Introduction to partial differential equations from Fourier series to boundary-value problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. u.a.
Addison-Wesley
1970
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| Schriftenreihe: | Addison-Wesley series in applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 179 S. |
Internformat
MARC
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| 100 | 1 | |a Broman, Arne |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to partial differential equations from Fourier series to boundary-value problems |
| 264 | 1 | |a Reading, Mass. u.a. |b Addison-Wesley |c 1970 | |
| 300 | |a X, 179 S. | ||
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Datensatz im Suchindex
| _version_ | 1804117025781448704 |
|---|---|
| adam_text | CONTENTS
Conventions vii
Symbols ix
Chapter 1 Fourier series 1
1.1 Basic concepts 1
1.2 Fourier series and Fourier coefficients 4
1.3 A minimizing property of the Fourier coefficients. The Riemann
Lebesgue theorem 10
1.4 Convergence of Fourier series 13
1.5 The Parseval formula 18
1.6 Determination of the sum of certain trigonometric series .... 23
Chapter 2 Orthogonal systems 26
2.1 Integration of complex valued functions of a real variable • • ¦ • 26
2.2 Orthogonal systems 27
2.3 Complete orthogonal systems 33
2.4 Integration of Fourier series 36
2.5 The Gram Schmidt orthogonalization process 38
2.6 Sturm Liouville problems 39
Chapter 3 Orthogonal polynomials 45
3.1 The Legendre polynomials 45
3.2 Legendre series 48
3.3 The Legendre differential equation. The generating function of the
Legendre polynomials 51
3.4 The Tchebycheff polynomials 54
3.5 Tchebycheff series 57
3.6 The Hermite polynomials. The Laguerre polynomials 59
Chapter 4 Fourier transforms 62
4.1 Infinite interval of integration 62
4.2 The Fourier integral formula: a heuristic introduction 63
4.3 Auxiliary theorems 65
v
vi CONTENTS
4.4 Proof of the Fourier integral formula. Fourier transforms • • • • 68
4.5 The convolution theorem. The Parseval formula 76
Chapter 5 Laplace transforms 80
5.1 Definition of the Laplace transform. Domain. Analyticity • 80
5.2 Inversion formula 83
5.3 Further properties of Laplace transforms. The convolution theorem ¦ 85
5.4 Applications to ordinary differential equations 93
Chapter 6 Bessel functions 99
6.1 The gamma function 99
6.2 The Bessel differential equation. Bessel functions 101
6.3 Some particular Bessel functions 104
6.4 Recursion formulas for the Bessel functions 106
6.5 Estimation of Bessel functions for large values of x. The zeros of the
Bessel functions 109
6.6 Bessel series 111
6.7 The generating function of the Bessel functions of integral order • ¦ 113
6.8 Neumann functions 115
Chapter 7 Partial differential equations of first order 118
7.1 Introduction 118
7.2 The differential equation of a family of surfaces 121
7.3 Homogeneous differential equations 124
7.4 Linear and quasilinear differential equations 127
Chapter 8 Partial differential equations of second order 131
8.1 Problems in physics leading to partial differential equations ¦ ¦ ¦ • 131
8.2 Definitions 135
8.3 The wave equation 140
8.4 The heat equation 148
8.5 The Laplace equation 159
Answers to exercises 165
Bibliography 174
Index 176
|
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| discipline | Mathematik |
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| language | English |
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| spelling | Broman, Arne Verfasser aut Introduction to partial differential equations from Fourier series to boundary-value problems Reading, Mass. u.a. Addison-Wesley 1970 X, 179 S. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in applied mathematics Partiella differentialekvationer Differential equations, Partial Laplace-Transformation (DE-588)4034577-4 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Bessel-Funktionen (DE-588)4069359-4 gnd rswk-swf Orthogonale Funktionen (DE-588)4475233-7 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Bessel-Funktionen (DE-588)4069359-4 s DE-604 Laplace-Transformation (DE-588)4034577-4 s Harmonische Analyse (DE-588)4023453-8 s Orthogonale Funktionen (DE-588)4475233-7 s Partielle Differentialgleichung (DE-588)4044779-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001697629&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 | Broman, Arne Introduction to partial differential equations from Fourier series to boundary-value problems Partiella differentialekvationer Differential equations, Partial Laplace-Transformation (DE-588)4034577-4 gnd Harmonische Analyse (DE-588)4023453-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Bessel-Funktionen (DE-588)4069359-4 gnd Orthogonale Funktionen (DE-588)4475233-7 gnd |
| subject_GND | (DE-588)4034577-4 (DE-588)4023453-8 (DE-588)4044779-0 (DE-588)4069359-4 (DE-588)4475233-7 (DE-588)4151278-9 |
| title | Introduction to partial differential equations from Fourier series to boundary-value problems |
| title_auth | Introduction to partial differential equations from Fourier series to boundary-value problems |
| title_exact_search | Introduction to partial differential equations from Fourier series to boundary-value problems |
| title_full | Introduction to partial differential equations from Fourier series to boundary-value problems |
| title_fullStr | Introduction to partial differential equations from Fourier series to boundary-value problems |
| title_full_unstemmed | Introduction to partial differential equations from Fourier series to boundary-value problems |
| title_short | Introduction to partial differential equations from Fourier series to boundary-value problems |
| title_sort | introduction to partial differential equations from fourier series to boundary value problems |
| topic | Partiella differentialekvationer Differential equations, Partial Laplace-Transformation (DE-588)4034577-4 gnd Harmonische Analyse (DE-588)4023453-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Bessel-Funktionen (DE-588)4069359-4 gnd Orthogonale Funktionen (DE-588)4475233-7 gnd |
| topic_facet | Partiella differentialekvationer Differential equations, Partial Laplace-Transformation Harmonische Analyse Partielle Differentialgleichung Bessel-Funktionen Orthogonale Funktionen Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001697629&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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