Laplace transforms and an introduction to distributions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Horwood
1991
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Mathematics and its applications : Statistics, operational research and computational mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 411 S. graph. Darst. |
| ISBN: | 0135235499 0135248108 |
Internformat
MARC
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| 100 | 1 | |a Guest, Paul B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Laplace transforms and an introduction to distributions |c P. B. Guest |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a New York u.a. |b Horwood |c 1991 | |
| 300 | |a 411 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Mathematics and its applications : Statistics, operational research and computational mathematics | |
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| 650 | 4 | |a Theory of distributions (Functional analysis) | |
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Datensatz im Suchindex
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Table of contents
Preface 9
Notation 11
Introduction 17
CHAPTER 1 SUMMABILITY OF FUNCTIONS 25
1 Convergence of integrals 25
2 Functions that vanish below 35
Exercises 1A 41
Exercises IB 42
CHAPTER 2 THE LAPLACE TRANSFORM 48
3 Definition of the Laplace transform 49
4 Rules for the calculation of Laplace transforms 53
Exercises 2A 60
Exercises 2B 63
CHAPTER 3 FURTHER TRANSFORM RESULTS 65
5 Further transform results 65
6 Step and half periodic functions 71
Exercises 3A 76
Exercises 3B 85
CHAPTER 4 ASYMPTOTIC RELATIONS 89
7 Asymptotic relations 89
Exercises 4A 93
Exercises 4B 94
6 Table of contents
CHAPTER 5 THE LAPLACE TRANSFORM OF A DERIVATIVE 95
8 The Laplace transform of derivatives 96
Exercises 5A 106
Exercises 5B 110
CHAPTER 6 THE INVERSE LAPLACE TRANSFORM 116
9 Uniqueness of the inverse transform 116
10 The calculation of elementary inverse transforms 118
11 The impulse response 125
Exercises 6A 126
Exercises 6B 131
CHAPTER 7 CONVOLUTION 137
12 Definition of convolution 137
13 Convolution with the impulse response 139
14 The Laplace transform of a convolution 140
Exercises 7A 143
CHAPTER 8 DIFFERENTIAL EQUATIONS 147
15 Solution by convolution 148
16 Solution by Laplace transform 153
Exercises 8A 158
Exercises 8B 164
CHAPTER 9 MATRICES OF POLYNOMIALS 166
17 Notation and elementary results 166
18 Regular matrices 171
19 Reduction to a regular matrix 174
Exercises 9A 176
Exercises 9B 178
CHAPTER 10 SIMULTANEOUS DIFFERENTIAL EQUATIONS 185
20 Regular systems: solution by convolution 186
21 Regular systems: solution by Laplace transform 193
Exercises 10A 195
Exercises 10B 199
CHAPTER 11 GENERAL HOMOGENEOUS SYSTEMS 202
22 Smoothness of solutions 202
23 The space of initial vectors 204
24 Calculation of the initial vectors 206
25 Solutions on the real line 211
Exercises 11A 213
Exercises 1 IB 215
CHAPTER 12 DISTRIBUTIONS 217
26 Functions as operators 218
Table of contents 7
27 The Dirac operator 221
28 Further examples of linear functional 222
29 Linear functional in general 224
30 The derivative of a distribution 225
31 Convergence of distributions 235
32 Distributions of finite order 242
Exercises 12A 244
Exercises 12B 249
CHAPTER 13 CONVOLUTION OF DISTRIBUTIONS 253
33 Distributions that vanish below 253
34 Definition of convolution 254
35 Properties of convolution 256
36 Convolution of a function and a distribution 261
37 Physical realization of distributions 265
Exercises 13A 272
Exercises 13B 275
CHAPTER 14 SUMMABILITY OF DISTRIBUTIONS 279
38 Definition of summability 279
39 Properties of summable distributions 280
40 Extending a distribution 282
41 Summation of series 285
42 Summability and convolution 288
Exercises 14A 289
Exercises 14B 292
CHAPTER 15 THE LAPLACE TRANSFORM OF A DISTRIBUTION 296
43 Definition of the Laplace transform 296
44 Properties of the Laplace transform 297
45 Generating functions 299
46 Asymptotic relations 305
47 The inverse Laplace transform for distributions 307
48 The Laplace transform of a convolution 310
Exercises 15A 311
Exercises 15B 314
CHAPTER 16 DISTRIBUTIONAL DIFFERENTIAL EQUATIONS 316
49 Solutions that vanish below 316
50 Initial value problems 319
51 The case of locally integrable input 321
Exercises 16A 323
Exercises 16B 327
CHAPTER 17 SIMULTANEOUS DISTRIBUTIONAL DIFFERENTIAL
EQUATIONS 329
52 Matrices of distributions 329
8 Table of contents
53 Solutions that vanish below 332
54 Initial value problems 334
55 The case of locally integrable input 338
Exercises 17A 339
Exercises 17B 341
CHAPTER 18 DIFFERENCE EQUATIONS 343
56 Generating functions and translation operators 343
57 Solutions that vanish below 347
58 Generalities 348
59 Difference equations for functions 351
60 Difference equations for distributions 354
61 Difference equations for sequences 356
62 Generalities for matrix operators 360
63 Simultaneous difference equations for functions 362
64 Simultaneous difference equations for sequences 369
Exercises 18A 375
Exercises 18B 383
Notes 399
Bibliography 405
Laplace transforms derived in the text 407
Index 409 |
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| illustrated | Illustrated |
| indexdate | 2024-07-20T05:38:00Z |
| institution | BVB |
| isbn | 0135235499 0135248108 |
| language | English |
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| physical | 411 S. graph. Darst. |
| publishDate | 1991 |
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| publisher | Horwood |
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| series2 | Mathematics and its applications : Statistics, operational research and computational mathematics |
| spelling | Guest, Paul B. Verfasser aut Laplace transforms and an introduction to distributions P. B. Guest 1. publ. New York u.a. Horwood 1991 411 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications : Statistics, operational research and computational mathematics Laplace transformation Theory of distributions (Functional analysis) Laplace-Transformation (DE-588)4034577-4 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Laplace-Transformation (DE-588)4034577-4 s DE-188 Distribution Funktionalanalysis (DE-588)4070505-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004214624&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Guest, Paul B. Laplace transforms and an introduction to distributions Laplace transformation Theory of distributions (Functional analysis) Laplace-Transformation (DE-588)4034577-4 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd |
| subject_GND | (DE-588)4034577-4 (DE-588)4070505-5 |
| title | Laplace transforms and an introduction to distributions |
| title_auth | Laplace transforms and an introduction to distributions |
| title_exact_search | Laplace transforms and an introduction to distributions |
| title_full | Laplace transforms and an introduction to distributions P. B. Guest |
| title_fullStr | Laplace transforms and an introduction to distributions P. B. Guest |
| title_full_unstemmed | Laplace transforms and an introduction to distributions P. B. Guest |
| title_short | Laplace transforms and an introduction to distributions |
| title_sort | laplace transforms and an introduction to distributions |
| topic | Laplace transformation Theory of distributions (Functional analysis) Laplace-Transformation (DE-588)4034577-4 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd |
| topic_facet | Laplace transformation Theory of distributions (Functional analysis) Laplace-Transformation Distribution Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004214624&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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