Mathematics of the 19th century: Vol. 2 Geometry, analytic function theory
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | X, 291 S. Ill., graph. Darst. |
| ISBN: | 3764350482 0817650482 |
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Datensatz im Suchindex
| _version_ | 1804138287395241984 |
|---|---|
| adam_text | MATHEMATICS OF THE 19TH CENTURY EDITED BY A.N. KOLMOGOROV A.P.
YUSHKEVICH GEOMETRY TRANSLATED FROM THE RUSSIAN BY ROGER COOKE ANALYTIC
FUNCTION THEORY BIRKHAEUSER VERLAG BASEL * BOSTON * BERLIN CONTENTS
PREFACE IX CHAPTER 1. GEOMETRY (B. L. LAPTEV AND B. A. ROZENFEL D) 1
INTRODUCTION 1 1. ANALYTIC AND DIFFERENTIAL GEOMETRY 3 ANALYTIC GEOMETRY
3 THE DIFFERENTIAL GEOMETRY OF MONGE S STUDENTS 5 GAUSS DISQUISITIONES
GENERALES CIRCA SUPERFICIES CURVAS 7 MINDING AND THE FORMULATION OF THE
PROBLEMS OF INTRINSIC GEOMETRY .... 12 THE FRENCH SCHOOL OF DIFFERENTIAL
GEOMETRY 17 DIFFERENTIAL GEOMETRY AT MIDCENTURY 21 DIFFERENTIAL GEOMETRY
IN RUSSIA 24 THE THEORY OF LINEAR CONGRUENCES 26 2. PROJECTIVE GEOMETRY
27 THE RISE OF PROJECTIVE GEOMETRY 27 PONCELET S TRAUE DES PROPRIETES
PROJECTIVES DES FIGURES 29 THE ANALYTIC PROJECTIVE GEOMETRY OF MOEBIUS
AND PLUECKER 31 THE SYNTHETIC PROJECTIVE GEOMETRY OF STEINER AND CHASLES
36 STAUDT AND THE FOUNDATION OF PROJECTIVE GEOMETRY 40 CAYLEY S
PROJECTIVE GEOMETRY 43 V VI CONTENTS 3. ALGEBRAIC GEOMETRY AND GEOMETRIC
ALGEBRA 44 ALGEBRAIC CURVES 44 ALGEBRAIC SURFACES 45 GEOMETRIE
COMPUTATIONS CONNECTED WITH ALGEBRAIC GEOMETRY 47 GRASSMANN S LINEALE
AUSDEHNUNGSLEHRE 47 HAMILTON S VECTORS 51 4. NON-EUCLIDEAN GEOMETRY 53
NIKOLAI IVANOVICH LOBACHEVSKII AND THE DISCOVERY OF NON-EUCLIDEAN
GEOMETRY 53 GAUSS RESEARCH IN NON-EUCLIDEAN GEOMETRY 56 JAENOS BOELYAI 57
HYPERBOLIC GEOMETRY 58 J. BOELYAI S ABSOLUTE GEOMETRY 61 THE
CONSISTENCY OF HYPERBOLIC GEOMETRY 62 PROPAGATION OF THE IDEAS OF
HYPERBOLIC GEOMETRY 65 BELTRAMI S INTERPRETATION 67 CAYLEY S
INTERPRETATION 69 KLEIN S INTERPRETATION 71 ELLIPTIC GEOMETRY 72 5.
MULTI-DIMENSIONAL GEOMETRY 75 JACOBI S FORMULAS FOR MULTI-DIMENSIONAL
GEOMETRY 75 CAYLEY S ANALYTIC GEOMETRY OF N DIMENSIONS 76 GRASSMANN S
MULTI-DIMENSIONAL GEOMETRY 77 PLUECKER S NEUE GEOMETRIE DES RAUMES 78
SCHLAEFLI S THEORIE DER VIELFACHEN KONTINUITAET 78 THE MULTI-DIMENSIONAL
GEOMETRY OF KLEIN AND JORDAN 81 RIEMANNIAN GEOMETRY 83 RIEMANN S IDEA OF
COMPLEX PARAMETERS OF EUCLIDEAN MOTIONS 87 RIEMANN S IDEAS ON PHYSICAL
SPACE 87 THE WORK OF CHRISTOFFEL, LIPSCHITZ, AND SUVOROV ON RIEMANNIAN
GEOMETRY 89 THE MULTI-DIMENSIONAL THEORY OF CURVES 90 MULTI-DIMENSIONAL
SURFACE THEORY 94 MULTI-DIMENSIONAL PROJECTIVE GEOMETRY 96 THE
TERMINOLOGY OF MULTI-DIMENSIONAL GEOMETRY 96 CONTENTS VII 6. TOPOLOGY 97
GAUSS TOPOLOGY 97 GENERALIZATIONS OF EULER S THEOREM ON POLYHEDRA IN
THE EARLY NINETEENTH CENTURY 98 LISTING S VORSTUDIEN ZUR TOPOLOGIE 99
MOEBIUS THEORIE DER ELEMENTAREN VERWANDSCHAFT 101 THE TOPOLOGY OF
SURFACES IN RIEMANN S THEORIE DER ABEL SCHEN FUNKTIONEN 102 THE
MULTI-DIMENSIONAL TOPOLOGY OF RIEMANN AND BETTI 103 JORDAN S TOPOLOGICAL
THEOREMS 104 THE KLEIN BOTTLE 105 7. GEOMETRIC TRANSFORMATIONS 106
GEOMETRIE TRANSFORMATIONS IN THE WORK OF MOEBIUS 106 HELMHOLTZ PAPER
UEBER DIE THATSACHEN, DIE DER GEOMETRIE ZU GRUNDE LIEGEN 107 KLEIN S
ERLANGER PROGRAMM 109 TRANSFERENCE PRINCIPLES 111 CREMONA
TRANSFORMATIONS 113 CONCLUSION 115 CHAPTER 2. ANALYTIC FUNCTION (A. I.
