Manifolds, tensor analysis, and applications:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo
Springer
1991
|
| Ausgabe: | 2. ed., [3. Dr.] |
| Schriftenreihe: | Applied mathematical sciences
Vol. 75 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 631 - 641 |
| Beschreibung: | 654 S. graph. Darst. 25 cm |
| ISBN: | 3540967907 0387967907 |
Internformat
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| 245 | 1 | 0 | |a Manifolds, tensor analysis, and applications |c R. Abraham ; J. E. Marsden ; T. Ratiu |
| 250 | |a 2. ed., [3. Dr.] | ||
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Datensatz im Suchindex
| _version_ | 1805068894474338304 |
|---|---|
| adam_text |
CONTENTS
PREFACE
V
BACKGROUND
NOTATION
VII
CHAPTER
1
TOPOLOGY
1
1.1
TOPOLOGICAL
SPACES
2
1.2
METRIC
SPACES
9
1.3
CONTINUITY
14
1.4
SUBSPACES,
PRODUCTS,
AND
QUOTIENTS
18
1.5
COMPACTNESS
24
1.6
CONNECTEDNESS
31
1.7
BAIRE
SPACES
37
CHAPTER
2
BANACH
SPACES
AND
DIFFERENTIAL
CALCULUS
40
2.1
BANACH
SPACES
40
2.2
LINEAR
AND
MULTILINEAR
MAPPINGS
56
2.3
THE
DERIVATIVE
75
2.4
PROPERTIES
OF
THE
DERIVATIVE
83
2.5
THE
INVERSE
AND
IMPLICIT
FUNCTION
THEOREMS
116
CHAPTER
3
MANIFOLDS
AND
VECTOR
BUNDLES
141
3.1
MANIFOLDS
141
3.2
SUBMANIFOLDS,
PRODUCTS,
AND
MAPPINGS
150
3.3
THE
TANGENT
BUNDLE
157
3.4
VECTOR
BUNDLES
167
3.5
SUBMERSIONS,
IMMERSIONS
AND
TRANSVERSALITY
196
CHAPTER
4
VECTOR
FIELDS
AND
DYNAMICAL
SYSTEMS
238
4.1
VECTOR
FIELDS
AND
FLOWS
238
4.2
VECTOR
FIELDS
AS
DIFFERENTIAL
OPERATORS
265
4.3
AN
INTRODUCTION
TO
DYNAMICAL
SYSTEMS
298
4.4
FROBENIUS
'
THEOREM
AND
FOLIATIONS
326
CHAPTER
5
TENSORS
338
5.1
TENSORS
IN
LINEAR
SPACES
338
5.2
TENSOR
BUNDLES
AND
TENSOR
FIELDS
349
5.3
THE
LIE
DERIVATIVE:
ALGEBRAIC
APPROACH
359
5.4
THE
LIE
DERIVATIVE:
DYNAMIC
APPROACH
370
5.5
PARTITIONS
OF
UNITY
377
CHAPTER
6
DIFFERENTIAL
FORMS
6.1
EXTERIOR
ALGEBRA
6.2
DETERMINANTS,
VOLUMES,
AND
THE
HODGE
STAR
OPERATOR
6.3
DIFFERENTIAL
FORMS
6.4
THE
EXTERIOR
DERIVATIVE,
INTERIOR
PRODUCT,
AND
LIE
DERIVATIVE
6.5
ORIENTATION,
VOLUME
ELEMENTS,
AND
THE
CODIFFERENTIAL
392
392
402
417
423
450
CHAPTER
7
INTEGRATION
ON
MANIFOLDS
7.1
THE
DEFINITION
OF
THE
INTEGRAL
7.2
STOKES
'
THEOREM
7.3
THE
CLASSICAL
THEOREMS
OF
GREEN,
GAUSS,
AND
STOKES
7.4
INDUCED
FLOWS
ON
FUNCTION
SPACES
AND
ERGODICITY
7.5
INTRODUCTION
TO
HODGE-DERHAM
THEORY
AND
TOPOLOGICAL
APPLICATIONS
OF
464
464
476
504
513
DIFFERENTIAL
FORMS
538
CHAPTER
8
APPLICATIONS
8.1
HAMILTONIAN
MECHANICS
8.2
FLUID
MECHANICS
8.3
ELECTROMAGNETISM
8.3
THE
LIE-POISSON
BRACKET
IN
CONTINUUM
MECHANICS
AND
PLASMA
PHYSICS
8.4
CONSTRAINTS
AND
CONTROL
560
560
584
599
609
624
REFERENCES
631
INDEX
643
SUPPLEMENTARY
CHAPTERS
-
AVAILABLE
FROM
THE
AUTHORS
AS
THEY
ARE
PRODUCED
S-L
LIE
GROUPS
S-2
INTRODUCTION
TO
DIFFERENTIAL
TOPOLOGY
S-3
TOPICS
IN
RIEMANNIAN
GEOMETRY |
| adam_txt |
CONTENTS
PREFACE
V
BACKGROUND
NOTATION
VII
CHAPTER
1
TOPOLOGY
1
1.1
TOPOLOGICAL
SPACES
2
1.2
METRIC
SPACES
9
1.3
CONTINUITY
14
1.4
SUBSPACES,
PRODUCTS,
AND
QUOTIENTS
18
1.5
COMPACTNESS
24
1.6
CONNECTEDNESS
31
1.7
BAIRE
SPACES
37
CHAPTER
2
BANACH
SPACES
AND
DIFFERENTIAL
CALCULUS
40
2.1
BANACH
SPACES
40
2.2
LINEAR
AND
MULTILINEAR
MAPPINGS
56
2.3
THE
DERIVATIVE
75
2.4
PROPERTIES
OF
