Laplace transform theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
van Nostrand
1966
|
| Schriftenreihe: | The new university mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 123 S. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804119872487030784 |
|---|---|
| adam_text | Contents
Preface
Chapter 1 The Z) Operator 1
1.1 Operational Techniques 1
1.2 Simple D algebra 2
1.3 The Inverse Operator 4
1.4 Expansion of the Inverse Operator 6
Worked Examples 7
Exercises 10
Answers 11
Chapter 2 The Laplace Integral 12
2.1 Conditions for Existence 12
2.2 Abscissae of Convergence 13
2.3 Elementary Transforms 14
2.4 Simple Applications 17
Worked Examples 18
Exercises 20
Answers 21
Chapter 3 Simple Properties of the Laplace Transform 22
3.1 Linear Property 22
3.2 Change of Scale 22
3.3 Shift of the Origin 23
3.4 Periodic Functions 23
3.5 Multiplication by a Simple Power 24
3.6 Expressions involving Inverse Powers of t 25
3.7 Transform of Integrals 25
3.8 Transform of an Integral Function 26
3.9 Examples illustrating 3.8 27
3.10 Behaviour for Large s 28
Exercises 28
Answers 29
vii
viii CONTENTS
Chapter 4 The Inverse Integral 30
4.1 The Inversion Problem 30
4.2 The Fourier Transform 30
4.3 The Inverse as a Contour Integral 32
4.4 Examples of Inversion 35
Exercises 40
Chapter 5 The Convolution or Faltung Integral 43
5.1 The Repeated Integral 43
5.2 Simple Application to Differential Equations 45
5.3 A Generalization of 5.2 46
5.4 Transform of a Product 48
5.5 A Simple Illustration 49
Exercises 49
Answers 50
Chapter 6 Application to Ordinary Linear Differential
Equations 51
6.1 Limitations of the Technique 51
6.2 The Bessel Equation 52
6.3 Another Related Equation 53
6.4 The Laguerre Equation 53
6.5 The Hermite Equation 57
6.6 The Laplace Linear Equation 58
6.7 A Further Illustrative Example 60
Exercises 61
Answers 62
Chapter 7 Partial Differential Equations 64
7.1 Limitations of the Technique 64
7.2 A Simple Equation of the First Order 65
7.3 The Diffusion Equation 66
7.4 The Wave Equation 68
7.4.1 The infinite string 68
7.4.2 The finite string 69
7.4.3 The axially symmetric equation 70
7.4.4 The equation in three dimensions 71
Exercises 73
Answers 74
CONTENTS ix
Chapter 8 Linear Integral Equations 75
8.1 Types of Integral Equations 75
8.2 The Difference Kernel 76
8.2.1 The equation of the first kind 76
8.2.2 The equation of the second kind 77
8.3 The Wiener Hopf Technique 79
8.4 The Milne Equation 82
Exercises 84
Answers 85
Chapter 9 Linear Difference Equations 86
9.1 The Difference Equations 86
9.2 Transform of a Step Function 87
9.3 Simple Applications 87
Worked Examples 89
9.4 Inhomogeneous Equations 90
Worked Examples 90
9.5 Variable Coefficients 91
Worked Examples 92
Exercises 93
Answers 94
Chapter 10 Asymptotic Formulae 95
10.1 Elementary Asymptotic Results 95
10.2 Asymptotic Form of a Transform for Large s 96
10.3 Asymptotic Series of a Transform for Large s 97
10.4 Application to the Exponential Integral 98
10.5 Asymptotic Behaviour of f(t) 99
10.5.1 Single valued function 99
10.5.2 Function with a branch point 100
Worked Examples 102
10.6 Terms involving Logarithms 104
A Simple Example 104
Exercises 105
Answers 106
x contents
Appendix 1 The Fourier Integral Theorem 107
Appendix 2 The Exponential Integral 112
Appendix 3 Operational Formulae 115
Appendix 4 Table of the More Common Laplace Transforms 118
References 120
Index 121
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:33:06Z |
| institution | BVB |
| language | English |
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| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | van Nostrand |
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| series2 | The new university mathematics series |
| spelling | Smith, M. G. Verfasser (DE-588)121993205 aut Laplace transform theory M. G. Smith London [u.a.] van Nostrand 1966 X, 123 S. txt rdacontent n rdamedia nc rdacarrier The new university mathematics series Laplace, Transformation de Laplace transformation Laplace-Transformation (DE-588)4034577-4 gnd rswk-swf Laplace-Transformation (DE-588)4034577-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003550102&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smith, M. G. Laplace transform theory Laplace, Transformation de Laplace transformation Laplace-Transformation (DE-588)4034577-4 gnd |
| subject_GND | (DE-588)4034577-4 |
| title | Laplace transform theory |
| title_auth | Laplace transform theory |
| title_exact_search | Laplace transform theory |
| title_full | Laplace transform theory M. G. Smith |
| title_fullStr | Laplace transform theory M. G. Smith |
| title_full_unstemmed | Laplace transform theory M. G. Smith |
| title_short | Laplace transform theory |
| title_sort | laplace transform theory |
| topic | Laplace, Transformation de Laplace transformation Laplace-Transformation (DE-588)4034577-4 gnd |
| topic_facet | Laplace, Transformation de Laplace transformation Laplace-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003550102&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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