Geometry from a differentiable viewpoint:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2013
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 341 - 349 |
| Beschreibung: | XV, 357 S. Ill., graph. Darst. |
| ISBN: | 9780521116077 9780521133111 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV040538779 | ||
| 003 | DE-604 | ||
| 005 | 20130222 | ||
| 007 | t | ||
| 008 | 121113s2013 ad|| |||| 00||| eng d | ||
| 010 | |a 2012017159 | ||
| 020 | |a 9780521116077 |9 978-0-521-11607-7 | ||
| 020 | |a 9780521133111 |9 978-0-521-13311-1 | ||
| 035 | |a (OCoLC)826540556 | ||
| 035 | |a (DE-599)GBV717138771 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-83 |a DE-19 |a DE-824 |a DE-188 |a DE-20 |a DE-11 | ||
| 050 | 0 | |a QA641 | |
| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 084 | |a 53-01 |2 msc | ||
| 084 | |a MAT 530f |2 stub | ||
| 100 | 1 | |a McCleary, John |d 1952- |e Verfasser |0 (DE-588)113779089 |4 aut | |
| 245 | 1 | 0 | |a Geometry from a differentiable viewpoint |c John McCleary |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2013 | |
| 300 | |a XV, 357 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 341 - 349 | ||
| 650 | 4 | |a Geometrie - Geschichte | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 655 | 4 | |a Lehrbuch - Differentialgeometrie | |
| 689 | 0 | 0 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025384735&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025384735 | ||
Datensatz im Suchindex
| _version_ | 1804149628966273024 |
|---|---|
| adam_text | Titel: Geometry from a differentiable viewpoint
Autor: McCleary, John
Jahr: 2013
- • - Contents Preface to the second edition page ix Introduction xi PART A Prelude and themes: Synthetic methods and results 1 Spherical geometry 3 2 Euclid 12 Euclid’s theory of parallels 19 Appendix: The Elements : Book I 24 3 The theory of parallels 27 Uniqueness of parallels 28 Equidistance and boundedness of parallels 29 On the angle sum of a triangle 31 Similarity of triangles 34 The work of Saccheri 37 4 Non-Euclidean geometry 43 The work of Gauss 43 The hyperbolic plane 47 Digression: Neutral space 55 Hyperbolic space 62 Appendix: The Elements: Selections from Book XI 72 PART B Development: Differential geometry 5 Curves in the plane 77 Early work on plane curves (Huygens, Leibniz, Newton, and Euler) 81 The tractrix 84 Oriented curvature 86 Involutes and evolutes 89 6 Curves in space 99 Appendix: On Euclidean rigid motions 110 7 Surfaces 116 The tangent plane 124 The first fundamental form . 128 Lengths, angles, and areas 130 l b,s Map projections 138 Stereographic projection 143 vii
Contents viii Central (gnomonic) projection 147 Cylindrical projections 148 Sinusoidal projection 152 Azimuthal projection 153 8 Curvature for surfaces 156 Euler’s work on surfaces 156 The Gauss map 159 9 Metric equivalence of surfaces 171 Special coordinates 179 10 Geodesics 185 Euclid revisited I: The Hopf-Rinow Theorem 195 11 The Gauss-Bonnet Theorem 201 Euclid revisited II: Uniqueness of lines 205 Compact surfaces 207 A digression on curves 211 12 Constant-curvature surfaces 218 Euclid revisited III: Congruences 223 The work of Minding 224 Hilbert’s Theorem 231 PART C Recapitulation and coda 13 Abstract surfaces 237 14 Modeling the non-Euclidean plane 251 The Beltrami disk 255 The Poincare disk 262 The Poincare half-plane 265 15 Epilogue: Where from here? 282 Manifolds (differential topology) 283 Vector and tensor fields 287 Metrical relations (Riemannian manifolds) 289 Curvature 294 Covariant differentiation 303 Riemann’s Habilitationsvortrag : On the hypotheses which lie at the foundations of geometry 313 Solutions to selected exercises 325 Bibliography 341 Symbol index 351 Name index 352 Subject index 354
|
| any_adam_object | 1 |
| author | McCleary, John 1952- |
| author_GND | (DE-588)113779089 |
| author_facet | McCleary, John 1952- |
| author_role | aut |
| author_sort | McCleary, John 1952- |
| author_variant | j m jm |
| building | Verbundindex |
| bvnumber | BV040538779 |
| callnumber-first | Q - Science |
| callnumber-label | QA641 |
| callnumber-raw | QA641 |
| callnumber-search | QA641 |
| callnumber-sort | QA 3641 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| classification_tum | MAT 530f |
| ctrlnum | (OCoLC)826540556 (DE-599)GBV717138771 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01553nam a2200421 c 4500</leader><controlfield tag="001">BV040538779</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130222 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">121113s2013 ad|| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2012017159</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521116077</subfield><subfield code="9">978-0-521-11607-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521133111</subfield><subfield code="9">978-0-521-13311-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)826540556</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBV717138771</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-83</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA641</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 370</subfield><subfield code="0">(DE-625)143234:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">53-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 530f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">McCleary, John</subfield><subfield code="d">1952-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)113779089</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Geometry from a differentiable viewpoint</subfield><subfield code="c">John McCleary</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2013</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 357 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 341 - 349</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometrie - Geschichte</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="4"><subfield code="a">Lehrbuch - Differentialgeometrie</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025384735&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-025384735</subfield></datafield></record></collection> |
| genre | Lehrbuch - Differentialgeometrie |
| genre_facet | Lehrbuch - Differentialgeometrie |
| id | DE-604.BV040538779 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:26:04Z |
| institution | BVB |
| isbn | 9780521116077 9780521133111 |
| language | English |
| lccn | 2012017159 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025384735 |
| oclc_num | 826540556 |
| open_access_boolean | |
| owner | DE-83 DE-19 DE-BY-UBM DE-824 DE-188 DE-20 DE-11 |
| owner_facet | DE-83 DE-19 DE-BY-UBM DE-824 DE-188 DE-20 DE-11 |
| physical | XV, 357 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | McCleary, John 1952- Verfasser (DE-588)113779089 aut Geometry from a differentiable viewpoint John McCleary 2. ed. Cambridge [u.a.] Cambridge Univ. Press 2013 XV, 357 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 341 - 349 Geometrie - Geschichte Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Lehrbuch - Differentialgeometrie Differentialgeometrie (DE-588)4012248-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025384735&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | McCleary, John 1952- Geometry from a differentiable viewpoint Geometrie - Geschichte Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 |
| title | Geometry from a differentiable viewpoint |
| title_auth | Geometry from a differentiable viewpoint |
| title_exact_search | Geometry from a differentiable viewpoint |
| title_full | Geometry from a differentiable viewpoint John McCleary |
| title_fullStr | Geometry from a differentiable viewpoint John McCleary |
| title_full_unstemmed | Geometry from a differentiable viewpoint John McCleary |
| title_short | Geometry from a differentiable viewpoint |
| title_sort | geometry from a differentiable viewpoint |
| topic | Geometrie - Geschichte Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Geometrie - Geschichte Differentialgeometrie Lehrbuch - Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025384735&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mcclearyjohn geometryfromadifferentiableviewpoint |