Graduate Texts in Mathematics Ser.: Fourier Analysis and Its Applications

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Item specifics

Condition
Good: A book that has been read but is in good condition. Very minimal damage to the cover including ...
Features
Ex-Library
ISBN
9780387008363
Category

About this product

Product Identifiers

Publisher
Springer New York
ISBN-10
0387008365
ISBN-13
9780387008363
eBay Product ID (ePID)
2840506

Product Key Features

Number of Pages
Xii, 272 Pages
Publication Name
Fourier Analysis and Its Applications
Language
English
Subject
Mathematical Analysis
Publication Year
2003
Type
Textbook
Subject Area
Mathematics
Author
Anders Vretblad
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover

Dimensions

Item Weight
45.2 Oz
Item Length
9.2 in
Item Width
6.1 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
2003-044941
Dewey Edition
21
Reviews
From the reviews: "This book is one in the Graduate Texts in Mathematics series published by Springer. ... There is a variety of worked examples as well as 350-plus exercises ... . The book is a valuable addition to the literature on Fourier analysis. It is written with more mathematical rigour than many texts ... without being totally opaque to the non-specialist. ... The examples at the end of each chapter are well structured and a reader working through most of them will achieve a good understanding of the topics." (Graham Brindley, The Mathematical Gazette, Vol. 90 (517), 2006) "The author ... presents the results of his experiences and choices for decades of teaching courses. ... The tables and formulas collected ... are of great service. At the end of each chapter there is a summary section that discusses the results, gives some history, and suggests instructive exercises. We thus have a solid course on Fourier analysis and its applications interesting for students and specialists in engineering as well as for mathematicians. ... I believe that the book will find numerous interested readers." (Elijah Liflyand, Zentralblatt MATH, Vol. 1032 (7), 2004) "This book is an interesting mixture of a traditional approach ... and a more modern one, emphasizing the role of (tempered) distributions and the application aspects of Fourier analysis. ... The book is certainly highly recommendable for those who want to learn the essence of Fourier analysis in a mathematically correct way without having to go through too much technical details." (H.G. Feichtinger, Monatshefte für Mathematik, Vol. 143 (2), 2004) "The book is appropriate for an advanced undergraduate or a master's level one-term introductory course on Fourier series with applications to boundary value problems. ... a deep idea is presented in a non-rigorous way both to show the usefulness of the idea and to stimulate interest in further study. ... The book has a good collection of exercises ... . Each chapter ends with both a summary of its main results and methods and historical notes." (Colin C. Graham, Mathematical Reviews, Issue 2004 e), From the reviews:"This book is one in the Graduate Texts in Mathematics series published by Springer. … There is a variety of worked examples as well as 350-plus exercises … . The book is a valuable addition to the literature on Fourier analysis. It is written with more mathematical rigour than many texts … without being totally opaque to the non-specialist. … The examples at the end of each chapter are well structured and a reader working through most of them will achieve a good understanding of the topics." (Graham Brindley, The Mathematical Gazette, Vol. 90 (517), 2006)"The author … presents the results of his experiences and choices for decades of teaching courses. … The tables and formulas collected … are of great service. At the end of each chapter there is a summary section that discusses the results, gives some history, and suggests instructive exercises. We thus have a solid course on Fourier analysis and its applications interesting for students and specialists in engineering as well as for mathematicians. … I believe that the book will find numerous interested readers." (Elijah Liflyand, Zentralblatt MATH, Vol. 1032 (7), 2004)"This book is an interesting mixture of a traditional approach … and a more modern one, emphasizing the role of (tempered) distributions and the application aspects of Fourier analysis. … The book is certainly highly recommendable for those who want to learn the essence of Fourier analysis in a mathematically correct way without having to go through too much technical details." (H.G. Feichtinger, Monatshefte für Mathematik, Vol. 143 (2), 2004)"The book is appropriate for an advanced undergraduate or a master's level one-term introductory course on Fourier series with applications to boundary value problems. … a deep idea is presented in a non-rigorous way both to show the usefulness of the idea and to stimulate interest in further study. … The book has a good collection of exercises … . Each chapter ends with both a summary of its main results and methods and historical notes." (Colin C. Graham, Mathematical Reviews, Issue 2004 e), From the reviews: "This book is one in the Graduate Texts in Mathematics series published by Springer. ... There is a variety of worked examples as well as 350-plus exercises ... . The book is a valuable addition to the literature on Fourier analysis. It is written with more mathematical rigour than many texts ... without being totally opaque to the non-specialist. ... The examples at the end of each chapter are well structured and a reader working through most of them will achieve a good understanding of the topics." (Graham Brindley, The Mathematical Gazette, Vol. 90 (517), 2006) "The author ... presents the results of his experiences