Exterior differential systems:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York [u.a.]
Springer
1991
|
| Series: | Mathematical Sciences Research Institute <Berkeley, Calif.>: Mathematical Sciences Research Institute publications
18 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | VII, 475 S. |
| ISBN: | 0387974113 3540974113 9781461397168 |
Staff View
MARC
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| 245 | 1 | 0 | |a Exterior differential systems |c R. L. Bryant ... |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1991 | |
| 300 | |a VII, 475 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical Sciences Research Institute <Berkeley, Calif.>: Mathematical Sciences Research Institute publications |v 18 | |
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Record in the Search Index
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|---|---|
| adam_text | Exterior Differential Systems
Table of Contents
Introduction 1
I. Preliminaries 6
§1. Review of Exterior Algebra 6
§2. The Notion of an Exterior Differential System 15
§3. Jet Bundles 18
II. Basic Theorems 27
§1. Probenius Theorem 27
§2. Cauchy Characteristics 30
§3. Theorems of Pfaff and Darboux 38
§4. Pfaffian Systems 43
§5. Pfaffian Systems of Codimension Two 49
III. Cartan Kahler Theory 58
§1. Integral Elements 65
§2. The Cartan Kahler Theorem 80
§3. Examples 88
IV. Linear Differential Systems 102
§1. Independence Condition and Involution 103
§2. Linear Differential Systems 109
§3. Tableaux 115
§4. Tableaux Associated to an Integral Element 122
§5. Linear Pfaffian Systems 128
vi CONTENTS
§6. Prolongation 147
§7. Examples 155
§8. Families of Isometric Surfaces in Euclidean Space . . 163
V. The Characteristic Variety 170
§1. Definition of the Characteristic Variety of
a Differential System 171
§2. The Characteristic Variety for Linear
Pfaffian Systems; Examples 179
§3. Properties of the Characteristic Variety 201
VI. Prolongation Theory 236
§1. The Notion of Prolongation 237
§2. Ordinary Prolongation 248
§3. The Prolongation Theorem 255
§4. The Process of Prolongation 260
VII. Examples 266
§1. First Order Equations for Two Functions
of Two Variables 266
§2. Finiteness of the Web Rank 285
§3. Orthogonal Coordinates 287
§4. Isometric Embedding 292
VIII. Applications of Commutative Algebra and
Algebraic Geometry to the Study of
Exterior Differential Systems 313
§1. Involutive Tableaux 315
§2. The Cartan Poincare Lemma, Spencer Cohomology . 320
§3. The Graded Module Associated to a Tableau;
Koszul Homology 333
§4. The Canonical Resolution of an Involutive Module . . 342
§5. Localization; the Proofs of Theorem 3.2 and
Proposition 3.8 354
§6. Proof of Theorem 3.8 in Chapter V; Guillemin s
Normal Form 371
§7. The Graded Module Associated to a Higher
Order Tableau 383
CONTENTS vii
IX. Partial Differential Equations 390
§1. An Integrability Criterion 390
§2. Quasi Linear Equations 393
§3. Existence Theorems 413
X. Linear Differential Operators 417
§1. Formal Theory and Complexes 418
§2. Examples 434
§3. Existence Theorems for Elliptic Equations 450
Bibliography 462
Index 471
|
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| discipline | Mathematik |
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| indexdate | 2024-07-09T16:11:23Z |
| institution | BVB |
| isbn | 0387974113 3540974113 9781461397168 |
| language | English |
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| physical | VII, 475 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series | Mathematical Sciences Research Institute <Berkeley, Calif.>: Mathematical Sciences Research Institute publications |
| series2 | Mathematical Sciences Research Institute <Berkeley, Calif.>: Mathematical Sciences Research Institute publications |
| spelling | Exterior differential systems R. L. Bryant ... New York [u.a.] Springer 1991 VII, 475 S. txt rdacontent n rdamedia nc rdacarrier Mathematical Sciences Research Institute <Berkeley, Calif.>: Mathematical Sciences Research Institute publications 18 Hier auch später erschienene, unveränderte Nachdrucke Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Äußeres Differentialsystem (DE-588)4141545-0 gnd rswk-swf Äußeres Differentialsystem (DE-588)4141545-0 s DE-604 Differentialgleichung (DE-588)4012249-9 s Bryant, Robert L. 1953- Sonstige (DE-588)112659721 oth Mathematical Sciences Research Institute <Berkeley, Calif.>: Mathematical Sciences Research Institute publications 18 (DE-604)BV000013092 18 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002685134&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Exterior differential systems Mathematical Sciences Research Institute <Berkeley, Calif.>: Mathematical Sciences Research Institute publications Differentialgleichung (DE-588)4012249-9 gnd Äußeres Differentialsystem (DE-588)4141545-0 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4141545-0 |
| title | Exterior differential systems |
| title_auth | Exterior differential systems |
| title_exact_search | Exterior differential systems |
| title_full | Exterior differential systems R. L. Bryant ... |
| title_fullStr | Exterior differential systems R. L. Bryant ... |
| title_full_unstemmed | Exterior differential systems R. L. Bryant ... |
| title_short | Exterior differential systems |
| title_sort | exterior differential systems |
| topic | Differentialgleichung (DE-588)4012249-9 gnd Äußeres Differentialsystem (DE-588)4141545-0 gnd |
| topic_facet | Differentialgleichung Äußeres Differentialsystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002685134&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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