Inversion theory and conformal mapping:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2000
|
| Series: | Student Mathematical Library
9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 118 Seiten graph. Darst. |
| ISBN: | 0821826360 |
Staff View
MARC
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| 245 | 1 | 0 | |a Inversion theory and conformal mapping |c David E. Blair |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2000 | |
| 300 | |a X, 118 Seiten |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
Preface ix
Chapter 1. Classical Inversion Theory in the Plane 1
§1.1. Definition and basic properties 1
§1.2. Cross ratio 9
§1.3. Applications 14
§1.4. Miquel s Theorem 17
§1.5. Feuerbach s Theorem 21
Chapter 2. Linear Fractional Transformations 27
§2.1. Complex numbers 27
§2.2. The extended complex plane and stereographic
projection 29
§2.3. Linear fractional transformations 34
§2.4. Cross ratio 37
§2.5. Some special linear fractional transformations 39
§2.6. Extended Mobius transformations 43
§2.7. The Poincare models of hyperbolic geometry 52
vii
viii Contents
§2.8. A distortion theorem 59
Chapter 3. Advanced Calculus and Conformal Maps 63
§3.1. Review of advanced calculus 63
§3.2. Inner products 70
§3.3. Conformal maps 73
Chapter 4. Conformal Maps in the Plane 75
§4.1. Complex function theory 75
§4.2. Abundance of conformal maps 78
Chapter 5. Conformal Maps in Euclidean Space 83
§5.1. Inversion in spheres 83
§5.2. Conformal maps in Euclidean space 87
§5.3. Sphere preserving transformations 92
Chapter 6. The Classical Proof of Liouville s Theorem 95
§6.1. Surface theory 95
§6.2. The classical proof 103
Chapter 7. When Does Inversion Preserve Convexity? 107
§7.1. Curve theory and convexity 107
§7.2. Inversion and convexity 110
§7.3. The problem for convex bodies 114
Bibliography 115
Index 117
|
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| indexdate | 2024-07-09T18:43:08Z |
| institution | BVB |
| isbn | 0821826360 |
| language | English |
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| physical | X, 118 Seiten graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Student Mathematical Library |
| series2 | Student Mathematical Library |
| spelling | Blair, David E. 1940- Verfasser (DE-588)171979559 aut Inversion theory and conformal mapping David E. Blair Providence, RI American Mathematical Society 2000 X, 118 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Student Mathematical Library 9 Inversionstheorie - Konforme Abbildung Inversion Mathematik (DE-588)4162235-2 gnd rswk-swf Konforme Abbildung (DE-588)4164968-0 gnd rswk-swf Konforme Abbildung (DE-588)4164968-0 s Inversion Mathematik (DE-588)4162235-2 s DE-604 Student Mathematical Library 9 (DE-604)BV013184751 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009057937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blair, David E. 1940- Inversion theory and conformal mapping Student Mathematical Library Inversionstheorie - Konforme Abbildung Inversion Mathematik (DE-588)4162235-2 gnd Konforme Abbildung (DE-588)4164968-0 gnd |
| subject_GND | (DE-588)4162235-2 (DE-588)4164968-0 |
| title | Inversion theory and conformal mapping |
| title_auth | Inversion theory and conformal mapping |
| title_exact_search | Inversion theory and conformal mapping |
| title_full | Inversion theory and conformal mapping David E. Blair |
| title_fullStr | Inversion theory and conformal mapping David E. Blair |
| title_full_unstemmed | Inversion theory and conformal mapping David E. Blair |
| title_short | Inversion theory and conformal mapping |
| title_sort | inversion theory and conformal mapping |
| topic | Inversionstheorie - Konforme Abbildung Inversion Mathematik (DE-588)4162235-2 gnd Konforme Abbildung (DE-588)4164968-0 gnd |
| topic_facet | Inversionstheorie - Konforme Abbildung Inversion Mathematik Konforme Abbildung |
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