Symmetries and differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kon
Springer
1996
|
| Ausgabe: | Corr. 2. printing |
| Schriftenreihe: | Applied mathematical sciences
81 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 384 - 392 |
| Beschreibung: | XIII, 412 S. |
| ISBN: | 3540969969 0387969969 |
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 Symmetries and differential equations |c George W. Bluman ; Sukeyuki Kumei |
| 250 | |a Corr. 2. printing | ||
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kon |b Springer |c 1996 | |
| 300 | |a XIII, 412 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 81 | |
| 500 | |a Literaturverz. S. 384 - 392 | ||
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
| 650 | 4 | |a Lie groups | |
| 650 | 0 | 7 | |a Lie-Gruppe |0 (DE-588)4035695-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
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| 689 | 1 | 2 | |a Lie-Gruppe |0 (DE-588)4035695-4 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Kumei, Sukeyuki |e Verfasser |4 aut | |
| 830 | 0 | |a Applied mathematical sciences |v 81 |w (DE-604)BV000005274 |9 81 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007480319&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1805067738069073920 |
|---|---|
| adam_text |
CONTENTS
PREFACE
V
INTRODUCTION
1
1
DIMENSIONAL
ANALYSIS,
MODELLING,
AND
INVARIANCE
4
1.1
INTRODUCTION
4
1.2
DIMENSIONAL
ANALYSIS
-
BUCKINGHAM
PI-THEOREM
4
1.2.1
ASSUMPTIONS
BEHIND
DIMENSIONAL
ANALYSIS
5
1.2.2
CONCLUSIONS
FROM
DIMENSIONAL
ANALYSIS
6
1.2.3
PROOF
OF
THE
BUCKINGHAM
PI-THEOREM
7
1.2.4
EXAMPLES
9
1.3
APPLICATION
OF
DIMENSIONAL
ANALYSIS
TO
PARTIAL
DIFFERENTIAL
EQUATIONS
14
1.3.1
EXAMPLES
15
1.4
GENERALIZATION
OF
DIMENSIONAL
ANALYSIS
-
INVARIANCE
OF
PARTIAL
DIFFERENTIAL
EQUATIONS
UNDER
SCALINGS
OF
VARIABLES
22
1.5
DISCUSSION
29
2
LIE
GROUPS
OF
TRANSFORMATIONS
AND
INFINITESIMAL
TRANSFORMATIONS
31
2.1
LIE
GROUPS
OF
TRANSFORMATIONS
31
2.1.1
GROUPS
31
2.1.2
EXAMPLES
OF
GROUPS
32
2.1.3
GROUPS
OF
TRANSFORMATIONS
33
2.1.4
ONE-PARAMETER
LIE
GROUP
OF
TRANSFORMATIONS
34
2.1.5
EXAMPLES
OF
ONE-PARAMETER
LIE
GROUPS
OF
TRANSFORMATIONS
35
2.2
INFINITESIMAL
TRANSFORMATIONS
36
2.2.1
FIRST
FUNDAMENTAL
THEOREM
OF
LIE
37
2.2.2
EXAMPLES
ILLUSTRATING
LIE
'
S
FIRST
FUNDAMENTAL
THEOREM
39
X
CONTENTS
2.2.3
INFINITESIMAL
GENERATORS
40
2.2.4
INVARIANT
FUNCTIONS
43
2.2.5
CANONICAL
COORDINATES
44
2.2.6
EXAMPLES
OF
SETS
OF
CANONICAL
COORDINATES
47
2.2.7
INVARIANT
SURFACES,
INVARIANT
CURVES,
INVARIANT
POINTS
48
2.3
EXTENDED
TI-ANSFORMATIONS
(PROLONGATIONS)
53
2.3.1
EXTENDED
GROUP
TRANSFORMATIONS
-
ONE
DEPENDENT
AND
ONE
INDEPENDENT
VARIABLE
55
2.3.2
EXTENDED
INFINITESIMAL
TRANSFORMATIONS
-
ONE
DEPENDENT
AND
ONE
INDEPENDENT
VARIABLE
61
2.3.3
EXTENDED
TRANSFORMATIONS
-
ONE
DEPENDENT
AND
N
INDEPENDENT
VARIABLES
63
2.3.4
EXTENDED
INFINITESIMAL
TRANSFORMATIONS