and choices for decades of teaching courses. ... The tables and formulas collected ... are of great service. At the end of each chapter there is a summary section that discusses the results, gives some history, and suggests instructive exercises. We thus have a solid course on Fourier analysis and its applications interesting for students and specialists in engineering as well as for mathematicians. ... I believe that the book will find numerous interested readers." (Elijah Liflyand, Zentralblatt MATH, Vol. 1032 (7), 2004) "This book is an interesting mixture of a traditional approach ... and a more modern one, emphasizing the role of (tempered) distributions and the application aspects of Fourier analysis. ... The book is certainly highly recommendable for those who want to learn the essence of Fourier analysis in a mathematically correct way without having to go through too much technical details." (H.G. Feichtinger, Monatshefte fr Mathematik, Vol. 143 (2), 2004) "The book is appropriate for an advanced undergraduate or a master's level one-term introductory course on Fourier series with applications to boundary value problems. ... a deep idea is presented in a non-rigorous way both to show the usefulness of the idea and to stimulate interest in further study. ... The book has a good collection of exercises ... . Each chapter ends with both a summary of its main results and methods and historical notes." (Colin C. Graham, Mathematical Reviews, Issue 2004 e), From the reviews: "This book is one in the Graduate Texts in Mathematics series published by Springer. ... There is a variety of worked examples as well as 350-plus exercises ... . The book is a valuable addition to the literature on Fourier analysis. It is written with more mathematical rigour than many texts ... without being totally opaque to the non-specialist. ... The examples at the end of each chapter are well structured and a reader working through most of them will achieve a good understanding of the topics." (Graham Brindley, The Mathematical Gazette, Vol. 90 (517), 2006) "The author ... presents the results of his experiences and choices for decades of teaching courses. ... The tables and formulas collected ... are of great service. At the end of each chapter there is a summary section that discusses the results, gives some history, and suggests instructive exercises. We thus have a solid course on Fourier analysis and its applications interesting for students and specialists in engineering as well as for mathematicians. ... I believe that the book will find numerous interested readers." (Elijah Liflyand, Zentralblatt MATH, Vol. 1032 (7), 2004) "This book is an interesting mixture of a traditional approach ... and a more modern one, emphasizing the role of (tempered) distributions and the application aspects of Fourier analysis. ... The book is certainly highly recommendable for those who want to learn the essence of Fourier analysis in a mathematically correct way without having to go through too much technical details." (H.G. Feichtinger, Monatshefte für Mathematik, Vol. 143 (2), 2004) "The book is appropriate for an advanced undergraduate or a master's level one-term introductory course on Fourier series with applications to boundary value problems. ... a deep idea is presented in a non-rigorous way both to show the usefulness of the idea and to stimulate interest in further study. ... The book has a goodcollection of exercises ... . Each chapter ends with both a summary of its main results and methods and historical notes." (Colin C. Graham, Mathematical Reviews, Issue 2004 e), From the reviews: "This book is one in the Graduate Texts in Mathematics series published by Springer. … There is a variety of worked examples as well as 350-plus exercises … . The book is a valuable addition to the literature on Fourier analysis. It is written with more mathematical rigour than many texts … without being totally opaque to the non-specialist. … The examples at the end of each chapter are well structured and a reader working through most of them will achieve a good understanding of the topics." (Graham Brindley, The Mathematical Gazette, Vol. 90 (517), 2006) "The author … presents the results of his experiences and choices for decades of teaching courses. … The tables and formulas collected … are of great service. At the end of each chapter there is a summary section that discusses the results, gives some history, and suggests instructive exercises. We thus have a solid course on Fourier analysis and its applications interesting for students and specialists in engineering as well as for mathematicians. … I believe that the book will find numerous interested readers." (Elijah Liflyand, Zentralblatt MATH, Vol. 1032 (7), 2004) "This book is an interesting mixture of a traditional approach … and a more modern one, emphasizing the role of (tempered) distributions and the application aspects of Fourier analysis. … The book is certainly highly recommendable for those who want to learn the essence of Fourier analysis in a mathematically correct way without having to go through too much technical details." (H.G. Feichtinger, Monatshefte für Mathematik, Vol. 143 (2), 2004) "The book is appropriate for an advanced undergraduate or a master's level one-term introductory course on Fourier series with applications to boundary value problems. … a deep idea is presented in a non-rigorous way both to show the usefulness of the idea and to stimulate interest in further study. … The book has a good collection of exercises … . Each chapter ends with both a summary of its main results and methods and historical notes." (Colin C. Graham, Mathematical Reviews, Issue 2004 e), From the reviews: "This book is one in the Graduate Texts in