Introduction to differential geometry for engineers:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Dekker
1990
|
| Schriftenreihe: | Pure and applied mathematics
136 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XII, 163 S. |
| ISBN: | 0824783964 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV004283577 | ||
| 003 | DE-604 | ||
| 005 | 20160630 | ||
| 007 | t | ||
| 008 | 910313s1990 |||| 00||| eng d | ||
| 020 | |a 0824783964 |9 0-8247-8396-4 | ||
| 035 | |a (OCoLC)21975691 | ||
| 035 | |a (DE-599)BVBBV004283577 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-91G |a DE-739 |a DE-703 |a DE-634 |a DE-83 |a DE-11 |a DE-188 |a DE-706 |a DE-824 | ||
| 050 | 0 | |a QA641 | |
| 082 | 0 | |a 516.3/6 |2 20 | |
| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a 00A06 |2 msc | ||
| 084 | |a MAT 530f |2 stub | ||
| 084 | |a 53Cxx |2 msc | ||
| 100 | 1 | |a Doolin, Bryan F. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to differential geometry for engineers |c Brian F. Doolin; Clyde F. Martin |
| 264 | 1 | |a New York |b Dekker |c 1990 | |
| 300 | |a XII, 163 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 136 | |
| 650 | 7 | |a Géométrie différentielle |2 ram | |
| 650 | 7 | |a algèbre extérieure |2 inriac | |
| 650 | 7 | |a calcul vectoriel |2 inriac | |
| 650 | 7 | |a champ vectoriel |2 inriac | |
| 650 | 7 | |a espace homogène |2 inriac | |
| 650 | 7 | |a groupe Lie |2 inriac | |
| 650 | 7 | |a géométrie différentielle |2 inriac | |
| 650 | 7 | |a variété différentiable |2 inriac | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Martin, Clyde |d 19XX- |e Verfasser |0 (DE-588)141607688 |4 aut | |
| 830 | 0 | |a Pure and applied mathematics |v 136 |w (DE-604)BV000001885 |9 136 | |
| 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=002664029&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 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=002664029&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-002664029 | ||
Datensatz im Suchindex
| _version_ | 1804118476558696448 |
|---|---|
| adam_text | Contents
PREFACE v
LIST OF FIGURES xi
1 INTRODUCTION 1
2 MANIFOLDS AND THEIR MAPS 5
2.1 Differentiable Manifolds 5
2.2 Examples 13
2.3 Manifold Maps 18
3 TANGENT SPACES 23
3.1 The Tangent Space of Sphere 24
3.2 Equivalence Classes of Curves 30
3.3 The Tangent Space in General 33
3.4 Tangent Space Maps 36
vii
viii CONTENTS
4 VECTOR FIELDS 45
4.1 Vector Fields 46
4.2 Derivations 49
4.3 A Digression on Notation 53
4.4 The Isomorphism 54
4.5 The Algebra 60
4.6 An Example of a Lie Algebra 63
5 EXTERIOR ALGEBRA 69
5.1 Addition of Forms 70
5.2 The Wedge Product 71
5.3 Contraction of Forms; Vectors 75
5.4 Equation of a Plane 79
5.5 Use of Determinants 81
5.6 Solution of Linear Equations 84
5.7 Linear Transformations 86
6 LIE GROUPS AND ACTIONS 91
6.1 Lie Groups 91
6.2 Group Action 93
6.3 One Parameter Subgroups 95
6.4 The Symplectic Group 101
7 HOMOGENEOUS SPACES 107
CONTENTS ix
8 GRASSMANNIAN TECHNIQUES 115
8.1 Linear Optimal Control 116
8.2 The Grassmannian 120
8.3 An Application 129
9 CONCLUDING REMARKS 141
10 APPENDIX: VECTOR CALCULUS 143
10.1 Real Euclidean Space 143
10.2 Topological Spaces 144
10.3 Compactness 147
10.4 Continuity 148
10.5 Derivative 149
10.6 Inverse Function Theorems 151
BIBLIOGRAPHY 155
INDEX 159
Contents
PREFACE v
LIST OF FIGURES xi
1 INTRODUCTION 1
2 MANIFOLDS AND THEIR MAPS 5
2.1 Differentiable Manifolds 5
2.2 Examples 13
2.3 Manifold Maps 18
3 TANGENT SPACES 23
3.1 The Tangent Space of Sphere 24
3.2 Equivalence Classes of Curves 30
3.3 The Tangent Space in General 33
3.4 Tangent Space Maps 36
vii
viii CONTENTS
4 VECTOR FIELDS 45
4.1 Vector Fields 46
4.2 Derivations 49
4.3 A Digression on Notation 53
4.4 The Isomorphism 54
4.5 The Algebra 60
4.6 An Example of a Lie Algebra 63
5 EXTERIOR ALGEBRA 69
5.1 Addition of Forms 70
5.2 The Wedge Product 71
5.3 Contraction of Forms; Vectors 75
5.4 Equation of a Plane 79
5.5 Use of Determinants 81
5.6 Solution of Linear Equations 84
5.7 Linear Transformations 86
6 LIE GROUPS AND ACTIONS 91
6.1 Lie Groups 91
6.2 Group Action 93
6.3 One-Parameter Subgroups 95
6.4 The Symplectic Group 101
7 HOMOGENEOUS SPACES 107
CONTENTS ix
8 GRASSMANNIAN TECHNIQUES 115
8.1 Linear Optimal Control 116
8.2 The Grassmannian 120
8.3 An Application 129
9 CONCLUDING REMARKS 141
10 APPENDIX: VECTOR CALCULUS 143
10.1 Real Euclidean Space 143
10.2 Topological Spaces 144
10.3 Compactness 147
10.4 Continuity 148
10.5 Derivative 149
10.6 Inverse Function Theorems 151
BIBLIOGRAPHY 155
INDEX 159
|
| any_adam_object | 1 |
| author | Doolin, Bryan F. Martin, Clyde 19XX- |
| author_GND | (DE-588)141607688 |
| author_facet | Doolin, Bryan F. Martin, Clyde 19XX- |
| author_role | aut aut |
| author_sort | Doolin, Bryan F. |
| author_variant | b f d bf bfd c m cm |
| building | Verbundindex |
| bvnumber | BV004283577 |
| 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 SK 950 |
| classification_tum | MAT 530f |
| ctrlnum | (OCoLC)21975691 (DE-599)BVBBV004283577 |
| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02309nam a2200553 cb4500</leader><controlfield tag="001">BV004283577</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160630 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">910313s1990 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0824783964</subfield><subfield code="9">0-8247-8396-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)21975691</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV004283577</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-824</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA641</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.3/6</subfield><subfield code="2">20</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">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">00A06</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="084" ind1=" " ind2=" "><subfield code="a">53Cxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Doolin, Bryan F.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to differential geometry for engineers</subfield><subfield code="c">Brian F. Doolin; Clyde F. Martin</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York</subfield><subfield code="b">Dekker</subfield><subfield code="c">1990</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XII, 163 S.</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="490" ind1="1" ind2=" "><subfield code="a">Pure and applied mathematics</subfield><subfield code="v">136</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Géométrie différentielle</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">algèbre extérieure</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">calcul vectoriel</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">champ vectoriel</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">espace homogène</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">groupe Lie</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">géométrie différentielle</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">variété différentiable</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, Differential</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="7"><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</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="700" ind1="1" ind2=" "><subfield code="a">Martin, Clyde</subfield><subfield code="d">19XX-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)141607688</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Pure and applied mathematics</subfield><subfield code="v">136</subfield><subfield code="w">(DE-604)BV000001885</subfield><subfield code="9">136</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=002664029&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</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=002664029&sequence=000004&line_number=0002&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:BVB01-002664029</subfield></datafield></record></collection> |
| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV004283577 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:10:54Z |
| institution | BVB |
| isbn | 0824783964 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002664029 |
| oclc_num | 21975691 |
| open_access_boolean | |
| owner | DE-384 DE-91G DE-BY-TUM DE-739 DE-703 DE-634 DE-83 DE-11 DE-188 DE-706 DE-824 |
| owner_facet | DE-384 DE-91G DE-BY-TUM DE-739 DE-703 DE-634 DE-83 DE-11 DE-188 DE-706 DE-824 |
| physical | XII, 163 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Doolin, Bryan F. Verfasser aut Introduction to differential geometry for engineers Brian F. Doolin; Clyde F. Martin New York Dekker 1990 XII, 163 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 136 Géométrie différentielle ram algèbre extérieure inriac calcul vectoriel inriac champ vectoriel inriac espace homogène inriac groupe Lie inriac géométrie différentielle inriac variété différentiable inriac Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Differentialgeometrie (DE-588)4012248-7 s DE-604 Martin, Clyde 19XX- Verfasser (DE-588)141607688 aut Pure and applied mathematics 136 (DE-604)BV000001885 136 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002664029&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002664029&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Doolin, Bryan F. Martin, Clyde 19XX- Introduction to differential geometry for engineers Pure and applied mathematics Géométrie différentielle ram algèbre extérieure inriac calcul vectoriel inriac champ vectoriel inriac espace homogène inriac groupe Lie inriac géométrie différentielle inriac variété différentiable inriac Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4151278-9 |
| title | Introduction to differential geometry for engineers |
| title_auth | Introduction to differential geometry for engineers |
| title_exact_search | Introduction to differential geometry for engineers |
| title_full | Introduction to differential geometry for engineers Brian F. Doolin; Clyde F. Martin |
| title_fullStr | Introduction to differential geometry for engineers Brian F. Doolin; Clyde F. Martin |
| title_full_unstemmed | Introduction to differential geometry for engineers Brian F. Doolin; Clyde F. Martin |
| title_short | Introduction to differential geometry for engineers |
| title_sort | introduction to differential geometry for engineers |
| topic | Géométrie différentielle ram algèbre extérieure inriac calcul vectoriel inriac champ vectoriel inriac espace homogène inriac groupe Lie inriac géométrie différentielle inriac variété différentiable inriac Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Géométrie différentielle algèbre extérieure calcul vectoriel champ vectoriel espace homogène groupe Lie géométrie différentielle variété différentiable Geometry, Differential Differentialgeometrie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002664029&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002664029&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT doolinbryanf introductiontodifferentialgeometryforengineers AT martinclyde introductiontodifferentialgeometryforengineers |
Es ist kein Print-Exemplar vorhanden.
Inhaltsverzeichnis