Differential geometry and its applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Upper Saddle River, NJ
Pearson Prentice Hall
2004
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| ISBN: | 0130652466 |
Internformat
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Datensatz im Suchindex
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|---|---|
| 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
|
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| dewey-full | 516.36 |
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| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| 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 |
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| 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 |
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