Mathematics series published by Springer. a? There is a variety of worked examples as well as 350-plus exercises a? . The book is a valuable addition to the literature on Fourier analysis. It is written with more mathematical rigour than many texts a? without being totally opaque to the non-specialist. a? The examples at the end of each chapter are well structured and a reader working through most of them will achieve a good understanding of the topics." (Graham Brindley, The Mathematical Gazette, Vol. 90 (517), 2006) "The author a? presents the results of his experiences and choices for decades of teaching courses. a? The tables and formulas collected a? are of great service. At the end of each chapter there is a summary section that discusses the results, gives some history, and suggests instructive exercises. We thus have a solid course on Fourier analysis and its applications interesting for students and specialists in engineering as well as for mathematicians. a? I believe that the book will find numerous interested readers." (Elijah Liflyand, Zentralblatt MATH, Vol. 1032 (7), 2004) "This book is an interesting mixture of a traditional approach a? and a more modern one, emphasizing the role of (tempered) distributions and the application aspects of Fourier analysis. a? The book is certainly highly recommendable for those who want to learn the essence of Fourier analysis in a mathematically correct way without having to go through too much technical details." (H.G. Feichtinger, Monatshefte f'r Mathematik, Vol. 143 (2), 2004)
Series Volume Number
223
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515/.2433
Table Of Content
Introduction.- Preparations.- Laplace and Z Transforms.- Fourier Series.- L^2 Theory.- Separation of Variables.- Fourier Transforms.- Distributions.- Multi-Dimensional Fourier Analysis.- Appendix A: The ubiquitous convolution.- Appendix B: The Discrete Fourier Transform.- Appendix C: Formulae.- Appendix D: Answers to exercises.- Appendix E: Literature.
Synopsis
TheclassicaltheoryofFourierseriesandintegrals,aswellasLaplacetra- forms, is of great importance for physical and technical applications, and its mathematical beauty makes it an interesting study for pure mathema- cians as well. I have taught courses on these subjects for decades to civil engineeringstudents,andalsomathematicsmajors,andthepresentvolume can be regarded as my collected experiences from this work. There is, of course, an unsurpassable book on Fourier analysis, the tr- tise by Katznelson from 1970. That book is, however, aimed at mathem- ically very mature students and can hardly be used in engineering courses. Ontheotherendofthescale,thereareanumberofmore-or-lesscookbo- styled books, where the emphasis is almost entirely on applications. I have felt the need for an alternative in between these extremes: a text for the ambitious and interested student, who on the other hand does not aspire to become an expert in the ?eld. There do exist a few texts that ful'll these requirements (see the literature list at the end of the book), but they do not include all the topics I like to cover in my courses, such as Laplace transforms and the simplest facts about distributions., This book is a carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge., TheclassicaltheoryofFourierseriesandintegrals,aswellasLaplacetra- forms, is of great importance for physical and technical applications, and its mathematical beauty makes it an interesting study for pure mathema- cians as well. I have taught courses on these subjects for decades to civil engineeringstudents,andalsomathematicsmajors,andthepresentvolume can be regarded as my collected experiences from this work. There is, of course, an unsurpassable book on Fourier analysis, the tr- tise by Katznelson from 1970. That book is, however, aimed at mathem- ically very mature students and can hardly be used in engineering courses. Ontheotherendofthescale,thereareanumberofmore-or-lesscookbo- styled books, where the emphasis is almost entirely on applications. I have felt the need for an alternative in between these extremes: a text for the ambitious and interested student, who on the other hand does not aspire to become an expert in the ?eld. There do exist a few texts that ful?ll these requirements (see the literature list at the end of the book), but they do not include all the topics I like to cover in my courses, such as Laplace transforms and the simplest facts about distributions., TheclassicaltheoryofFourierseriesandintegrals, aswellasLaplacetra- forms, is of great importance for physical and technical applications, and its mathematical beauty makes it an interesting study for pure mathema- cians as well. I have taught courses on these subjects for decades to civil engineeringstudents, andalsomathematicsmajors, andthepresentvolume can be regarded as my collected experiences from this work. There is, of course, an unsurpassable book on Fourier analysis, the tr- tise by Katznelson from 1970. That book is, however, aimed at mathem- ically very mature students and can hardly be used in engineering courses. Ontheotherendofthescale, thereareanumberofmore-or-lesscookbo- styled books, where the emphasis is almost entirely on applications. I have felt the need for an alternative in between these extremes: a text for the ambitious and interested student, who on the other hand does not aspire to become an expert in the ?eld. There do exist a few texts that ful'll these requirements (see the literature list at the end of the book), but they do not include all the topics I like to cover in my courses, such as Laplace transforms and the simplest facts about distributi
LC Classification Number
QA403.5-404.5

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