Partial differential equations in fluid dynamics:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2008
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 282 S. graph. Darst. |
| ISBN: | 9780521888240 |
Staff View
MARC
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| 100 | 1 | |a Herron, Isom H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Partial differential equations in fluid dynamics |c Isom H. Herron, Michael R. Foster |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2008 | |
| 300 | |a XIII, 282 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Dynamique des fluides numérique | |
| 650 | 4 | |a Fluides, Dynamique des - Mathématiques | |
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Fluid dynamics |x Mathematics |v Textbooks | |
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| 700 | 1 | |a Foster, Michael R. |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804138003326566400 |
|---|---|
| adam_text | Contents
Preface
page
xi
Acknowledgments
xiii
1
Review of Analytic Function Theory
.......................1
1.1
Preamble
1
1.2
Fundamentals of Complex Numbers
1
1.3
Analytic Functions
4
1.4
Integration and Cauchy s Theorem
8
1.5
Application to Real Integrals
19
REFERENCES
30
EXERCISES
30
2
Special Functions
..................................37
2.1
Preamble
37
2.2
The Gamma Function
39
2.3
Functions Defined by Differential Equations
43
2.4
Integral Representations
51
REFERENCES
55
EXERCISES
55
3
Eigenvalue Problems and Eigenfunction Expansions
............62
3.1
Preamble
62
3.2
Synge s Setup for Rayleigh s Criterion
62
3.3
Sturm-Liouville Problems
65
3.4
Expansions in Eigenfunctions
71
3.5
Worked Examples
74
3.6
Nonstandard
Eigenvalue Problems
78
3.7
Fourier-Bessel Series
85
3.8
Continuous versus Discrete Spectra
91
REFERENCES
94
EXERCISES
95
vu
viii Contents
4
Green s Functions for Boundary-Value Problems
.............106
4.1
Preamble
106
4.2
Green s Function
110
4.3
Connections with Distributions
119
4.4
First-Order System: Green s Matrices
121
4.5
Generalized Green s Functions
122
4.6
Expansions in Eigenfunctions
125
REFERENCES
132
EXERCISES
133
4.7
Appendix: Linear Ordinary Differential Equations
142
5
Laplace Transform Methods
..........................148
5.1
Preamble
148
5.2
The Laplace Transform and Its Inverse
148
5.3
Worked Examples
156
5.4
Bilateral Laplace Transform
171
REFERENCES
175
EXERCISES
176
6
Fourier Transform Methods
...........................183
6.1
Preamble
183
6.2
The Fourier Transform and Its Inverse
183
6.3
Worked Examples
188
6.4
Mellin Transforms
200
6.5
Worked Examples
205
REFERENCES
207
EXERCISES
208
7
Particular Physical Problems
..........................217
7.1
Preamble
217
7.2
Lee Waves
217
7.3
The Far Momentum Wake
220
7.4
Kelvin-Helmholtz Instability
223
7.5
The Boundary-Layer Signal Problem
225
7.6
Stability of Plane
Couette
Flow
228
7.7
Generalized Transform Techniques
231
REFERENCES
235
EXERCISES
236
8
Asymptotic Expansions of Integrals
......................244
8.1
Preamble
244
8.2
Asymptotic Expansions
244
8.3
Integration by Parts
245
Contents ix
8.4
Laplace-Type
Integrals;
Watson s
Lemma 246
8.5
Generalized Laplace Integrals: Laplace s Method
253
8.6
Method of Steepest Descent
256
8.7
Method of Stationary Phase; Kelvin s Results
266
REFERENCES
268
EXERCISES
268
Index
279
|
| adam_txt |
Contents
Preface
page
xi
Acknowledgments
xiii
1
Review of Analytic Function Theory
.1
1.1
Preamble
1
1.2
Fundamentals of Complex Numbers
1
1.3
Analytic Functions
4
1.4
Integration and Cauchy's Theorem
8
1.5
Application to Real Integrals
19
REFERENCES
30
EXERCISES
30
2
Special Functions
.37
2.1
Preamble
37
2.2
The Gamma Function
39
2.3
Functions Defined by Differential Equations
43
2.4
Integral Representations
51
REFERENCES
55
EXERCISES
55
3
Eigenvalue Problems and Eigenfunction Expansions
.62
3.1
Preamble
62
3.2
Synge's Setup for Rayleigh's Criterion
62
3.3
Sturm-Liouville Problems
65
3.4
Expansions in Eigenfunctions
71
3.5
Worked Examples
74
3.6
Nonstandard
