An introduction to laplace transforms and fourier series:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2014
|
| Edition: | 2. ed. |
| Series: | Springer undergraduate mathematics series
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XV, 318 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9781447163947 9781447163954 |
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MARC
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Record in the Search Index
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| adam_text |
Titel: An introduction to Laplace transforms and Fourier series
Autor: Dyke, Phil P. G
Jahr: 2014
Contents
1 The Laplace Transform.1
1.1 Introduction.1
1.2 The Laplace Transform.2
1.3 Elementary Properties.5
1.4 Exercises.12
2 Further Properties of the Laplace Transform.13
2.1 Real Functions.13
2.2 Derivative Property of the Laplace Transform.14
2.3 Heaviside's Unit Step Function.18
2.4 Inverse Laplace Transform.19
2.5 Limiting Theorems.24
2.6 The Impulse Function.26
2.7 Periodic Functions.33
2.8 Exercises.36
3 Convolution and the Solution of Ordinary
Differential Equations.39
3.1 Introduction.39
3.2 Convolution.39
3.3 Ordinary Differential Equations.51
3.3.1 Second Order Differential Equations.57
3.3.2 Simultaneous Differential Equations.66
3.4 Using Step and Impulse Functions.71
3.5 Integral Equations.77
3.6 Exercises.79
4 Fourier Series.83
4.1 Introduction.83
4.2 Definition of a Fourier Series.85
4.3 Odd and Even Functions.97
4.4 Complex Fourier Series.99
xiii
xiv Contents
4.5 Half Range Series.103
4.6 Properties of Fourier Series.107
4.7 Generalised Fourier Series.115
4.8 Exercises.119
5 Partial Differential Equations.123
5.1 Introduction.123
5.2 Classification of Partial Differential Equations.125
5.3 Separation of Variables.128
5.4 Using Laplace Transforms to Solve PDEs.131
5.5 Boundary Conditions and Asymptotics.137
5.6 Exercises.141
6 Fourier Transforms.145
6.1 Introduction.145
6.2 Deriving the Fourier Transform.145
6.3 Basic Properties of the Fourier Transform.151
6.4 Fourier Transforms and Partial Differential Equations.159
6.5 Windowing.163
6.6 Exercises.171
7 Wavelets and Signal Processing.175
7.1 Introduction.175
7.2 Wavelets.175
7.3 Basis Functions.176
7.4 The Four Wavelet Case.181
7.5 Transforming Wavelets.187
7.6 Wavelets and Fourier Series.191
7.7 Localisation.200
7.8 Short Time Fourier Transfomi.204
7.9 Exercises.207
8 Complex Variables and Laplace Transforms.209
8.1 Introduction.209
8.2 Rudiments of Complex Analysis.209
8.3 Complex Integration.212
8.4 Branch Points.219
8.5 The Inverse Laplace Transform. 225
8.6 Using the Inversion Formula in Asymptotics.230
8.7 Exercises. 235
Contents xv
Appendix A: Answers to Exercises.239
Appendix B: Table of Laplace Transforms.293
Appendix C: Linear Spaces.299
Bibliography.313
Index.315 |
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| author | Dyke, Phil P. G. 1948- |
| author_GND | (DE-588)121604276 |
| author_facet | Dyke, Phil P. G. 1948- |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.723 21 |
| dewey-sort | 3515 3723 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| isbn | 9781447163947 9781447163954 |
| language | English |
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| publishDate | 2014 |
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| spelling | Dyke, Phil P. G. 1948- Verfasser (DE-588)121604276 aut An introduction to laplace transforms and fourier series Phil Dyke 2. ed. London [u.a.] Springer 2014 XV, 318 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Laplace transformation Fourier series Laplace-Transformation (DE-588)4034577-4 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Laplace-Transformation (DE-588)4034577-4 s DE-604 Fourier-Reihe (DE-588)4155109-6 s X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4593896&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027238502&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dyke, Phil P. G. 1948- An introduction to laplace transforms and fourier series Laplace transformation Fourier series Laplace-Transformation (DE-588)4034577-4 gnd Fourier-Reihe (DE-588)4155109-6 gnd |
| subject_GND | (DE-588)4034577-4 (DE-588)4155109-6 |
| title | An introduction to laplace transforms and fourier series |
| title_auth | An introduction to laplace transforms and fourier series |
| title_exact_search | An introduction to laplace transforms and fourier series |
| title_full | An introduction to laplace transforms and fourier series Phil Dyke |
| title_fullStr | An introduction to laplace transforms and fourier series Phil Dyke |
| title_full_unstemmed | An introduction to laplace transforms and fourier series Phil Dyke |
| title_short | An introduction to laplace transforms and fourier series |
| title_sort | an introduction to laplace transforms and fourier series |
| topic | Laplace transformation Fourier series Laplace-Transformation (DE-588)4034577-4 gnd Fourier-Reihe (DE-588)4155109-6 gnd |
| topic_facet | Laplace transformation Fourier series Laplace-Transformation Fourier-Reihe |
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