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Delta Functions

Delta Functions
Introduction to Generalised Functions

by R F Hoskins

  • Publisher : Elsevier
  • Release : 2009-03-31
  • Pages : 280
  • ISBN : 0857099353
  • Language : En, Es, Fr & De
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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 Functions

Delta Functions
An Introduction to Generalised Functions

by R. F. Hoskins

  • Publisher : ISBS
  • Release : 1999
  • Pages : 262
  • ISBN : 9781898563440
  • Language : En, Es, Fr & De
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Signals and Systems Primer with MATLAB

Signals and Systems Primer with MATLAB
A Book

by Alexander D. Poularikas

  • Publisher : CRC Press
  • Release : 2018-10-03
  • Pages : 680
  • ISBN : 1351837737
  • Language : En, Es, Fr & De
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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.

Diffractive Optics

Diffractive Optics
Design, Fabrication, and Test

by Donald C. O'Shea,Thomas J. Suleski,Alan D. Kathman,Dennis W. Prather

  • Publisher : SPIE Press
  • Release : 2004
  • Pages : 241
  • ISBN : 9780819451712
  • Language : En, Es, Fr & De
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This book provides the reader with the broad range of materials that were discussed in a series of short courses presented at Georgia Tech on the design, fabrication, and testing of diffractive optical elements (DOEs). Although there are not long derivations or detailed methods for specific engineering calculations, the reader should be familiar and comfortable with basic computational techniques. This text is not a 'cookbook' for producing DOEs, but it should provide readers with sufficient information to assess whether this technology would benefit their work, and to understand the requirements for using the concepts and techniques presented by the authors.

Mathematical Methods

Mathematical Methods
For Students of Physics and Related Fields

by Sadri Hassani

  • Publisher : Springer Science & Business Media
  • Release : 2008-10-27
  • Pages : 832
  • ISBN : 0387095039
  • Language : En, Es, Fr & De
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Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.

Signals, Sound, and Sensation

Signals, Sound, and Sensation
A Book

by William M. Hartmann

  • Publisher : Springer Science & Business Media
  • Release : 2004-09-14
  • Pages : 647
  • ISBN : 9781563962837
  • Language : En, Es, Fr & De
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Designed to follow an introductory text on psychoacoustics, this book takes readers through the mathematics of signal processing from its beginnings in the Fourier transform to advanced topics in modulation, dispersion relations, minimum phase systems, sampled data, and nonlinear distortion. While organised like an introductory engineering text on signals, the examples and exercises come from research on the perception of sound. A unique feature of this book is its consistent application of the Fourier transform, which unifies topics as diverse as cochlear filtering and digital recording. More than 250 exercises are included, many of them devoted to practical research in perception, while others explore surprising auditory illusions generated by special signals. Periodic signals, aperiodic signals, and noise -- along with their linear and nonlinear transformations -- are covered in detail. More advanced mathematical topics are treated in the appendices. A working knowledge of elementary calculus is the only prerequisite. Indispensable for researchers and advanced students in the psychology of auditory perception.

Advanced Mathematical Methods in Science and Engineering

Advanced Mathematical Methods in Science and Engineering
A Book

by S.I. Hayek

  • Publisher : CRC Press
  • Release : 2000-10-13
  • Pages : 752
  • ISBN : 9780824704667
  • Language : En, Es, Fr & De
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Gathering an extensive range of mathematical topics into a plenary reference/text for solving science and engineering problems, Advanced Mathematical Models in Science and Engineering elucidates integral methods, field equation derivations, and operations applicable to modern science systems. Applying academic skills to practical problems in science and engineering, the author reviews basic methods of integration and series solutions for ordinary differential equations; introduces derivations and solution methods for linear boundary value problems in one dimension, covering eigenfunctions and eigenfunction expansions, orthogonality, and adjoint and self-adjoint systems; discusses complex variables, calculus, and integrals as well as application of residues and the integration of multivalued functions; considers linear partial differential equations in classical physics and engineering with derivations for the topics of wave equations, heat flow, vibration, and strength of materials; clarifies the calculus for integral transforms; explains Green's functions for ordinary and partial differential equations for unbounded and bounded media; examines asymptotic methods; presents methods for asymptotic solutions of ordinary differential equations; and more.

An Introduction to Classical Electromagnetic Radiation

An Introduction to Classical Electromagnetic Radiation
A Book

by Glenn S. Smith

  • Publisher : Cambridge University Press
  • Release : 1997-08-13
  • Pages : 653
  • ISBN : 9780521586986
  • Language : En, Es, Fr & De
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A thorough description of classical electromagnetic radiation, for electrical engineers and physicists.

Introduction to Fourier Optics

Introduction to Fourier Optics
A Book

by Joseph W. Goodman

  • Publisher : Roberts and Company Publishers
  • Release : 2005
  • Pages : 491
  • ISBN : 9780974707723
  • Language : En, Es, Fr & De
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This textbook deals with fourier analysis applications in optics, and in particular with its applications to diffraction, imaging, optical data processing, holography and optical communications. Fourier analysis is a universal tool that has found application within a wide range of areas in physics and engineering and this third edition has been written to help your students understand the complexity of a subject that can be challenging to grasp at times. Chapters cover foundations of scalar diffraction theory, Fresnel and Fraunhofer diffraction moving onto Wave-Optics Analysis of Coherent Optical Systems and Wavefront Modulation. Joseph Goodman’s work in Electrical Engineering has been recognised by a variety of awards and honours, so his text is able to guide students through a comprehensive introduction into Fourier Optics.

