Curves and singularities: a geometrical introduction to singularity theory
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
1992
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 321 S. graph. Darst. |
| ISBN: | 0521419859 0521429994 |
Staff View
MARC
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| 245 | 1 | 0 | |a Curves and singularities |b a geometrical introduction to singularity theory |c J. W. Bruce ; P. J. Giblin |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 1992 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface to the second edition xiii
Preface to the first edition xv
1 Introductory example: a gravitational catastrophe machine 1
2 Curves, and functions on them 10
Parametrized curves 13
Tangent vectors 15
Contact 18
Reparametrization 23
Curvature 28
Functions on plane curves 32
Space curves 41
3 More about functions 48
Right equivalence 48
Flat functions 54
Jets 55
4 Regular values and smooth manifolds 59
Smooth maps and parametrized manifolds 60
Regular values 65
Tangent spaces 74
The Morse lemma 85
Morse lemma with parameters 95
5 Envelopes 99
Families and envelopes 99
ix
x Contents
Other definitions of envelope 107
Local structure of envelopes 110
Examples of envelopes 118
Envelopes and differential equations 131
6 Unfoldings 133
Unfoldings and (p)versal unfoldings 134 j
Versal unfoldings 148
Cusps 153
7 Unfoldings: applications 160
Distance squared and height functions 160
Envelopes 168
Developable surfaces and the tangent developable of a
space curve 178 j
Some different local pictures 182
Symmetry sets 184
Caustics by reflexion 192
Duals and differential equations 200
8 Transversality 206
Smooth manifolds 207
Transversality 211
Thorn s transversality lemma 216
Algebraic surfaces and more on apparent contours 220
Open and dense properties 222
9 Generic properties of curves 226
The Monge Taylor map 227
A transversality theorem for space curves 237
10 More on unfoldings 240
Determining the power series 241
Proof of convergence 243
11 Singular points, several variables, generic surfaces 250
The geometry of surfaces in Euclidean 3 space 250
Functions of one variable (again) 253
Families of differential equations 257
Differential equations 262
Functions of several variables 263
^ trivial families 266
Contents X1
A little algebra 269
The determinacy theorem 273
Classification of functions 278
Surfaces in Euclidean 3 space again 284
Moduli and simple singularities 288
Simple singularities ¦ •
Appendix Null sets and Sard s theorem 297
Historical note
Further reading
References 306
Index of notation JUV
Index 311
|
| any_adam_object | 1 |
| author | Bruce, James W. Giblin, P. J. |
| author_facet | Bruce, James W. Giblin, P. J. |
| author_role | aut aut |
| author_sort | Bruce, James W. |
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| ctrlnum | (OCoLC)25508407 (DE-599)BVBBV008205455 |
| dewey-full | 516/.362 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.362 |
| dewey-search | 516/.362 |
| dewey-sort | 3516 3362 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV008205455 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:16:17Z |
| institution | BVB |
| isbn | 0521419859 0521429994 |
| language | English |
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| physical | XVIII, 321 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Cambridge Univ. Press |
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| spelling | Bruce, James W. Verfasser aut Curves and singularities a geometrical introduction to singularity theory J. W. Bruce ; P. J. Giblin 2. ed. Cambridge Cambridge Univ. Press 1992 XVIII, 321 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Courbes ram Singularités (Mathématiques) ram Curves Singularities (Mathematics) Kurvensingularität (DE-588)4166228-3 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Glatte Kurve (DE-588)4157470-9 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Glatte Kurve (DE-588)4157470-9 s Singularität Mathematik (DE-588)4077459-4 s DE-604 Kurvensingularität (DE-588)4166228-3 s DE-188 Differentialgeometrie (DE-588)4012248-7 s 1\p DE-604 Giblin, P. J. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005414825&sequence=000002&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 | Bruce, James W. Giblin, P. J. Curves and singularities a geometrical introduction to singularity theory Courbes ram Singularités (Mathématiques) ram Curves Singularities (Mathematics) Kurvensingularität (DE-588)4166228-3 gnd Singularität Mathematik (DE-588)4077459-4 gnd Glatte Kurve (DE-588)4157470-9 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4166228-3 (DE-588)4077459-4 (DE-588)4157470-9 (DE-588)4012248-7 |
| title | Curves and singularities a geometrical introduction to singularity theory |
| title_auth | Curves and singularities a geometrical introduction to singularity theory |
| title_exact_search | Curves and singularities a geometrical introduction to singularity theory |
| title_full | Curves and singularities a geometrical introduction to singularity theory J. W. Bruce ; P. J. Giblin |
| title_fullStr | Curves and singularities a geometrical introduction to singularity theory J. W. Bruce ; P. J. Giblin |
| title_full_unstemmed | Curves and singularities a geometrical introduction to singularity theory J. W. Bruce ; P. J. Giblin |
| title_short | Curves and singularities |
| title_sort | curves and singularities a geometrical introduction to singularity theory |
| title_sub | a geometrical introduction to singularity theory |
| topic | Courbes ram Singularités (Mathématiques) ram Curves Singularities (Mathematics) Kurvensingularität (DE-588)4166228-3 gnd Singularität Mathematik (DE-588)4077459-4 gnd Glatte Kurve (DE-588)4157470-9 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Courbes Singularités (Mathématiques) Curves Singularities (Mathematics) Kurvensingularität Singularität Mathematik Glatte Kurve Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005414825&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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