-
ONE
DEPENDENT
AND
N
INDEPENDENT
VARIABLES
66
2.3.5
EXTENDED
TRANSFORMATIONS
AND
EXTENDED
INFINITESIMAL
TRANSFORMATIONS
-
M
DEPENDENT
AND
N
INDEPENDENT
VARIABLES
70
2.4
MULTI-PARAMETER
LIE
GROUPS
OF
TRANSFORMATIONS;
LIE
ALGEBRAS
75
2.4.1
R-PARAMETER
LIE
GROUPS
OF
TRANSFORMATIONS
75
2.4.2
LIE
ALGEBRAS
80
2.4.3
EXAMPLES
OF
LIE
ALGEBRAS
82
2.4.4
SOLVABLE
LIE
ALGEBRAS
85
2.5
DISCUSSION
88
3
ORDINARY
DIFFERENTIAL
EQUATIONS
90
3.1
INTRODUCTION
-
INVARIANCE
OF
AN
ORDINARY
DIFFERENTIAL
EQUATION
90
3.1.1
INVARIANCE
OF
AN
ODE
90
3.1.2
ELEMENTARY
EXAMPLES
92
3.1.3
MAPPING
OF
SOLUTIONS
TO
OTHER
SOLUTIONS
FROM
GROUP
INVARIANCE
OF
AN
ODE
94
3.2
FIRST
ORDER
ODE
'
S
97
3.2.1
CANONICAL
COORDINATES
98
3.2.2
INTEGRATING
FACTORS
100
3.2.3
DETERMINING
EQUATION
FOR
INFINITESIMAL
TRANSFORMATIONS
OF
A
FIRST
ORDER
ODE
102
3.2.4
DETERMINATION
OF
FIRST
ORDER
ODE
'
S
INVARIANT
UNDER
A
GIVEN
GROUP
104
3.3
SECOND
AND
HIGHER
ORDER
ODE
'
S
109
3.3.1
REDUCTION
OF
ORDER
BY
CANONICAL
COORDINATES
110
CONTENTS
XI
3.3.2
REDUCTION
OF
ORDER
BY
DIFFERENTIAL
INVARIANTS
112
3.3.3
EXAMPLES
OF
REDUCTION
OF
ORDER
115
3.3.4
DETERMINING
EQUATIONS
FOR
INFINITESIMAL
TRANSFORMATIONS
OF
AN
NTH
ORDER
ODE
120
3.3.5
DETERMINATION
OF
NTH
ORDER
ODE
'
S
INVARIANT
UNDER
A
GIVEN
GROUP
124
3.4
INVARIANCE
OF
ODE
'
S
UNDER
MULTI-PARAMETER
GROUPS
128
3.4.1
INVARIANCE
OF
A
SECOND
ORDER
ODE
UNDER
A
TWO-PARAMETER
GROUP
129
3.4.2
INVARIANCE
OF
AN
NTH
ORDER
ODE
UNDER
A
TWO-PARAMETER
GROUP
132
3.4.3
INVARIANCE
OF
AN
NTH
ORDER
ODE
UNDER
AN
R-PARAMETER
LIE
GROUP
WITH
A
SOLVABLE
LIE
ALGEBRA
135
3.5
APPLICATIONS
TO
BOUNDARY
VALUE
PROBLEMS
147
3.6
INVARIANT
SOLUTIONS
149
3.6.1
INVARIANT
SOLUTIONS
FOR
FIRST
ORDER
ODE
'
S
-
SEPARATRICES
AND
ENVELOPES
154
3.7
DISCUSSION
160
4
PARTIAL
DIFFERENTIAL
EQUATIONS
163
4.1
INTRODUCTION
-
INVARIANCE
OF
A
PARTIAL
DIFFERENTIAL
EQUATION
163
4.1.1
INVARIANCE
OF
A
PDE
163
4.1.2
ELEMENTARY
EXAMPLES
165
4.2
INVARIANCE
FOR
SCALAR
PDE
'
S
169
4.2.1
INVARIANT
SOLUTIONS
169
4.2.2
MAPPING
OF
SOLUTIONS
TO
OTHER
SOLUTIONS
FROM
GROUP
INVARIANCE
OF
A
PDE
171
4.2.3
DETERMINING
EQUATIONS
FOR
INFINITESIMAL
TRANSFOR
MATIONS
OF
A
FCTH
ORDER
PDE
172
4.2.4
EXAMPLES
176
4.3
INVARIANCE
FOR
SYSTEMS
OF
PDE
'
S
195
4.3.1
INVARIANCE
OF
A
SYSTEM
OF
PDE
'
S
196
4.3.2
INVARIANT
SOLUTIONS
196
4.3.3
DETERMINING
EQUATIONS
FOR
INFINITESIMAL
TRANSFOR
MATIONS
OF
A
SYSTEM
OF
PDE
'
S
199
4.3.4
EXAMPLES
201
4.4
APPLICATIONS
TO
BOUNDARY
VALUE
PROBLEMS
215
4.4.1
FORMULATION
OF
INVARIANCE
OF
A
BVP
FOR
A
SCALAR
PDE
216
4.4.2
INCOMPLETE
INVARIANCE
FOR
A
LINEAR
SCALAR
PDE
232
XII
CONTENTS
4.4.3
INCOMPLETE
INVARIANCE
FOR
A
LINEAR
SYSTEM
OF
PDE
'
S
241
4.5
DISCUSSION
249
5
NOETHER
'
S
THEOREM
AND
LIE-BACKLUND
SYMMETRIES
252
5.1
INTRODUCTION
252
5.2
NOETHER
'
S
THEOREM
253
5.2.1
EULER-LAGRANGE
EQUATIONS
254
5.2.2
VARIATIONAL
SYMMETRIES
AND
CONSERVATION
LAWS;
BOYER
'
S
FORMULATION
257
5.2.3
EQUIVALENT
