Similarity methods for differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1974
|
| Schriftenreihe: | Applied mathematical sciences
13 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 332 S. graph. Darst. |
| ISBN: | 0387901078 3540901078 |
Internformat
MARC
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| 100 | 1 | |a Bluman, George W. |d 1943- |e Verfasser |0 (DE-588)143539035 |4 aut | |
| 245 | 1 | 0 | |a Similarity methods for differential equations |c G. W. Bluman ; J. D. Cole |
| 264 | 1 | |a New York u.a. |b Springer |c 1974 | |
| 300 | |a VII, 332 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 13 | |
| 650 | 7 | |a Differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Homothétie | |
| 650 | 4 | |a Lie, Séries de | |
| 650 | 7 | |a Lie-groepen |2 gtt | |
| 650 | 7 | |a Partiële differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Équations aux dérivées partielles - Solutions numériques | |
| 650 | 4 | |a Équations différentielles - Solutions numériques | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
| 650 | 4 | |a Series, Lie | |
| 650 | 4 | |a Similarity transformations | |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Cole, Julian D. |e Verfasser |4 aut | |
| 830 | 0 | |a Applied mathematical sciences |v 13 |w (DE-604)BV000005274 |9 13 | |
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Datensatz im Suchindex
| _version_ | 1804117026335096832 |
|---|---|
| adam_text | TABLE OF CONTENTS
INTRODUCTION v
PART 1. ORDINARY DIFFERENTIAL EQUATIONS 1
1.0. Ordinary Differential Equations 4
1.1. Example: Global Similarity Transformation,
Invariance and Reduction to Ouadrature 6
1.2. Simple Examples of Groups of Transformations;
Abstract Definition 13
1.3. One-Parameter Group in the Plane 22
1.4. Proof That a One-Parameter Group
Essentially Contains Only One Infinitesimal
Transformation and Is Determined by It 31
1.5. Transformations; Symbol of the Infinitesimal
Transformation U 36
1.6. Invariant Functions and Curves 46
1.7. Important Classes of Transformations 49
1.8. Applications to Differential Equations;
Invariant Families of Curves 54
1.9. First-Order Differential Equations Which
Admit a Group; Integrating Factor;
Commutator 59
1.10. Geometric Interpretation of the
Integrating Factor 67
1.11. Determination of First-Order Equations Which
Admit a Given Group 71
1.12. One-Parameter Group in Three Variables;
More Variables 74
1.13. Extended Transformation in the Plane 84
1.14. A Second Criterion That a First-Order
Differential Equation Admits a Group 89
1.15. Construction of All Differential Equations of
First-Order Which Admit a Given Group 92
1.16. Criterion That a Second-Order Differential
Equation Admits a Group 101
1.17. Construction of All Differential Equations
of Second-Order Which Admit a Given Group ... 107
1.18. Examples of Application of the Method 116
PART 2. PARTIAL DIFFERENTIAL EQUATIONS 143
2.0. Partial Differential Equations 143
2.1. Formulation of Invariance for the Special
Case of One dependent and Two
Independent Variables 147
2.2. Formulation of Invariance in General 156
2.3. Fundamental Solution of the Heat Equation;
Dimensional Analysis 167
2.4. Fundamental Solutions of Heat Equation
Global Affinity 170
2.5. The Relationship Between the Use of
Dimensional Analysis and Stretching Groups to
Reduce the Number of Variables of a Partial
Differential Equation 1B1
2.6. Use of Group Invariance to Obtain New
Solutions from Given Solutions 199
2.7. The General Similarity Solution
of the Heat Equation 20fi
2.8. Applications of the General Similarity
Solution of the Heat Equation ,., 221
2.9. -Axially-Symmetric Wave Equation 248
2.10. Similarity Solutions of the One-Dimensional
Fokker-Planck Equation 258
2.11. The Green s Function for an Instantaneous Line
Particle Source Diffusing in a Gravitational
Field and Under the Influence of a Linear
Shear Wind - An Example of a P.D.E. in Three
Variables Invariant Under a
Two-Parameter Group 275
2.12. Infinite Parameter Groups - Derivation
of the Poisson Kernel 282
2.13. Far Field of Transonic Flow 286
2.14. Nonlinear and Other Examples 295
2.15. Construction of Partial Differential
Equations Invariant Under a Given
Multi-parameter Group 303
APPENDIX. SOLUTION OF QUASILINEAR FIRST-ORDER
PARTIAL DIFFERENTIAL EQUATIONS 318
BIBLIOGRAPHY. PART 1 324
BIBLIOGRAPHY. PART 2 325
INDEX 327
|
| any_adam_object | 1 |
| author | Bluman, George W. 1943- Cole, Julian D. |
| author_GND | (DE-588)143539035 |
| author_facet | Bluman, George W. 1943- Cole, Julian D. |
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| classification_rvk | SK 500 QH 150 |
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| dewey-full | 515/.35 510/.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 510 - Mathematics |
| dewey-raw | 515/.35 510/.8 |
| dewey-search | 515/.35 510/.8 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV002646408 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:47:51Z |
| institution | BVB |
| isbn | 0387901078 3540901078 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001697987 |
| oclc_num | 1055615 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-739 DE-19 DE-BY-UBM DE-703 DE-355 DE-BY-UBR DE-20 DE-29T DE-706 DE-83 DE-11 DE-188 |
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| physical | VII, 332 S. graph. Darst. |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Bluman, George W. 1943- Verfasser (DE-588)143539035 aut Similarity methods for differential equations G. W. Bluman ; J. D. Cole New York u.a. Springer 1974 VII, 332 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 13 Differentiaalvergelijkingen gtt Homothétie Lie, Séries de Lie-groepen gtt Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Differential equations Numerical solutions Differential equations, Partial Numerical solutions Series, Lie Similarity transformations Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s DE-604 Cole, Julian D. Verfasser aut Applied mathematical sciences 13 (DE-604)BV000005274 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001697987&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bluman, George W. 1943- Cole, Julian D. Similarity methods for differential equations Applied mathematical sciences Differentiaalvergelijkingen gtt Homothétie Lie, Séries de Lie-groepen gtt Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Differential equations Numerical solutions Differential equations, Partial Numerical solutions Series, Lie Similarity transformations Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012249-9 |
| title | Similarity methods for differential equations |
| title_auth | Similarity methods for differential equations |
| title_exact_search | Similarity methods for differential equations |
| title_full | Similarity methods for differential equations G. W. Bluman ; J. D. Cole |
| title_fullStr | Similarity methods for differential equations G. W. Bluman ; J. D. Cole |
| title_full_unstemmed | Similarity methods for differential equations G. W. Bluman ; J. D. Cole |
| title_short | Similarity methods for differential equations |
| title_sort | similarity methods for differential equations |
| topic | Differentiaalvergelijkingen gtt Homothétie Lie, Séries de Lie-groepen gtt Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Differential equations Numerical solutions Differential equations, Partial Numerical solutions Series, Lie Similarity transformations Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differentiaalvergelijkingen Homothétie Lie, Séries de Lie-groepen Partiële differentiaalvergelijkingen Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Differential equations Numerical solutions Differential equations, Partial Numerical solutions Series, Lie Similarity transformations Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001697987&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT blumangeorgew similaritymethodsfordifferentialequations AT colejuliand similaritymethodsfordifferentialequations |