MARKUSHEVICH) 119 RESULTS ACHIEVED IN ANALYTIC FUNCTION THEORY IN THE
EIGHTEENTH CENTURY 119 DEVELOPMENT OF THE CONCEPT OF A COMPLEX NUMBER
121 COMPLEX INTEGRATION 125 THE CAUCHY INTEGRAL THEOREM. RESIDUES 128
ELLIPTIC FUNCTIONS IN THE WORK OF GAUSS 132 HYPERGEOMETRIC FUNCTIONS 138
THE FIRST APPROACH TO MODULAR FUNCTIONS 145 POWER SERIES. THE METHOD OF
MAJORANTS 148 ELLIPTIC FUNCTIONS IN THE WORK OF ABEL 153 CG. J. JACOBI.
FUNDAMENTA NOVA FUNCTIONUM ELLIPTICARUM 158 THE JACOBI THETA FUNCTIONS
162 ELLIPTIC FUNCTIONS IN THE WORK OF EISENSTEIN AND LIOUVILLE. THE
FIRST TEXTBOOKS 166 VIII CONTENTS ABELIAN INTEGRALS. ABEL S THEOREM 173
QUADRUPLY PERIODIC FUNCTIONS 178 SUMMARY OF THE DEVELOPMENT OF ANALYTIC
FUNCTION THEORY OVER THE FIRST HALF OF THE NINETEENTH CENTURY 183 V.
PUISEUX. ALGEBRAIC FUNCTIONS 189 BERNHARD RIEMANN 198 RIEMANN S DOCTORAL
DISSERTATION. THE DIRICHLET PRINCIPLE 201 CONFORMAL MAPPINGS 215 KARL
WEIERSTRASS 220 ANALYTIC FUNCTION THEORY IN RUSSIA. YU.V. SOKHOTSKII AND
THE SOKHOTSKII-CASORATI-WEIERSTRASS THEOREM 227 ENTIRE AND MEROMORPHIC
FUNCTIONS. PICARD S THEOREM 236 ABELIAN FUNCTIONS 247 ABELIAN FUNCTIONS
(CONTINUATION) 249 AUTOMORPHIC FUNCTIONS. UNIFORMIZATION 257 SEQUENCES
AND SERIES OF ANALYTIC FUNCTIONS 264 CONCLUSION 270 LITERATURE (F. A.
MEDVEDEV) 273 GENERAL WORKS 273 COLLECTED WORKS AND OTHER ORIGINAL
SOURCES 274 AUXILIARY LITERATURE TO CHAPTER 1 278 AUXILIARY LITERATURE
TO CHAPTER 2 280 INDEX OF NAMES (A. F. LAPKO) 283
|
| adam_txt |
MATHEMATICS OF THE 19TH CENTURY EDITED BY A.N. KOLMOGOROV A.P.