CLASSES
OF
LIE-BACKLUND
TRANSFOR
MATIONS;
LIE-BACKLUND
SYMMETRIES
260
5.2.4
CONTACT
TRANSFORMATIONS;
CONTACT
SYMMETRIES
267
5.2.5
FINDING
VARIATIONAL
SYMMETRIES
272
5.2.6
NOETHER
'
S
FORMULATION
274
5.2.7
EXAMPLES
OF
HIGHER
ORDER
CONSERVATION
LAWS
279
5.3
RECURSION
OPERATORS
FOR
LIE-BACKLUND
SYMMETRIES
283
5.3.1
RECURSION
OPERATORS
FOR
LINEAR
DIFFERENTIAL
EQUATIONS
283
5.3.2
RECURSION
OPERATORS
FOR
NONLINEAR
DIFFERENTIAL
EQUATIONS
286
5.3.3
INTEGRO-DIFFERENTIAL
RECURSION
OPERATORS
290
5.3.4
LIE-BACKLUND
CLASSIFICATION
PROBLEM
294
5.4
DISCUSSION
300
6
CONSTRUCTION
OF
MAPPINGS
RELATING
DIFFERENTIAL
EQUATIONS
302
6.1
INTRODUCTION
302
6.2
NOTATIONS;
MAPPINGS
OF
INFINITESIMAL
GENERATORS
303
6.2.1
THEOREMS
ON
INVERTIBLE
MAPPINGS
307
6.3
MAPPING
OF
A
GIVEN
DE
TO
A
SPECIFIC
TARGET
DE
308
6.3.1
CONSTRUCTION
OF
NON-INVERTIBLE
MAPPINGS
308
6.3.2
CONSTRUCTION
OF
INVERTIBLE
POINT
MAPPINGS
313
6.4
INVERTIBLE
MAPPINGS
OF
NONLINEAR
PDE
'
S
TO
LINEAR
PDE
'
S
319
6.4.1
INVERTIBLE
MAPPINGS
OF
NONLINEAR
SYSTEMS
OF
PDE
'
S
TO
LINEAR
SYSTEMS
OF
PDE
'
S
320
6.4.2
INVERTIBLE
MAPPINGS
OF
NONLINEAR
SCALAR
PDE
'
S
TO
LINEAR
SCALAR
PDE
'
S
325
CONTENTS
XIII
6.5
INVERTIBLE
MAPPINGS
OF
LINEAR
PDE
'
S
TO
LINEAR
PDE
'
S
WITH
CONSTANT
COEFFICIENTS
336
6.5.1
EXAMPLES
OF
MAPPING
VARIABLE
COEFFICIENT
PDE
'
S
TO
CONSTANT
COEFFICIENT
PDE
'
S
341
6.5.2
MAPPING
CONSTANT
COEFFICIENT
PDE
'
S
TO
CONSTANT
COEFFICIENT
PDE
'
S
347
6.6
DISCUSSION
350
7
POTENTIAL
SYMMETRIES
352
7.1
INTRODUCTION
352
7.2
POTENTIAL
SYMMETRIES
FOR
PARTIAL
DIFFERENTIAL
EQUATIONS
353
7.2.1
EXAMPLES
OF
POTENTIAL
SYMMETRIES
356
7.2.2
COMPARISON
OF
POINT
SYMMETRIES
OF
R{X,
U)
AND
S{X,U,V}
362
7.2.3
TYPES
OF
POTENTIAL
SYMMETRIES
OF
LINEAR
PDE
'
S
366
7.2.4
APPLICATIONS
TO
BOUNDARY
VALUE
PROBLEMS
368
7.2.5
NON-INVERTIBLE
MAPPINGS
OF
NONLINEAR
PDE
'
S
TO
LINEAR
PDE
'
S
369
7.2.6
CONSERVED
FORMS
372
7.2.7
INHERITED
SYMMETRIES
374
7.3
POTENTIAL
SYMMETRIES
FOR
ORDINARY
DIFFERENTIAL
EQUATIONS
379
7.3.1
AN
EXAMPLE
380
7.4
DISCUSSION
382
REFERENCES
384
AUTHOR
INDEX
393
SUBJECT
INDEX
397 |
| any_adam_object | 1 |
| author | Bluman, George W. 1943- Kumei, Sukeyuki |
| author_GND | (DE-588)143539035 |
| author_facet | Bluman, George W. 1943- Kumei, Sukeyuki |
| author_role | aut aut |
| author_sort | Bluman, George W. 1943- |
| author_variant | g w b gw gwb s k sk |
| building | Verbundindex |
| bvnumber | BV011157849 |
| callnumber-first | Q - Science |
| callnumber-label | QA1 |
| callnumber-raw | QA1 |
| callnumber-search | QA1 |
| callnumber-sort | QA 11 |
| callnumber-subject | QA - Mathematics |
| classification_tum | PHY 013f MAT 350f MAT 340f |
| ctrlnum | (OCoLC)35115161 (DE-599)BVBBV011157849 |
| dewey-full | 510 515/.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510 515/.35 |
| dewey-search | 510 515/.35 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | Corr. 2. printing |
