total pages :454
  • ISBN : 9780817681302
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Summary : "...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic

Quantum Mechanics

Quantum Mechanics
  • Author : Ajoy Ghatak,S. Lokanathan
  • Publisher :Unknown
  • Release Date :2004-03-31
  • Total pages :858
  • ISBN : 1402021291
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Summary : An understanding of quantum mechanics is vital to all students of physics, chemistry and electrical engineering, but requires a lot of mathematical concepts, the details of which are given with great clarity in this book. Various concepts have been derived from first principles, so it can also be used for self-study. The chapters on the JWKB approximation, time-independent perturbation theory and effects of magnetic field stand out for their clarity and easy-to-understand mathematics. Two complete chapters on the linear harmonic oscillator provide a very detailed discussion of one of the most fundamental problems in quantum mechanics. Operator algebra is used to show the ease with which one can calculate the harmonic oscillator wave functions and study the evolution of the coherent state. Similarly, three chapters on angular momentum give a detailed account of this important problem. Perhaps the most attractive feature of the book is the excellent balance between theory and applications and the large number of applications in such diverse areas as astrophysics, nuclear physics, atomic and molecular spectroscopy, solid-state physics, and quantum well structures.

An Introduction to Quantum Theory

An Introduction to Quantum Theory
  • Author : F. S. Levin
  • Publisher :Unknown
  • Release Date :2002
  • Total pages :793
  • ISBN : 0521598419
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Summary : An undergraduate introductory quantum mechanics textbook with a large number of figures and exercises.