YUSHKEVICH GEOMETRY TRANSLATED FROM THE RUSSIAN BY ROGER COOKE ANALYTIC
FUNCTION THEORY BIRKHAEUSER VERLAG BASEL * BOSTON * BERLIN CONTENTS
PREFACE IX CHAPTER 1. GEOMETRY (B. L. LAPTEV AND B. A. ROZENFEL'D) 1
INTRODUCTION 1 1. ANALYTIC AND DIFFERENTIAL GEOMETRY 3 ANALYTIC GEOMETRY
3 THE DIFFERENTIAL GEOMETRY OF MONGE'S STUDENTS 5 GAUSS' DISQUISITIONES
GENERALES CIRCA SUPERFICIES CURVAS 7 MINDING AND THE FORMULATION OF THE
PROBLEMS OF INTRINSIC GEOMETRY . 12 THE FRENCH SCHOOL OF DIFFERENTIAL
GEOMETRY 17 DIFFERENTIAL GEOMETRY AT MIDCENTURY 21 DIFFERENTIAL GEOMETRY
IN RUSSIA 24 THE THEORY OF LINEAR CONGRUENCES 26 2. PROJECTIVE GEOMETRY
27 THE RISE OF PROJECTIVE GEOMETRY 27 PONCELET'S TRAUE DES PROPRIETES
PROJECTIVES DES FIGURES 29 THE ANALYTIC PROJECTIVE GEOMETRY OF MOEBIUS
AND PLUECKER 31 THE SYNTHETIC PROJECTIVE GEOMETRY OF STEINER AND CHASLES
36 STAUDT AND THE FOUNDATION OF PROJECTIVE GEOMETRY 40 CAYLEY'S
PROJECTIVE GEOMETRY 43 V VI CONTENTS 3. ALGEBRAIC GEOMETRY AND GEOMETRIC
ALGEBRA 44 ALGEBRAIC CURVES 44 ALGEBRAIC SURFACES 45 GEOMETRIE
COMPUTATIONS CONNECTED WITH ALGEBRAIC GEOMETRY 47 GRASSMANN'S LINEALE
AUSDEHNUNGSLEHRE 47 HAMILTON'S VECTORS 51 4. NON-EUCLIDEAN GEOMETRY 53
NIKOLAI IVANOVICH LOBACHEVSKII AND THE DISCOVERY OF NON-EUCLIDEAN
GEOMETRY 53 GAUSS' RESEARCH IN NON-EUCLIDEAN GEOMETRY 56 JAENOS BOELYAI 57
HYPERBOLIC GEOMETRY 58 J. BOELYAI'S "ABSOLUTE GEOMETRY" 61 THE
CONSISTENCY OF HYPERBOLIC GEOMETRY 62 PROPAGATION OF THE IDEAS OF
HYPERBOLIC GEOMETRY 65 BELTRAMI'S INTERPRETATION 67 CAYLEY'S
INTERPRETATION 69 KLEIN'S INTERPRETATION 71 ELLIPTIC GEOMETRY 72 5.
MULTI-DIMENSIONAL GEOMETRY 75 JACOBI'S FORMULAS FOR MULTI-DIMENSIONAL
GEOMETRY 75 CAYLEY'S ANALYTIC GEOMETRY OF N DIMENSIONS 76 GRASSMANN'S
MULTI-DIMENSIONAL GEOMETRY 77 PLUECKER'S NEUE GEOMETRIE DES RAUMES 78
SCHLAEFLI'S THEORIE DER VIELFACHEN KONTINUITAET 78 THE MULTI-DIMENSIONAL
GEOMETRY OF KLEIN AND JORDAN 81 RIEMANNIAN GEOMETRY 83 RIEMANN'S IDEA OF
COMPLEX PARAMETERS OF EUCLIDEAN MOTIONS 87 RIEMANN'S IDEAS ON PHYSICAL
SPACE 87 THE WORK OF CHRISTOFFEL, LIPSCHITZ, AND SUVOROV ON RIEMANNIAN
GEOMETRY 89 THE MULTI-DIMENSIONAL THEORY OF CURVES 90 MULTI-DIMENSIONAL
SURFACE THEORY 94 MULTI-DIMENSIONAL PROJECTIVE GEOMETRY 96 THE
TERMINOLOGY OF MULTI-DIMENSIONAL GEOMETRY 96 CONTENTS VII 6. TOPOLOGY 97
GAUSS' TOPOLOGY 97 GENERALIZATIONS OF EULER'S THEOREM ON POLYHEDRA IN
THE EARLY NINETEENTH CENTURY 98 LISTING'S VORSTUDIEN ZUR TOPOLOGIE 99
MOEBIUS' "THEORIE DER ELEMENTAREN VERWANDSCHAFT" 101 THE TOPOLOGY OF
SURFACES IN RIEMANN'S "THEORIE DER ABEL'SCHEN FUNKTIONEN" 102 THE
MULTI-DIMENSIONAL TOPOLOGY OF RIEMANN AND BETTI 103 JORDAN'S TOPOLOGICAL
THEOREMS 104 THE "KLEIN BOTTLE" 105 7. GEOMETRIC TRANSFORMATIONS 106
GEOMETRIE TRANSFORMATIONS IN THE WORK OF MOEBIUS 106 HELMHOLTZ' PAPER
"UEBER DIE THATSACHEN, DIE DER GEOMETRIE ZU GRUNDE LIEGEN" 107 KLEIN'S
"ERLANGER PROGRAMM" 109 TRANSFERENCE PRINCIPLES 111 CREMONA
TRANSFORMATIONS 113 CONCLUSION 115 CHAPTER 2. ANALYTIC FUNCTION (A. I.