| format | Book |
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| id | DE-604.BV011157849 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T03:39:00Z |
| institution | BVB |
| isbn | 3540969969 0387969969 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007480319 |
| oclc_num | 35115161 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM |
| owner_facet | DE-91 DE-BY-TUM |
| physical | XIII, 412 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Bluman, George W. 1943- Verfasser (DE-588)143539035 aut Symmetries and differential equations George W. Bluman ; Sukeyuki Kumei Corr. 2. printing New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kon Springer 1996 XIII, 412 S. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 81 Literaturverz. S. 384 - 392 Differential equations Numerical solutions Differential equations, Partial Numerical solutions Lie groups Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Lie-Gruppe (DE-588)4035695-4 s DE-604 Differentialgleichung (DE-588)4012249-9 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Kumei, Sukeyuki Verfasser aut Applied mathematical sciences 81 (DE-604)BV000005274 81 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007480319&sequence=000001&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 | Bluman, George W. 1943- Kumei, Sukeyuki Symmetries and differential equations Applied mathematical sciences Differential equations Numerical solutions Differential equations, Partial Numerical solutions Lie groups Lie-Gruppe (DE-588)4035695-4 gnd Differentialgleichung (DE-588)4012249-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4012249-9 (DE-588)4044779-0 (DE-588)4128130-5 |
| title | Symmetries and differential equations |
| title_auth | Symmetries and differential equations |
| title_exact_search | Symmetries and differential equations |
| title_full | Symmetries and differential equations George W. Bluman ; Sukeyuki Kumei |
| title_fullStr | Symmetries and differential equations George W. Bluman ; Sukeyuki Kumei |
| title_full_unstemmed | Symmetries and differential equations George W. Bluman ; Sukeyuki Kumei |
| title_short | Symmetries and differential equations |
| title_sort | symmetries and differential equations |
| topic | Differential equations Numerical solutions Differential equations, Partial Numerical solutions Lie groups Lie-Gruppe (DE-588)4035695-4 gnd Differentialgleichung (DE-588)4012249-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Differential equations Numerical solutions Differential equations, Partial Numerical solutions Lie groups Lie-Gruppe Differentialgleichung Partielle Differentialgleichung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007480319&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT blumangeorgew symmetriesanddifferentialequations AT kumeisukeyuki symmetriesanddifferentialequations |