Applications of Lie's theory of ordinary and partial differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Bristol [u.a.]
Inst. of Physics Publ.
1999
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 225 S. graph. Darst. |
| ISBN: | 0750305304 0750305312 |
Internformat
MARC
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| 100 | 1 | |a Dresner, Lawrence |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applications of Lie's theory of ordinary and partial differential equations |c Lawrence Dresner |
| 264 | 1 | |a Bristol [u.a.] |b Inst. of Physics Publ. |c 1999 | |
| 300 | |a XI, 225 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Diffusion |2 lc | |
| 650 | 7 | |a Equation aux dérivées partielles |2 lc | |
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| 650 | 7 | |a Exercice équation différentielle |2 lc | |
| 650 | 7 | |a Lie, groupe de |2 ram | |
| 650 | 7 | |a Onde mobile |2 lc | |
| 650 | 7 | |a Solution singulière |2 lc | |
| 650 | 7 | |a Théorie Lie équation différentielle |2 lc | |
| 650 | 7 | |a Équations aux dérivées partielles - Solutions numériques |2 ram | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
| 650 | 4 | |a Lie groups | |
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Datensatz im Suchindex
| _version_ | 1804127341166723072 |
|---|---|
| adam_text | Contents
Preface ix
Conventions Used in this Book xii
Dedication xiii
1 One Parameter Groups 1
1.1 Groups of Transformations 1
1.2 Infinitesimal Transformations 2
1.3 Group Invariants 4
1.4 Invariant Curves and Families of Curves 5
1.5 Transformation of Derivatives: the Extended Group 8
1.6 Transformation of Derivatives (continued) 10
1.7 Invariant Differential Equations of the First Order 11
Notes 12
Problems for Chapter 1 13
2 First Order Ordinary Differential Equations 15
2.1 Lie s Integrating Factor 15
2.2 The Converse of Lie s Theorem 17
2.3 Invariant Integral Curves 19
2.4 Singular Solutions 20
2.5 Change of Variables 22
2.6 Tabulation of Differential Equations 26
Notes 28
Problems for Chapter 2 28
vi Contents
3 Second Order Ordinary Differential Equations 34
3.1 Invariant Differential Equations of the Second Order 34
3.2 Lie s Reduction Theorem 35
3.3 Stretching Groups 39
3.4 Singularities of the Associated Differential
Equation 46
3.5 A Caution in Applying Theorems 3.4.1 and 3.4.2 50
3.6 Other Groups 53
3.7 Equations Invariant to Two Groups 56
3.8 Two Parameter Groups 59
3.9 Noether s Theorem2 60
3.10 Tabulation of Differential Equations Using
Noether s Theorem 64
3.11 The Determining Equations 65
Notes 67
Problems for Chapter 3 68
4 Similarity Solutions of Partial Differential Equations 72
4.1 Introduction 72
4.2 Similarity Solutions 74
4.3 The Associated Group 77
4.4 The Asymptotic Behavior of Similarity Solutions 78
4.5 Proof of the Ordering Theorem 80
4.6 Functions Invariant to an Entire Family of
Stretching Groups 83
4.7 The Shock Loaded Membrane 85
4.8 Further Use of the Associated Group 90
4.9 More Wave Propagation Problems 92
4.10 Wave Propagation Problems (continued) 95
4.11 Shocks 100
Notes 102
Problems for Chapter 4 102
5 Traveling Wave Solutions 108
5.1 One Parameter Families of Translation Groups 108
5.2 The Diffusion Equation with Source 111
5.3 Determination of the Propagation Velocity a 112
Contents vii
5.4 Determination of the Propagation Velocity: Role
of the Initial Condition 117
5.5 The Approach to Traveling Waves 120
5.6 The Approach to Traveling Waves (part 2) 122
5.7 A Final Example 128
5.8 Concluding Remarks 129
Notes 130
Problems for Chapter 5 132
6 Approximate Methods 135
6.1 Introduction 135
6.2 Superfluid Diffusion Equation with a Slowly
Varying Face Temperature 137
6.3 Ordinary Diffusion with a Non Constant
Diffusion Coefficient 140
6.4 Check on the Accuracy of the Approximate
Formula (6.3.8) 142
Problems for Chapter 6 144
Epilog 146
Appendices 149
A Linear, First Order Partial Differential Equations 149
A. 1 Introduction 149
A.2 Characteristic Curves 150
A.3 Integrals of the Characteristic Equations 151
B Riemann s Method of Characteristics 152
B.I Introduction 152
B.2 The Motion of Water in a Long, Narrow, Open
Channel 153
C The Calculus of Variations and the Euler Lagrange