Mathematical Methods for Optical Physics and Engineering

Mathematical Methods for Optical Physics and Engineering
A Book

by Gregory J. Gbur

  • Publisher : Cambridge University Press
  • Release : 2011-01-06
  • Pages : 129
  • ISBN : 1139492691
  • Language : En, Es, Fr & De
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The first textbook on mathematical methods focusing on techniques for optical science and engineering, this text is ideal for upper division undergraduate and graduate students in optical physics. Containing detailed sections on the basic theory, the textbook places strong emphasis on connecting the abstract mathematical concepts to the optical systems to which they are applied. It covers many topics which usually only appear in more specialized books, such as Zernike polynomials, wavelet and fractional Fourier transforms, vector spherical harmonics, the z-transform, and the angular spectrum representation. Most chapters end by showing how the techniques covered can be used to solve an optical problem. Essay problems based on research publications and numerous exercises help to further strengthen the connection between the theory and its applications.

Generalized Functions Theory and Technique

Generalized Functions Theory and Technique
Theory and Technique

by Ram P. Kanwal

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 474
  • ISBN : 1468400355
  • Language : En, Es, Fr & De
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This second edition of Generalized Functions has been strengthened in many ways. The already extensive set of examples has been expanded. Since the publication of the first edition, there has been tremendous growth in the subject and I have attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised. The bibliography has been enlarged considerably. Some of the material has been reorganized. For example, Chapters 12 and 13 of the first edition have been consolidated into Chapter 12 of this edition by a judicious process of elimination and addition of the subject matter. The new Chapter 13 explains the interplay between the theories of moments, asymptotics, and singular perturbations. Similarly, some sections of Chapter 15 have been revised and included in earlier chapters to improve the logical flow of ideas. However, two sections are retained. The section dealing with the application of the probability theory has been revised, and I am thankful to Professor Z.L. Crvenkovic for her help. The new material included in this chapter pertains to the modern topics of periodic distributions and microlocal theory. I have demonstrated through various examples that familiarity with the generalized functions is very helpful for students in physical sciences and technology. For instance, the reader will realize from Chapter 6 how the generalized functions have revolutionized the Fourier analysis which is being used extensively in many fields of scientific activity.

Signal Treatment and Signal Analysis in NMR

Signal Treatment and Signal Analysis in NMR
A Book

by D.N. Rutledge

  • Publisher : Elsevier
  • Release : 1996-06-10
  • Pages : 547
  • ISBN : 9780080541204
  • Language : En, Es, Fr & De
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Signal analysis and signal treatment are integral parts of all types of Nuclear Magnetic Resonance. In the last ten years, much has been achieved in the development of dimensional spectra. At the same time new NMR techniques such as NMR Imaging and multidimensional spectroscopy have appeared, requiring entirely new methods of signal analysis. Up until now, most NMR texts and reference books limited their presentation of signal processing to a short introduction to the principles of the Fourier Transform, signal convolution, apodisation and noise reduction. To understand the mathematics of the newer signal processing techniques, it was necessary to go back to the primary references in NMR, chemometrics and mathematics journals. The objective of this book is to fill this void by presenting, in a single volume, both the theory and applications of most of these new techniques to Time-Domain, Frequency-Domain and Space-Domain NMR signals. Details are provided on many of the algorithms used and a companion CD-ROM is also included which contains some of the computer programs, either as source code or in executable form. Although it is aimed primarily at NMR users in the medical, industrial and academic fields, it should also interest chemometricians and programmers working with other techniques.

Theories of Generalised Functions

Theories of Generalised Functions
Distributions, Ultradistributions and Other Generalised Functions

by R F Hoskins,J S Pinto

  • Publisher : Elsevier
  • Release : 2005-01-01
  • Pages : 306
  • ISBN : 0857099485
  • Language : En, Es, Fr & De
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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

Computational Modeling in Biomechanics

Computational Modeling in Biomechanics
A Book

by Suvranu De,Farshid Guilak,Mohammad Mofrad

  • Publisher : Springer Science & Business Media
  • Release : 2010-03-10
  • Pages : 581
  • ISBN : 9789048135752
  • Language : En, Es, Fr & De
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Availability of advanced computational technology has fundamentally altered the investigative paradigm in the field of biomechanics. Armed with sophisticated computational tools, researchers are seeking answers to fundamental questions by exploring complex biomechanical phenomena at the molecular, cellular, tissue and organ levels. The computational armamentarium includes such diverse tools as the ab initio quantum mechanical and molecular dynamics methods at the atomistic scales and the finite element, boundary element, meshfree as well as immersed boundary and lattice-Boltzmann methods at the continuum scales. Multiscale methods that link various scales are also being developed. While most applications require forward analysis, e.g., finding deformations and stresses as a result of loading, others involve determination of constitutive parameters based on tissue imaging and inverse analysis. This book provides a glimpse of the diverse and important roles that modern computational technology is playing in various areas of biomechanics including biofluids and mass transfer, cardiovascular mechanics, musculoskeletal mechanics, soft tissue mechanics, and biomolecular mechanics.