MARKUSHEVICH) 119 RESULTS ACHIEVED IN ANALYTIC FUNCTION THEORY IN THE
EIGHTEENTH CENTURY 119 DEVELOPMENT OF THE CONCEPT OF A COMPLEX NUMBER
121 COMPLEX INTEGRATION 125 THE CAUCHY INTEGRAL THEOREM. RESIDUES 128
ELLIPTIC FUNCTIONS IN THE WORK OF GAUSS 132 HYPERGEOMETRIC FUNCTIONS 138
THE FIRST APPROACH TO MODULAR FUNCTIONS 145 POWER SERIES. THE METHOD OF
MAJORANTS 148 ELLIPTIC FUNCTIONS IN THE WORK OF ABEL 153 CG. J. JACOBI.
FUNDAMENTA NOVA FUNCTIONUM ELLIPTICARUM 158 THE JACOBI THETA FUNCTIONS
162 ELLIPTIC FUNCTIONS IN THE WORK OF EISENSTEIN AND LIOUVILLE. THE
FIRST TEXTBOOKS 166 VIII CONTENTS ABELIAN INTEGRALS. ABEL'S THEOREM 173
QUADRUPLY PERIODIC FUNCTIONS 178 SUMMARY OF THE DEVELOPMENT OF ANALYTIC
FUNCTION THEORY OVER THE FIRST HALF OF THE NINETEENTH CENTURY 183 V.
PUISEUX. ALGEBRAIC FUNCTIONS 189 BERNHARD RIEMANN 198 RIEMANN'S DOCTORAL
DISSERTATION. THE DIRICHLET PRINCIPLE 201 CONFORMAL MAPPINGS 215 KARL
WEIERSTRASS 220 ANALYTIC FUNCTION THEORY IN RUSSIA. YU.V. SOKHOTSKII AND
THE SOKHOTSKII-CASORATI-WEIERSTRASS THEOREM 227 ENTIRE AND MEROMORPHIC
FUNCTIONS. PICARD'S THEOREM 236 ABELIAN FUNCTIONS 247 ABELIAN FUNCTIONS
(CONTINUATION) 249 AUTOMORPHIC FUNCTIONS. UNIFORMIZATION 257 SEQUENCES
AND SERIES OF ANALYTIC FUNCTIONS 264 CONCLUSION 270 LITERATURE (F. A.
MEDVEDEV) 273 GENERAL WORKS 273 COLLECTED WORKS AND OTHER ORIGINAL
SOURCES 274 AUXILIARY LITERATURE TO CHAPTER 1 278 AUXILIARY LITERATURE
TO CHAPTER 2 280 INDEX OF NAMES (A. F. LAPKO) 283 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:44:15Z |
| indexdate | 2024-07-09T21:25:47Z |
| institution | BVB |
| isbn | 3764350482 0817650482 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016939537 |
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| publisher | Birkhäuser |
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| spelling | Matematika XIX veka Mathematics of the 19th century Vol. 2 Geometry, analytic function theory ed. by A. N. Kolmogorov ... Basel [u.a.] Birkhäuser 1996 X, 291 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Russ. übers. Geschichte 1800-1900 gnd rswk-swf Geschichte 1801-1900 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Mathematik (DE-588)4037944-9 s Geschichte 1800-1900 z DE-604 Geschichte 1801-1900 z Kolmogorov, Andrej Nikolaevič 1903-1987 Sonstige (DE-588)119056399 oth (DE-604)BV013585500 2 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016939537&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematics of the 19th century Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4143413-4 |
| title | Mathematics of the 19th century |
| title_alt | Matematika XIX veka |
| title_auth | Mathematics of the 19th century |
| title_exact_search | Mathematics of the 19th century |
| title_exact_search_txtP | Mathematics of the 19th century |
| title_full | Mathematics of the 19th century Vol. 2 Geometry, analytic function theory ed. by A. N. Kolmogorov ... |
| title_fullStr | Mathematics of the 19th century Vol. 2 Geometry, analytic function theory ed. by A. N. Kolmogorov ... |
| title_full_unstemmed | Mathematics of the 19th century Vol. 2 Geometry, analytic function theory ed. by A. N. Kolmogorov ... |
| title_short | Mathematics of the 19th century |
| title_sort | mathematics of the 19th century geometry analytic function theory |
| topic | Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematik Aufsatzsammlung |
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