Transform methods in applied mathematics: an introduction
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1996
|
| Series: | Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts
[15] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz.: S. 326 - 327 |
| Physical Description: | X, 332 S. Ill., graph. Darst. |
| ISBN: | 0471008109 |
Staff View
MARC
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| 100 | 1 | |a Lancaster, Peter |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Transform methods in applied mathematics |b an introduction |c Peter Lancaster ; Kȩstutis Šalkauskas |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1996 | |
| 300 | |a X, 332 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter 1 The Laplace Transform 1
1.1 Definition and Examples 1
1.2 An Existence Theorem 6
1.3 Laplace Transforms of Derivatives 8
1.4 Laplace Transforms and Integrals 14
1.5 The Shifting Theorems 16
1.6 Convolution 22
1.7 The Zero State Response of a System 25
Chapter 2 Elementary Functions of a Complex Variable 28
2.1 The Power Function 28
2.2 Polynomials and Their Zeros 33
2.3 Factorization of Polynomials 35
2.4 Rational Functions 37
2.5 The Exponential Function 37
2.6 The Trigonometric and Hyperbolic Functions 39
2.7 The Logarithm 40
2.8 The Inverse Trigonometric and Hyperbolic Functions 41
2.9 Limits and Continuity 42
2.10 The Derivative 44
2.11 Analytic Functions 46
2.12 The Cauchy Riemann Equations 48
2.13 Integration 50
Chapter 3 Fourier Series and the Discrete Fourier Transformation 52
3.1 Periodic Functions 52
3.2 Trigonometric Polynomials 56
3.3 Complex Notation for Trigonometric Polynomials 57
3.4 Approximation by Trigonometric Polynomials 61
3.5 Even and Odd Functions 68
3.6 Filters and Periodic Functions 72
3.7 A Discrete Orthogonality Condition 77
vii
viii Contents
3.8 The Discrete Fourier Transform and Its Inverse 81
3.9 Illustrations of the Discrete Fourier Transform 88
3.10 The Fast Fourier Transform 92
3.11 Illustrations of the DFT 95
Chapter 4 Complex Integrals and Power Series 99
4.1 Line Integrals 99
4.2 The Cauchy Goursat Theorem and Cauchy s Formula 104
4.3 Taylor Series 113
4.4 Laurent Series 117
4.5 Some Properties of Power Series 121
4.6 Zeros, Singularities, and Poles 123
4.7 Computation of Residues 126
4.8 Evaluation of Real Integrals 129
4.9 The Dirichlet Integral 134
4.10 Inversion of Laplace Transforms 136
Chapter 5 The z Transform and Discrete Filters 140
5.1 The z Transform of a Sequence 140
5.2 The z Transform of a Sinusoid 145
5.3 Inversion of the z Transform 146
5.4 Discrete Linear Systems and Filters 150
5.5 The Impulse Response of a Discrete Filter 153
5.6 The Transfer Function of a Discrete Filter 157
5.7 Wave Forming Filters 161
5.8 Least Squares Construction of a Wave Forming Filter 163
5.9 Difference Equations 165
5.10 Cascades and Inverses of Discrete Filters 169
5.11 Stability 171
5.12 Frequency Analysis of Discrete Filters 174
5.13 Examples of Frequency Analyses of Discrete Filters 176
Chapter 6 The Fourier Transform and Continuous Filters 182
6.1 Introduction to the Fourier Transform 182
6.2 Basic Properties and Examples 188
6.3 Examples of Transforms and Inverse Transforms 196
6.4 The Shannon Sampling Formula 202
6.5 Cumulative Amplitude for the Transform of a Truncated
Sinusoid 206
6.6 The Delta Function: Distributions 209
6.7 Transforms Involving Distributions 217
6.8 Convolution 221
6.9 Continuous Linear Systems and Filters 224
Contents ix
6.10 The Impulse Response of a Filter 227
6.11 Transforms and Filters 229
6.12 Examples of Continuous Filters 231
6.13 The Hilbert Transform 236
6.14 Fourier Transforms and Periodic Functions 239
Chapter 7 Wavelets 242
7.1 Introduction 242
7.2 Periodic and Modulated Periodic Functions 243
7.3 Fourier Approximation with Wavelets 247
7.4 Some Computational Aspects 249
7.5 Localization in Time and Frequency 253
7.6 Least Squares Approximation by Piecewise Constant
Functions 255
7.7 The Haar Wavelet 259
7.8 The Haar Basis 263
7.9 The Two Scale Relation 265
7.10 The Shannon Wavelets 267
7.11 Computation 271
7.12 Wavelet Transforms 276
7.13 Daubechies Wavelets 278
