Holdings: Differential geometry and its applications

Differential geometry and its applications:

Saved in:

Bibliographic Details
Main Author:	Oprea, John (Author)
Format:	Book
Language:	English
Published:	Upper Saddle River, NJ Pearson Prentice Hall 2004
Edition:	2. ed.
Subjects:	Differentialgeometrie Lehrbuch
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index
ISBN:	0130652466

Staff View

MARC


LEADER	00000nam a2200000zc 4500
001	BV019333832
003	DE-604
005	20041202
007	t
008	040709s2004 xxu \|\|\|\| 00\|\|\| eng d
020			\|a 0130652466 \|9 0-13-065246-6
035			\|a (OCoLC)249242024
035			\|a (DE-599)BVBBV019333832
040			\|a DE-604 \|b ger \|e aacr
041	0		\|a eng
044			\|a xxu \|c US
049			\|a DE-898 \|a DE-91G \|a DE-634 \|a DE-83 \|a DE-11
050		0	\|a QA614
082	0		\|a 516.36
084			\|a SK 370 \|0 (DE-625)143234: \|2 rvk
084			\|a MAT 530f \|2 stub
084			\|a 17,1 \|2 ssgn
084			\|a 53-01 \|2 msc
100	1		\|a Oprea, John \|e Verfasser \|4 aut
245	1	0	\|a Differential geometry and its applications \|c John Oprea
250			\|a 2. ed.
264		1	\|a Upper Saddle River, NJ \|b Pearson Prentice Hall \|c 2004
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
500			\|a Includes bibliographical references and index
650		4	\|a Differentialgeometrie
650	0	7	\|a Differentialgeometrie \|0 (DE-588)4012248-7 \|2 gnd \|9 rswk-swf
655		7	\|8 1\p \|0 (DE-588)4123623-3 \|a Lehrbuch \|2 gnd-content
689	0	0	\|a Differentialgeometrie \|0 (DE-588)4012248-7 \|D s
689	0		\|5 DE-604
856	4	2	\|m GBV Datenaustausch \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012798728&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
999			\|a oai:aleph.bib-bvb.de:BVB01-012798728
883	1		\|8 1\p \|a cgwrk \|d 20201028 \|q DE-101 \|u https://d-nb.info/provenance/plan#cgwrk

