Verfügbarkeit: Differential geometry and its applications

Differential geometry and its applications:

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Bibliographische Detailangaben
Beteilige Person:	Oprea, John (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Upper Saddle River, NJ Pearson Prentice Hall 2004
Ausgabe:	2. ed.
Schlagwörter:	Differentialgeometrie Lehrbuch
Links:	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
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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discipline	Mathematik
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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
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