DELTA FUNCTIONS INTRODUCTION TO GENERALISED FUNCTIONS

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Author : R F Hoskins
ISBN : 9780857099358
Genre : Mathematics
File Size : 30.5 MB
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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

Author : R F Hoskins
ISBN : 9780857099488
Genre : Mathematics
File Size : 49.64 MB
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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

Author : M. Rahman
ISBN : 9781845645649
Genre : Mathematics
File Size : 21.71 MB
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The generalized function is one of the important branches of mathematics which has enormous applications in practical fields. In particular its applications to the theory of distribution and signal processing are very much essential. In this computer age, information science plays a very important role and the Fourier transform is extremely significant in deciphering obscured information to be made understandable. The book contains six chapters and three appendices. Chapter 1 deals with the preliminary remarks of Fourier series from general point of view. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. Chapter 4 deals with the asymptotic estimation of Fourier transforms. Chapter 5 is devoted to the study of Fourier series as a series of generalized functions. Chapter 6 deals with the fast Fourier transforms.Appendix A contains the extended list of Fourier transform pairs.Appendix B illustrates the properties of impulse function.Appendix C contains an extended list of biographical references

Author : D. C. Champeney
ISBN : 0521366887
Genre : Mathematics
File Size : 46.47 MB
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This handbook presents a collection of the most important theorems in Fourier analysis. Proofs are presented intuitively, without burdensome mathematical rigor, in a form that is accurate but also accessible to a reader who is not a specialized mathematician. This text bridges the gap between books presently on the market by discussing the finer points of the theory. It is self-contained in that it includes examples of the use of the various theorems.

Author : P A Firby
ISBN : 9780857099679
Genre : Mathematics
File Size : 25.79 MB
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This updated and revised edition of a widely acclaimed and successful text for undergraduates examines topology of recent compact surfaces through the development of simple ideas in plane geometry. Containing over 171 diagrams, the approach allows for a straightforward treatment of its subject area. It is particularly attractive for its wealth of applications and variety of interactions with branches of mathematics, linked with surface topology, graph theory, group theory, vector field theory, and plane Euclidean and non-Euclidean geometry. Examines topology of recent compact surfaces through the development of simple ideas in plane geometry Contains a wealth of applications and a variety of interactions with branches of mathematics, linked with surface topology, graph theory, group theory, vector field theory, and plane Euclidean and non-Euclidean geometry

Author : Matthew C. M. Wright
ISBN : 1860946550
Genre : Technology & Engineering
File Size : 76.46 MB
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This book aims to give a thorough grounding in the mathematical tools necessary for research in acoustics. Twelve authors, all highly-respected researchers in the field of acoustics, provide a comprehensive introduction to mathematical analysis and its applications in acoustics, through material developed for a summer school in mathematics for acoustics researchers funded by the UK Engineering and Physical Sciences Research Council. Mathematical Methods, Wave Motion, Aeroacoustics and Signal Processing are covered in fourteen chapters by authors including Keith Attenborough (Hull), John Chapman (Keele), Trevor Cox (Salford), Chris Linton and Maureen McIver (Loughborough), and Nigel Peake (Cambridge). There are worked examples, exercises and suggestions for further reading where appropriate. This book is suitable for advanced undergraduate and graduate courses in acoustics and will form an important reference source for researchers in the field.

Author : J Campos Ferreira
ISBN : 0582311446
Genre : Mathematics
File Size : 48.25 MB
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A topic of major importance to engineers and physicists, the theory of distributions remains a difficult subject for the non-mathematician. This version of the theory presents a more natural approach.