THE
DERIVATIVE
83
2.5
THE
INVERSE
AND
IMPLICIT
FUNCTION
THEOREMS
116
CHAPTER
3
MANIFOLDS
AND
VECTOR
BUNDLES
141
3.1
MANIFOLDS
141
3.2
SUBMANIFOLDS,
PRODUCTS,
AND
MAPPINGS
150
3.3
THE
TANGENT
BUNDLE
157
3.4
VECTOR
BUNDLES
167
3.5
SUBMERSIONS,
IMMERSIONS
AND
TRANSVERSALITY
196
CHAPTER
4
VECTOR
FIELDS
AND
DYNAMICAL
SYSTEMS
238
4.1
VECTOR
FIELDS
AND
FLOWS
238
4.2
VECTOR
FIELDS
AS
DIFFERENTIAL
OPERATORS
265
4.3
AN
INTRODUCTION
TO
DYNAMICAL
SYSTEMS
298
4.4
FROBENIUS
'
THEOREM
AND
FOLIATIONS
326
CHAPTER
5
TENSORS
338
5.1
TENSORS
IN
LINEAR
SPACES
338
5.2
TENSOR
BUNDLES
AND
TENSOR
FIELDS
349
5.3
THE
LIE
DERIVATIVE:
ALGEBRAIC
APPROACH
359
5.4
THE
LIE
DERIVATIVE:
DYNAMIC
APPROACH
370
5.5
PARTITIONS
OF
UNITY
377
CHAPTER
6
DIFFERENTIAL
FORMS
6.1
EXTERIOR
ALGEBRA
6.2
DETERMINANTS,
VOLUMES,
AND
THE
HODGE
STAR
OPERATOR
6.3
DIFFERENTIAL
FORMS
6.4
THE
EXTERIOR
DERIVATIVE,
INTERIOR
PRODUCT,
AND
LIE
DERIVATIVE
6.5
ORIENTATION,
VOLUME
ELEMENTS,
AND
THE
CODIFFERENTIAL
392
392
402
417
423
450
CHAPTER
7
INTEGRATION
ON
MANIFOLDS
7.1
THE
DEFINITION
OF
THE
INTEGRAL
7.2
STOKES
'
THEOREM
7.3
THE
CLASSICAL
THEOREMS
OF
GREEN,
GAUSS,
AND
STOKES
7.4
INDUCED
FLOWS
ON
FUNCTION
SPACES
AND
ERGODICITY
7.5
INTRODUCTION
TO
HODGE-DERHAM
THEORY
AND
TOPOLOGICAL
APPLICATIONS
OF
464
464
476
504
513
DIFFERENTIAL
FORMS
538
CHAPTER
8
APPLICATIONS
8.1
HAMILTONIAN
MECHANICS
8.2
FLUID
MECHANICS
8.3
ELECTROMAGNETISM
8.3
THE
LIE-POISSON
BRACKET
IN
CONTINUUM
MECHANICS
AND
PLASMA
PHYSICS
8.4
CONSTRAINTS
AND
CONTROL
560
560
584
599
609
624
REFERENCES
631
INDEX
643
SUPPLEMENTARY
CHAPTERS
-
AVAILABLE
FROM
THE
AUTHORS
AS
THEY
ARE
PRODUCED
S-L
LIE
GROUPS
S-2
INTRODUCTION
TO
DIFFERENTIAL
TOPOLOGY
S-3
TOPICS
IN
RIEMANNIAN
GEOMETRY |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Abraham, Ralph Marsden, Jerrold E. 1942-2010 Ratiu, Tudor |
| author_GND | (DE-588)124171141 |
| author_facet | Abraham, Ralph Marsden, Jerrold E. 1942-2010 Ratiu, Tudor |
| author_role | aut aut aut |
| author_sort | Abraham, Ralph |
| author_variant | r a ra j e m je jem t r tr |
| building | Verbundindex |
| bvnumber | BV023597154 |
| callnumber-first | Q - Science |
| callnumber-label | QA1 QA614 |
| callnumber-raw | QA1 QA614.A647 vol. 75 |
| callnumber-search | QA1 QA614.A647 vol. 75 |
| callnumber-sort | QA 11 _Q A614 A647 VOL 275 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)613382984 (DE-599)BVBBV023597154 |
| dewey-full | 510S514/.7420 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 s 514/.74 20 |
| dewey-search | 510 s 514/.74 20 |
| dewey-sort | 3510 S 3514 274 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed., [3. Dr.] |
| format | Book |
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| id | DE-604.BV023597154 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:42:06Z |
| indexdate | 2024-07-20T03:57:22Z |
| institution | BVB |
| isbn | 3540967907 0387967907 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016912300 |
| oclc_num | 613382984 |
| open_access_boolean | |
| owner | DE-521 |
| owner_facet | DE-521 |
| physical | 654 S. graph. Darst. 25 cm |
