Fourier analysis and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
1992
|
| Series: | Pure and applied undergraduate texts
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Originally published: Pacific Grove, Calif. : Wadsworth & Brooks/Cole Advanced Books & Software, c1992 |
| Physical Description: | X, 433 S. graph. Darst. |
| ISBN: | 9780821847909 |
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MARC
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| 245 | 1 | 0 | |a Fourier analysis and its applications |c Gerald B. Folland |
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| 300 | |a X, 433 S. |b graph. Darst. | ||
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| 490 | 1 | |a Pure and applied undergraduate texts |v 4 | |
| 500 | |a Originally published: Pacific Grove, Calif. : Wadsworth & Brooks/Cole Advanced Books & Software, c1992 | ||
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Record in the Search Index
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CONTENTS
1
Overture
1
1.1
Some equations of mathematical physics
2
1.2
Linear differential operators
8
1.3
Separation of variables
12
2
Fourier Series
18
2.1
The Fourier series of a periodic function
18
2.2
A convergence theorem
31
2.3
Derivatives, integrals, and uniform convergence
38
2.4
Fourier series on intervals
43
2.5
Some applications
48
2.6
Further remarks on Fourier series
57
3
Orthogonal Sets of Functions
62
3.1
Vectors and inner products
62
3.2
Functions and inner products
68
3.3
Convergence and completeness
72
3.4
More about I? spaces; the dominated convergence theorem
81
3.5
Regular Sturm-Liouville problems
86
3.6
Singular Sturm-Liouville problems
95
4
Some Boundary Value Problems
97
4.1
Some useful techniques
98
4.2
One-dimensional heat flow
101
4.3
One-dimensional wave motion
108
4.4
The Dirichlet problem
114
4.5
Multiple Fourier series and applications
121
5
Bessel Functions
127
5.1
Solutions of
Besseľs
equation
128
5'.2 Bessel function identities
133
5.3
Asymptotics and zeros of Bessel functions
138
5.4
Orthogonal sets of Bessel functions
143
5.5
Applications of Bessel functions
149
5.6
Variants of Bessel functions
158
6
Orthogonal Polynomials
164
6.1
Introduction
164
6.2
Legendre polynomials
166
6.3
Spherical coordinates and Legendre functions
174
6.4
Hermite polynomials
184
6.5
Laguerre polynomials
190
6.6
Other orthogonal bases
196
χ
Contents
7
The Fourier Transform
204
7.1
Convolutions
206
7.2
The Fourier transform
213
7.3
Some applications
225
7.4
Fourier transforms and Sturm-Liouville problems
236
7.5 Multivariable
convolutions and Fourier transforms
241
7.6
Transforms related to the Fourier transform
249
8
The Laplace Transform
256
8.1
The Laplace transform
256
8.2
The inversion formula
266
8.3
Applications: Ordinary differential equations
273
8.4
Applications: Partial differential equations
279
8.5
Applications: Integral equations
286
8.6
Asymptotics of Laplace transforms
292
9
Generalized Functions
303
9.1
Distributions
304
9.2
Convergence, convolution, and approximation
314
9.3
More examples: Periodic distributions and finite parts
320
9.4
Tempered distributions and Fourier transforms
330
9.5
Weak solutions of differential equations
341
10
Green's Functions
349
10.1
Green's functions for ordinary differential operators
350
10.2
Green's functions for partial differential operators
358
10.3
Green's functions and regular Sturm-Liouville problems
369
10.4
Green's functions and singular Sturm-Liouville problems
379
Appendices
1
Some physical derivations
386
2
Summary of complex variable theory
392
3
The gamma function
399
4
Calculations in polar coordinates
404
5
The fundamental theorem of ordinary differential equations
409
Answers to the Exercises
413
References
426
Index of Symbols
429
Index
430
This book presents the theory and applications of Fourier series and integrals,
eigenfunction expansions, and related topics, on a level suitable for advanced
undergraduates. It includes material on Bessel functions, orthogonal polyno¬
mials, and Laplace transforms, and it concludes with chapters on generalized
functions and Green's functions for ordinary and partial differential equations.
The book deals almost exclusively with aspects of these subjects that are useful
in physics and engineering, and includes a wide variety of applications. On the
theoretical side, it uses ideas from modern analysis to develop the concepts and
reasoning behind the techniques without getting bogged down in the techni¬
calities of rigorous proofs. |
| any_adam_object | 1 |
| author | Folland, Gerald B. 1947- |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 9780821847909 |
| language | English |
| lccn | 2008047394 |
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| physical | X, 433 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Pure and applied undergraduate texts |
| series2 | Pure and applied undergraduate texts |
| spelling | Folland, Gerald B. 1947- Verfasser (DE-588)137062486 aut Fourier analysis and its applications Gerald B. Folland Providence, R.I. American Mathematical Society 1992 X, 433 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied undergraduate texts 4 Originally published: Pacific Grove, Calif. : Wadsworth & Brooks/Cole Advanced Books & Software, c1992 Fourier analysis Textbooks Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Pure and applied undergraduate texts 4 (DE-604)BV035489189 4 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017617245&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017617245&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Folland, Gerald B. 1947- Fourier analysis and its applications Pure and applied undergraduate texts Fourier analysis Textbooks Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 |
| title | Fourier analysis and its applications |
| title_auth | Fourier analysis and its applications |
| title_exact_search | Fourier analysis and its applications |
| title_full | Fourier analysis and its applications Gerald B. Folland |
| title_fullStr | Fourier analysis and its applications Gerald B. Folland |
| title_full_unstemmed | Fourier analysis and its applications Gerald B. Folland |
| title_short | Fourier analysis and its applications |
| title_sort | fourier analysis and its applications |
| topic | Fourier analysis Textbooks Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Fourier analysis Textbooks Harmonische Analyse |
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