Equation 157
C.I Introduction 157
C.2 The Euler Lagrange Equation 158
C.3 The Brachistochrone Concluded 159
D Computation of Invariants and First Differential
Invariants from the Transformation Equations 162
viii Contents
Solutions to Problems 165
References 217
Symbols and their Definitions 219
Index 222
|
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| id | DE-604.BV012679526 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:31:48Z |
| institution | BVB |
| isbn | 0750305304 0750305312 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008617901 |
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| owner_facet | DE-703 DE-824 DE-634 DE-188 |
| physical | XI, 225 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Inst. of Physics Publ. |
| record_format | marc |
| spelling | Dresner, Lawrence Verfasser aut Applications of Lie's theory of ordinary and partial differential equations Lawrence Dresner Bristol [u.a.] Inst. of Physics Publ. 1999 XI, 225 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Diffusion lc Equation aux dérivées partielles lc Equation différentielle - Solutions numériques ram Exercice équation différentielle lc Lie, groupe de ram Onde mobile lc Solution singulière lc Théorie Lie équation différentielle lc Équations aux dérivées partielles - Solutions numériques ram Differential equations Numerical solutions Differential equations, Partial Numerical solutions Lie groups Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Differentialgleichung (DE-588)4012249-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008617901&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dresner, Lawrence Applications of Lie's theory of ordinary and partial differential equations Diffusion lc Equation aux dérivées partielles lc Equation différentielle - Solutions numériques ram Exercice équation différentielle lc Lie, groupe de ram Onde mobile lc Solution singulière lc Théorie Lie équation différentielle lc Équations aux dérivées partielles - Solutions numériques ram Differential equations Numerical solutions Differential equations, Partial Numerical solutions Lie groups Differentialgleichung (DE-588)4012249-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4044779-0 (DE-588)4130355-6 |
| title | Applications of Lie's theory of ordinary and partial differential equations |
| title_auth | Applications of Lie's theory of ordinary and partial differential equations |
| title_exact_search | Applications of Lie's theory of ordinary and partial differential equations |
| title_full | Applications of Lie's theory of ordinary and partial differential equations Lawrence Dresner |
| title_fullStr | Applications of Lie's theory of ordinary and partial differential equations Lawrence Dresner |
| title_full_unstemmed | Applications of Lie's theory of ordinary and partial differential equations Lawrence Dresner |
| title_short | Applications of Lie's theory of ordinary and partial differential equations |
| title_sort | applications of lie s theory of ordinary and partial differential equations |
| topic | Diffusion lc Equation aux dérivées partielles lc Equation différentielle - Solutions numériques ram Exercice équation différentielle lc Lie, groupe de ram Onde mobile lc Solution singulière lc Théorie Lie équation différentielle lc Équations aux dérivées partielles - Solutions numériques ram Differential equations Numerical solutions Differential equations, Partial Numerical solutions Lie groups Differentialgleichung (DE-588)4012249-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Diffusion Equation aux dérivées partielles Equation différentielle - Solutions numériques Exercice équation différentielle Lie, groupe de Onde mobile Solution singulière Théorie Lie équation différentielle Équations aux dérivées partielles - Solutions numériques Differential equations Numerical solutions Differential equations, Partial Numerical solutions Lie groups Differentialgleichung Partielle Differentialgleichung Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008617901&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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