| publishDate | 1991 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Abraham, Ralph Verfasser aut Manifolds, tensor analysis, and applications R. Abraham ; J. E. Marsden ; T. Ratiu 2. ed., [3. Dr.] New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo Springer 1991 654 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences Vol. 75 Literaturverz. S. 631 - 641 Global analysis (Mathematics) Manifolds (Mathematics) Calculus of tensors Differentialform (DE-588)4149772-7 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Globale Analysis (DE-588)4021285-3 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 s DE-604 Differentialform (DE-588)4149772-7 s Dynamisches System (DE-588)4013396-5 s Globale Analysis (DE-588)4021285-3 s Tensorrechnung (DE-588)4192487-3 s Mannigfaltigkeit (DE-588)4037379-4 s 1\p DE-604 Nichtlineare Analysis (DE-588)4177490-5 s 2\p DE-604 Marsden, Jerrold E. 1942-2010 Verfasser (DE-588)124171141 aut Ratiu, Tudor Verfasser aut Applied mathematical sciences Vol. 75 (DE-604)BV000005274 75 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016912300&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Abraham, Ralph Marsden, Jerrold E. 1942-2010 Ratiu, Tudor Manifolds, tensor analysis, and applications Applied mathematical sciences Global analysis (Mathematics) Manifolds (Mathematics) Calculus of tensors Differentialform (DE-588)4149772-7 gnd Tensoranalysis (DE-588)4204323-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dynamisches System (DE-588)4013396-5 gnd Globale Analysis (DE-588)4021285-3 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| subject_GND | (DE-588)4149772-7 (DE-588)4204323-2 (DE-588)4037379-4 (DE-588)4013396-5 (DE-588)4021285-3 (DE-588)4177490-5 (DE-588)4192487-3 |
| title | Manifolds, tensor analysis, and applications |
| title_auth | Manifolds, tensor analysis, and applications |
| title_exact_search | Manifolds, tensor analysis, and applications |
| title_exact_search_txtP | Manifolds, tensor analysis, and applications |
| title_full | Manifolds, tensor analysis, and applications R. Abraham ; J. E. Marsden ; T. Ratiu |
| title_fullStr | Manifolds, tensor analysis, and applications R. Abraham ; J. E. Marsden ; T. Ratiu |
| title_full_unstemmed | Manifolds, tensor analysis, and applications R. Abraham ; J. E. Marsden ; T. Ratiu |
| title_short | Manifolds, tensor analysis, and applications |
| title_sort | manifolds tensor analysis and applications |
| topic | Global analysis (Mathematics) Manifolds (Mathematics) Calculus of tensors Differentialform (DE-588)4149772-7 gnd Tensoranalysis (DE-588)4204323-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dynamisches System (DE-588)4013396-5 gnd Globale Analysis (DE-588)4021285-3 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| topic_facet | Global analysis (Mathematics) Manifolds (Mathematics) Calculus of tensors Differentialform Tensoranalysis Mannigfaltigkeit Dynamisches System Globale Analysis Nichtlineare Analysis Tensorrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016912300&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT abrahamralph manifoldstensoranalysisandapplications AT marsdenjerrolde manifoldstensoranalysisandapplications AT ratiutudor manifoldstensoranalysisandapplications |