Integral transformations, operational calculus, and generalized functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1996
|
| Schriftenreihe: | Mathematics and its applications
377 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 231 S. graph. Darst. |
| ISBN: | 079234183X |
Internformat
MARC
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| 245 | 1 | 0 | |a Integral transformations, operational calculus, and generalized functions |c by R. G. Buschman |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1996 | |
| 300 | |a XII, 231 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Mathematics and its applications |v 377 | |
| 650 | 7 | |a Transformations intégrales |2 ram | |
| 650 | 4 | |a Calculus, Operational | |
| 650 | 4 | |a Integral transforms | |
| 650 | 4 | |a Theory of distributions (Functional analysis) | |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
PREFACE xi
ACKNOWLEDGEMENTS xiii
CHAPTER 1. LAPLACE TRANSFORMATIONS 1
1.0 Introduction 1
1.1 An Initital Value Problem 1
1.2 A Partial Differential Equation Problem 7
1.3 Basic Properties 16
1.4 Addidtional Properties 22
1.5 Ordinary Differential Equations 27
1.6 Convolution 38
1.7 Partial Differential Equations 43
1.8 Integral Equations and Fractional Integrals 48
1.9 Further Uses of LaPlace Transformations 54
CHAPTER 2. MIKUSINSKI OPERATORS 63
2.0 Introduction 63
2.1 Properties of Numbers and Convolutions 64
2.2 Construction of the Rational Numbers 69
2.3 Construction of the Mikusinski Operators 71
2.4 Applications to Differential and Integral Equations 77
viii Table of Contents
CHAPTER 3. FOURIER TRANSFORMATIONS 81
3.0 Introduction 81
3.1 Problems from Heat Flow 81
3.2 Operational Properties 85
3.3 Convoltuion and Inversion 89
3.4 Applications 93
3.5 Cosine and Sine Transformations 99
CHAPTER 4. GENERALIZED FUNCTIONS 107
4.0 Introduction 107
4.1 Sequences of Rational Numbers 107
4.2 Good Functions and Their Properties 110
4.3 Generalized Functions 115
4.4 Fourier Transforms and Differential Equations 121
CHAPTER 5. OTHER TRANSFORMATIONS 127
5.0 Introduction 127
5.1 Mellin Transformation 128
5.2 Power Series Transformation 132
5.3 Finite Fourier Transformation 140
5.4 Finite LaPlace Transformation 146
5.5 Two Dimensional LaPlace Transformation 152
5.6 Design of Transformations 161
REFERENCES 167
APPENDICES 171
A. The Titchmarsh Theorem 171
B. Inversion Integrals 173
C. Interchange of Order of Infinite Processes 175
D. Definitions and Properties of Some Special Functions .. 177
Table of Contents ix
TABLES OF TRANSFORMS 181
1. Laplace 181
2. Inverse Laplace 186
3. Fourier 192
4. Fourier Cosine 194
5. Fourier Sine 196
6. Mellin 198
7. Power Series 200
8. Finite Fourier 203
9. Finite Fourier Cosine 206
10. Finite Fourier Sine 208
11. Finite Laplace 210
12. Two Dimensional Laplace 214
13. Inverse Two Dimensional Laplace 216
INDEX 221
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:02:52Z |
| institution | BVB |
| isbn | 079234183X |
| language | English |
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| physical | XII, 231 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Kluwer |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Buschman, Robert G. Verfasser aut Integral transformations, operational calculus, and generalized functions by R. G. Buschman Dordrecht [u.a.] Kluwer 1996 XII, 231 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 377 Transformations intégrales ram Calculus, Operational Integral transforms Theory of distributions (Functional analysis) Integraltransformation (DE-588)4027235-7 gnd rswk-swf Integraltransformation (DE-588)4027235-7 s DE-604 Mathematics and its applications 377 (DE-604)BV008163334 377 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007385521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buschman, Robert G. Integral transformations, operational calculus, and generalized functions Mathematics and its applications Transformations intégrales ram Calculus, Operational Integral transforms Theory of distributions (Functional analysis) Integraltransformation (DE-588)4027235-7 gnd |
| subject_GND | (DE-588)4027235-7 |
| title | Integral transformations, operational calculus, and generalized functions |
| title_auth | Integral transformations, operational calculus, and generalized functions |
| title_exact_search | Integral transformations, operational calculus, and generalized functions |
| title_full | Integral transformations, operational calculus, and generalized functions by R. G. Buschman |
| title_fullStr | Integral transformations, operational calculus, and generalized functions by R. G. Buschman |
| title_full_unstemmed | Integral transformations, operational calculus, and generalized functions by R. G. Buschman |
| title_short | Integral transformations, operational calculus, and generalized functions |
| title_sort | integral transformations operational calculus and generalized functions |
| topic | Transformations intégrales ram Calculus, Operational Integral transforms Theory of distributions (Functional analysis) Integraltransformation (DE-588)4027235-7 gnd |
| topic_facet | Transformations intégrales Calculus, Operational Integral transforms Theory of distributions (Functional analysis) Integraltransformation |
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