Generalized Functions Theory and Technique

Generalized Functions Theory and Technique
Theory and Technique

by Ram P. Kanwal

  • Publisher : Springer Science & Business Media
  • Release : 1998-01-01
  • Pages : 474
  • ISBN : 9780817640064
  • Language : En, Es, Fr & De
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This second edition of Generalized Functions has been strengthened in many ways. The already extensive set of examples has been expanded. Since the publication of the first edition, there has been tremendous growth in the subject and I have attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised. The bibliography has been enlarged considerably. Some of the material has been reorganized. For example, Chapters 12 and 13 of the first edition have been consolidated into Chapter 12 of this edition by a judicious process of elimination and addition of the subject matter. The new Chapter 13 explains the interplay between the theories of moments, asymptotics, and singular perturbations. Similarly, some sections of Chapter 15 have been revised and included in earlier chapters to improve the logical flow of ideas. However, two sections are retained. The section dealing with the application of the probability theory has been revised, and I am thankful to Professor Z.L. Crvenkovic for her help. The new material included in this chapter pertains to the modern topics of periodic distributions and microlocal theory. I have demonstrated through various examples that familiarity with the generalized functions is very helpful for students in physical sciences and technology. For instance, the reader will realize from Chapter 6 how the generalized functions have revolutionized the Fourier analysis which is being used extensively in many fields of scientific activity.

A Guided Tour of Mathematical Methods for the Physical Sciences

A Guided Tour of Mathematical Methods for the Physical Sciences
A Book

by Roel Snieder,Kasper van Wijk

  • Publisher : Cambridge University Press
  • Release : 2015-03-05
  • Pages : 129
  • ISBN : 131624086X
  • Language : En, Es, Fr & De
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Mathematical methods are essential tools for all physical scientists. This book provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students across the physical sciences. In contrast to more traditional textbooks, all the material is presented in the form of exercises. Within these exercises, basic mathematical theory and its applications in the physical sciences are well integrated. In this way, the mathematical insights that readers acquire are driven by their physical-science insight. This third edition has been completely revised: new material has been added to most chapters, and two completely new chapters on probability and statistics and on inverse problems have been added. This guided tour of mathematical techniques is instructive, applied, and fun. This book is targeted for all students of the physical sciences. It can serve as a stand-alone text, or as a source of exercises and examples to complement other textbooks.

Geometrical Methods of Mathematical Physics

Geometrical Methods of Mathematical Physics
A Book

by Bernard F. Schutz,Director Bernard F Schutz

  • Publisher : Cambridge University Press
  • Release : 1980-01-28
  • Pages : 250
  • ISBN : 9780521298872
  • Language : En, Es, Fr & De
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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.

Modern Optics

Modern Optics
A Book

by B. D. Guenther

  • Publisher : OUP Oxford
  • Release : 2015-10-23
  • Pages : 752
  • ISBN : 0191058920
  • Language : En, Es, Fr & De
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Modern Optics is a fundamental study of the principles of optics using a rigorous physical approach based on Maxwell's Equations. The treatment provides the mathematical foundations needed to understand a number of applications such as laser optics, fiber optics and medical imaging covered in an engineering curriculum as well as the traditional topics covered in a physics based course in optics. In addition to treating the fundamentals in optical science, the student is given an exposure to actual optics engineering problems such as paraxial matrix optics, aberrations with experimental examples, Fourier transform optics (Fresnel-Kirchhoff formulation), Gaussian waves, thin films, photonic crystals, surface plasmons, and fiber optics. Through its many pictures, figures, and diagrams, the text provides a good physical insight into the topics covered. The course content can be modified to reflect the interests of the instructor as well as the student, through the selection of optional material provided in appendixes.

Integratal Equation & Boundary Value Problem

Integratal Equation & Boundary Value Problem
A Book

by M.D.Raisinghania

  • Publisher : S. Chand Publishing
  • Release : 2007
  • Pages : 129
  • ISBN : 8121928052
  • Language : En, Es, Fr & De
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Strictly according to the latest syllabus of U.G.C.for Degree level students and for various engineering and professional examinations such as GATE, C.S.I.R NET/JRFand SLET etc. For M.A./M.Sc (Mathematics) also.

An Introduction to Statistical Mechanics and Thermodynamics

An Introduction to Statistical Mechanics and Thermodynamics
A Book

by Robert H. Swendsen

  • Publisher : Oxford University Press
  • Release : 2012-03
  • Pages : 401
  • ISBN : 0199646945
  • Language : En, Es, Fr & De
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This text presents statistical mechanics and thermodynamics as a theoretically integrated field of study. It stresses deep coverage of fundamentals, providing a natural foundation for advanced topics. The large problem sets (with solutions for teachers) include many computational problems to advance student understanding.