Eigenvalue Problems
78
3.7
Fourier-Bessel Series
85
3.8
Continuous versus Discrete Spectra
91
REFERENCES
94
EXERCISES
95
vu
viii Contents
4
Green's Functions for Boundary-Value Problems
.106
4.1
Preamble
106
4.2
Green's Function
110
4.3
Connections with Distributions
119
4.4
First-Order System: Green's Matrices
121
4.5
Generalized Green's Functions
122
4.6
Expansions in Eigenfunctions
125
REFERENCES
132
EXERCISES
133
4.7
Appendix: Linear Ordinary Differential Equations
142
5
Laplace Transform Methods
.148
5.1
Preamble
148
5.2
The Laplace Transform and Its Inverse
148
5.3
Worked Examples
156
5.4
Bilateral Laplace Transform
171
REFERENCES
175
EXERCISES
176
6
Fourier Transform Methods
.183
6.1
Preamble
183
6.2
The Fourier Transform and Its Inverse
183
6.3
Worked Examples
188
6.4
Mellin Transforms
200
6.5
Worked Examples
205
REFERENCES
207
EXERCISES
208
7
Particular Physical Problems
.217
7.1
Preamble
217
7.2
Lee Waves
217
7.3
The Far Momentum Wake
220
7.4
Kelvin-Helmholtz Instability
223
7.5
The Boundary-Layer Signal Problem
225
7.6
Stability of Plane
Couette
Flow
228
7.7
Generalized Transform Techniques
231
REFERENCES
235
EXERCISES
236
8
Asymptotic Expansions of Integrals
.244
8.1
Preamble
244
8.2
Asymptotic Expansions
244
8.3
Integration by Parts
245
Contents ix
8.4
Laplace-Type
Integrals;
Watson's
Lemma 246
8.5
Generalized Laplace Integrals: Laplace's Method
253
8.6
Method of Steepest Descent
256
8.7
Method of Stationary Phase; Kelvin's Results
266
REFERENCES
268
EXERCISES
268
Index
279 |
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| spelling | Herron, Isom H. Verfasser aut Partial differential equations in fluid dynamics Isom H. Herron, Michael R. Foster 1. publ. Cambridge Cambridge University Press 2008 XIII, 282 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Dynamique des fluides numérique Fluides, Dynamique des - Mathématiques Équations aux dérivées partielles Mathematik Fluid dynamics Mathematics Textbooks Differential equations, Partial Textbooks Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Foster, Michael R. Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016728101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Herron, Isom H. Foster, Michael R. Partial differential equations in fluid dynamics Dynamique des fluides numérique Fluides, Dynamique des - Mathématiques Équations aux dérivées partielles Mathematik Fluid dynamics Mathematics Textbooks Differential equations, Partial Textbooks Partielle Differentialgleichung (DE-588)4044779-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4077970-1 |
| title | Partial differential equations in fluid dynamics |
| title_auth | Partial differential equations in fluid dynamics |
| title_exact_search | Partial differential equations in fluid dynamics |
| title_exact_search_txtP | Partial differential equations in fluid dynamics |
| title_full | Partial differential equations in fluid dynamics Isom H. Herron, Michael R. Foster |
| title_fullStr | Partial differential equations in fluid dynamics Isom H. Herron, Michael R. Foster |
| title_full_unstemmed | Partial differential equations in fluid dynamics Isom H. Herron, Michael R. Foster |
| title_short | Partial differential equations in fluid dynamics |
| title_sort | partial differential equations in fluid dynamics |
| topic | Dynamique des fluides numérique Fluides, Dynamique des - Mathématiques Équations aux dérivées partielles Mathematik Fluid dynamics Mathematics Textbooks Differential equations, Partial Textbooks Partielle Differentialgleichung (DE-588)4044779-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Dynamique des fluides numérique Fluides, Dynamique des - Mathématiques Équations aux dérivées partielles Mathematik Fluid dynamics Mathematics Textbooks Differential equations, Partial Textbooks Partielle Differentialgleichung Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016728101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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