The mathematics of soap films: explorations with Maple
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
2000
|
| Series: | Student mathematical library
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 266 S. graph. Darst. |
| ISBN: | 0821821180 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface xi
Chapter 1. Surface Tension 1
§1.1. Introduction 1
§1.2. The Basics of Surface Tension 2
§1.3. Experiments with Soap Films 6
§1.4. The Laplace-Young Equation 13
§1.5. Plateau s Rules for Soap Films and Consequences 15
§1.6. A Sampling of Capillary Action 23
§1.7. Final Remarks 29
Chapter 2. A Quick Trip through Differential Geometry and
Complex Variables 31
§2.1. Parametrized Surfaces 31
§2.2. Normal Curvature 37
§2.3. Mean Curvature 40
§2.4. Complex Variables 43
§2.5. Gauss Curvature 50
vii
viii Contents
Chapter 3. The Mathematics of Soap Films 59
§3.1. The Connection 59
§3.2. The Basics of Minimal Surfaces 60
§3.3. Area Minimization and Soap Films 67
§3.4. Isothermal Parameters 72
§3.5. Harmonic Functions and Minimal Surfaces 75
§3.6. The Weierstrass-Enneper Representations 77
§3.7. The Gauss Map 86
§3.8. Stereographic Projection and the Gauss Map 91
§3.9. Creating Minimal Surfaces from Curves 95
§3.10. To Be or Not To Be Area Minimizing 105
§3.11. Constant Mean Curvature 114
Chapter 4. The Calculus of Variations and Shape 121
§4.1. Introduction 121
§4.2. Minimizing Integrals 124
§4.3. Necessary Conditions: Euler-Lagrange Equations 127
§4.4. Solving the Fundamental Examples 136
§4.5. Problems with Extra Constraints 146
Chapter 5. Maple, Soap Films, and Minimal Surfaces 159
§5.1. Introduction 159
§5.2. Fused Bubbles 159
§5.3. Capillarity: Inclined Planes 166
§5.4. Capillarity: Thin Tubes 172
§5.5. Minimal Surfaces of Revolution 175
§5.6. The Catenoid versus Two Disks 181
Contents ix
§5.7. Some Minimal Surfaces 192
§5.8. Enneper s Surface 199
§5.9. The Weierstrass-Enneper Representation 207
§5.10. Bjorling s Problem 221
§5.11. The Euler-Lagrange Equations 225
§5.12. The Brachistochrone 236
§5.13. Surfaces of Delaunay 243
§5.14. The Mylar Balloon 258
Bibliography 261
Index 265
|
| any_adam_object | 1 |
| author | Oprea, John |
| author_facet | Oprea, John |
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| author_sort | Oprea, John |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.362 |
| dewey-search | 516.362 |
| dewey-sort | 3516.362 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T21:37:42Z |
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| isbn | 0821821180 |
| language | English |
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| physical | XIII, 266 S. graph. Darst. |
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| spelling | Oprea, John Verfasser aut The mathematics of soap films explorations with Maple John Oprea Providence, RI AMS 2000 XIII, 266 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Student mathematical library 10 Oberflächenspannung (DE-588)4139720-4 gnd rswk-swf Minimalfläche (DE-588)4127814-8 gnd rswk-swf Seifenblase (DE-588)4180735-2 gnd rswk-swf Maple Programm (DE-588)4209397-1 gnd rswk-swf Minimalfläche (DE-588)4127814-8 s Seifenblase (DE-588)4180735-2 s Oberflächenspannung (DE-588)4139720-4 s Maple Programm (DE-588)4209397-1 s DE-604 Student mathematical library 10 (DE-604)BV013184751 10 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017477791&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Oprea, John The mathematics of soap films explorations with Maple Student mathematical library Oberflächenspannung (DE-588)4139720-4 gnd Minimalfläche (DE-588)4127814-8 gnd Seifenblase (DE-588)4180735-2 gnd Maple Programm (DE-588)4209397-1 gnd |
| subject_GND | (DE-588)4139720-4 (DE-588)4127814-8 (DE-588)4180735-2 (DE-588)4209397-1 |
| title | The mathematics of soap films explorations with Maple |
| title_auth | The mathematics of soap films explorations with Maple |
| title_exact_search | The mathematics of soap films explorations with Maple |
| title_full | The mathematics of soap films explorations with Maple John Oprea |
| title_fullStr | The mathematics of soap films explorations with Maple John Oprea |
| title_full_unstemmed | The mathematics of soap films explorations with Maple John Oprea |
| title_short | The mathematics of soap films |
| title_sort | the mathematics of soap films explorations with maple |
| title_sub | explorations with Maple |
| topic | Oberflächenspannung (DE-588)4139720-4 gnd Minimalfläche (DE-588)4127814-8 gnd Seifenblase (DE-588)4180735-2 gnd Maple Programm (DE-588)4209397-1 gnd |
| topic_facet | Oberflächenspannung Minimalfläche Seifenblase Maple Programm |
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