Appendix A Vectors, Matrices, and Linear Spaces 281
A.I Vectors 281
A.2 Addition of Vectors 283
A.3 Scalar Multiplication 284
A.4 Inner Products 285
A.5 Matrices 288
A.6 Multiplication of Matrices 289
A.7 Linear Algebraic Equations 292
A.8 Linear Spaces 294
A.9 Inner Products Spaces 296
Appendix B Classes of Functions 300
Appendix C Two Important Limits 304
Appendix D Improper Integrals 306
Appendix E Complex Numbers 315
E. 1 Definition of Complex Numbers and Their Arithmetic 316
E.2 Complex Numbers in Cartesian Form and
the Argand Diagram 320
x Contents
E.3 Polar Coordinates 321
E.4 Geometric Considerations 323
Bibliography 326
Index 329
|
| any_adam_object | 1 |
| author | Lancaster, Peter Šalkauskas, Ke̢stutis |
| author_facet | Lancaster, Peter Šalkauskas, Ke̢stutis |
| author_role | aut aut |
| author_sort | Lancaster, Peter |
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| dewey-raw | 515/.723 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| spelling | Lancaster, Peter Verfasser aut Transform methods in applied mathematics an introduction Peter Lancaster ; Kȩstutis Šalkauskas New York [u.a.] Wiley 1996 X, 332 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts [15] Literaturverz.: S. 326 - 327 Fourier-transformatie gtt Laplace-transformaties gtt Transformaties (wiskunde) gtt Wavelets gtt Transformations (Mathematics) Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Anwendung (DE-588)4196864-5 gnd rswk-swf Laplace-Transformation (DE-588)4034577-4 gnd rswk-swf Transformation Mathematik (DE-588)4060637-5 gnd rswk-swf Z-Transformation (DE-588)4191048-5 gnd rswk-swf Transformation Mathematik (DE-588)4060637-5 s Laplace-Transformation (DE-588)4034577-4 s Anwendung (DE-588)4196864-5 s Fourier-Transformation (DE-588)4018014-1 s Z-Transformation (DE-588)4191048-5 s 1\p DE-604 Šalkauskas, Ke̢stutis Verfasser aut Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts [15] (DE-604)BV012067942 15 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007403122&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lancaster, Peter Šalkauskas, Ke̢stutis Transform methods in applied mathematics an introduction Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts Fourier-transformatie gtt Laplace-transformaties gtt Transformaties (wiskunde) gtt Wavelets gtt Transformations (Mathematics) Fourier-Transformation (DE-588)4018014-1 gnd Anwendung (DE-588)4196864-5 gnd Laplace-Transformation (DE-588)4034577-4 gnd Transformation Mathematik (DE-588)4060637-5 gnd Z-Transformation (DE-588)4191048-5 gnd |
| subject_GND | (DE-588)4018014-1 (DE-588)4196864-5 (DE-588)4034577-4 (DE-588)4060637-5 (DE-588)4191048-5 |
| title | Transform methods in applied mathematics an introduction |
| title_auth | Transform methods in applied mathematics an introduction |
| title_exact_search | Transform methods in applied mathematics an introduction |
| title_full | Transform methods in applied mathematics an introduction Peter Lancaster ; Kȩstutis Šalkauskas |
| title_fullStr | Transform methods in applied mathematics an introduction Peter Lancaster ; Kȩstutis Šalkauskas |
| title_full_unstemmed | Transform methods in applied mathematics an introduction Peter Lancaster ; Kȩstutis Šalkauskas |
| title_short | Transform methods in applied mathematics |
| title_sort | transform methods in applied mathematics an introduction |
| title_sub | an introduction |
| topic | Fourier-transformatie gtt Laplace-transformaties gtt Transformaties (wiskunde) gtt Wavelets gtt Transformations (Mathematics) Fourier-Transformation (DE-588)4018014-1 gnd Anwendung (DE-588)4196864-5 gnd Laplace-Transformation (DE-588)4034577-4 gnd Transformation Mathematik (DE-588)4060637-5 gnd Z-Transformation (DE-588)4191048-5 gnd |
| topic_facet | Fourier-transformatie Laplace-transformaties Transformaties (wiskunde) Wavelets Transformations (Mathematics) Fourier-Transformation Anwendung Laplace-Transformation Transformation Mathematik Z-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007403122&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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