Record in the Search Index

_version_	1804132754758041600
adam_text	DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS SECOND EDITION JOHN OPREA CLEVELAND STATE UNIVERSITY PEARSON PRENTICE HALL UPPER SADDLE RIVER, NEW JERSEY 07458 CONTENTS PREFACE TO FIRST EDITION (REVISED) IX NOTE TO STUDENTS XV CHAPTER 1. THE GEOMETRY OF CURVES 1 1.1. INTRODUCTION 1 1.2. ARCLENGTH PARAMETRIZATION 16 1.3. FRENET FORMULAS 19 1.4. NON-UNIT SPEED CURVES 30 1.5. SOME IMPLICATIONS OF CURVATURE AND TORSION 37 1.6. GREEN S THEOREM AND THE ISOPERIMETRIC INEQUALITY 42 1.7. THE GEOMETRY OF CURVES AND MAPLE 46 CHAPTER 2. SURFACES 71 2.1. INTRODUCTION 71 2.2. THE GEOMETRY OF SURFACES 83 2.3. THE LINEAR ALGEBRA OF SURFACES 93 2.4. NORMAL CURVATURE 98 2.5. SURFACES AND MAPLE 105 CHAPTER 3. CURVATURES 115 3.1. INTRODUCTION 115 3.2. CALCULATING CURVATURE 119 3.3. SURFACES OF REVOLUTION 128 3.4. A FORMULA FOR GAUSS CURVATURE 133 3.5. SOME EFFECTS OF CURVATURE(S) 137 3.6. SURFACES OF DELAUNAY 144 3.7. ELLIPTIC FUNCTIONS, MAPLE AND GEOMETRY 148 ^ 3.8. CALCULATING CURVATURE WITH MAPLE 160 CHAPTER 4. CONSTANT MEAN CURVATURE SURFACES 17 3 4.1. INTRODUCTION 173 4.2. FIRST NOTIONS IN MINIMAL SURFACES 176 4.3. AREA MINIMIZATION 183 4.4. CONSTANT MEAN CURVATURE 186 4.5. HARMONIC FUNCTIONS 193 VI CONTENTS 4.6. COMPLEX VARIABLES 196 4.7. ISOTHERMAL COORDINATES 199 4.8. THE WEIERSTRASS-ENNEPER REPRESENTATIONS 201 4.9. MAPLE AND MINIMAL SURFACES 212 CHAPTER 5. GEODESIES, METRICS AND ISOMETRIES 223 5.1. INTRODUCTION 223 5.2. THE GEODESIC EQUATIONS AND THE CLAIRAUT RELATION 230 5.3. A BRIEF DIGRESSION ON COMPLETENESS 240 5.4. SURFACES NOT IN E 3 242 5.5. ISOMETRIES AND CONFORMAL MAPS 251 5.6. GEODESIES AND MAPLE 258 5.7. AN INDUSTRIAL APPLICATION 281 CHAPTER 6. HOLONOMY AND THE GAUSS-BONNET THEOREM 295 6.1. INTRODUCTION 295 6.2. THE COVARIANT DERIVATIVE REVISITED 298 6.3. PARALLEL VECTOR FIELDS AND HOLONOMY 301 6.4. FOUCAULT S PENDULUM 305 6.5. THE ANGLE EXCESS THEOREM 307 6.6. THE GAUSS-BONNET THEOREM 311 6.7. APPLICATIONS OF GAUSS-BONNET 314 6.8. GEODESIC POLAR COORDINATES 319 6.9. MAPLE AND HOLONOMY 328 CHAPTER 7. THE CALCULUS OF VARIATIONS AND GEOMETRY 335 7.1. THE EULER-LAGRANGE EQUATIONS 335 7.2. TRANSVERSALITY AND NATURAL BOUNDARY CONDITIONS 342 7.3. THE BASIC EXAMPLES 347 7.4. HIGHER ORDER PROBLEMS 352 7.5. THE WEIERSTRASS ^-FUNCTION 360 7.6. PROBLEMS WITH CONSTRAINTS 372 7.7. FURTHER APPLICATIONS TO GEOMETRY AND MECHANICS 383 7.8. THE PONTRYAGIN MAXIMUM PRINCIPLE 394 7.9. AN APPLICATION TO THE SHAPE OF A BALLOON 399 7.10. THE CALCULUS OF VARIATIONS AND MAPLE 408 CHAPTER 8. A GLIMPSE AT HIGHER DIMENSIONS 425 8.1. INTRODUCTION 425 8.2. MANIFOLDS 425 8.3. THE COVARIANT DERIVATIVE 430 8.4. CHRISTOFFEL SYMBOLS 438 8.5. CURVATURES 446 8.6. THE CHARMING DOUBLENESS 461 CONTENTS VII APPENDIX A. HINTS AND SOLUTIONS TO SELECTED PROBLEMS 469 A.I. CHAPTER 1: THE GEOMETRY OF CURVES 469 A.2. CHAPTER 2: SURFACES 472 A.3. CHAPTER 3: CURVATURE(S) 473 A.4. CHAPTER 4: CONSTANT MEAN CURVATURE SURFACES 475 A.5. CHAPTER 5: GEODESIES, METRICS AND ISOMETRIES 477 A.6. CHAPTER 6: HOLONOMY AND THE GAUSS-BONNET THEOREM 478 A.7. CHAPTER 7: THE CALCULUS OF VARIATIONS AND GEOMETRY 479 A.8. CHAPTER 8: A GLIMPSE AT HIGHER DIMENSIONS 480 BIBLIOGRAPHY 483 INDEX 487
any_adam_object	1
author	Oprea, John
author_facet	Oprea, John
author_role	aut
author_sort	Oprea, John
author_variant	j o jo
building	Verbundindex
bvnumber	BV019333832
callnumber-first	Q - Science
callnumber-label	QA614
callnumber-raw	QA614
callnumber-search	QA614
callnumber-sort	QA 3614
callnumber-subject	QA - Mathematics
classification_rvk	SK 370
classification_tum	MAT 530f
ctrlnum	(OCoLC)249242024 (DE-599)BVBBV019333832
dewey-full	516.36
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	516 - Geometry
dewey-raw	516.36
dewey-search	516.36
dewey-sort	3516.36
dewey-tens	510 - Mathematics
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>01583nam a2200433zc 4500</leader><controlfield tag="001">BV019333832</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20041202 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">040709s2004 xxu \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0130652466</subfield><subfield code="9">0-13-065246-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)249242024</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV019333832</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-898</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA614</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.36</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">MAT 530f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">53-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Oprea, John</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Differential geometry and its applications</subfield><subfield code="c">John Oprea</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Upper Saddle River, NJ</subfield><subfield code="b">Pearson Prentice Hall</subfield><subfield code="c">2004</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">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differentialgeometrie</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="8">1\p</subfield><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</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="856" ind1="4" ind2="2"><subfield code="m">GBV 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=012798728&sequence=000001&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:BVB01-012798728</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection>
genre	1\p (DE-588)4123623-3 Lehrbuch gnd-content
genre_facet	Lehrbuch
id	DE-604.BV019333832
illustrated	Not Illustrated
indexdate	2024-07-09T19:57:51Z
institution	BVB
isbn	0130652466
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-012798728
oclc_num	249242024
open_access_boolean
owner	DE-898 DE-BY-UBR DE-91G DE-BY-TUM DE-634 DE-83 DE-11
owner_facet	DE-898 DE-BY-UBR DE-91G DE-BY-TUM DE-634 DE-83 DE-11
publishDate	2004
publishDateSearch	2004
publishDateSort	2004
publisher	Pearson Prentice Hall
record_format	marc
spelling	Oprea, John Verfasser aut Differential geometry and its applications John Oprea 2. ed. Upper Saddle River, NJ Pearson Prentice Hall 2004 txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Differentialgeometrie Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Differentialgeometrie (DE-588)4012248-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012798728&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
spellingShingle	Oprea, John Differential geometry and its applications Differentialgeometrie Differentialgeometrie (DE-588)4012248-7 gnd
subject_GND	(DE-588)4012248-7 (DE-588)4123623-3
title	Differential geometry and its applications
title_auth	Differential geometry and its applications
title_exact_search	Differential geometry and its applications
title_full	Differential geometry and its applications John Oprea
title_fullStr	Differential geometry and its applications John Oprea
title_full_unstemmed	Differential geometry and its applications John Oprea
title_short	Differential geometry and its applications
title_sort	differential geometry and its applications
topic	Differentialgeometrie Differentialgeometrie (DE-588)4012248-7 gnd
topic_facet	Differentialgeometrie Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012798728&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT opreajohn differentialgeometryanditsapplications

Holdings

There is no print copy available.

Interlibrary loan Place Request Caution: Not in THWS collection! Indexes

MARC

Record in the Search Index

There is no print copy available.

Similar Items