The Mathematics Of Soap Films: Explorations With Maple (Student Mathematical Library) - Softcover

Oprea, John

Softcover

ISBN 10: 0821821180 ISBN 13: 9780821821183

Verlag: American Mathematical Society, 2000

Inhaltsangabe

Book by Oprea John

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Críticas

... a book like Oprea's has been sorely needed (MAA Online )

Reseña del editor

Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the Maple applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautiful subject, which naturally introduces the reader to fascinating, yet accessible, topics in mathematics. Oprea's presentation is rich with examples, explanations, and applications. It would make an excellent text for a senior seminar or for independent study by upper-division mathematics or science majors.

Details zur Ausgabe

• Verlag: American Mathematical Society
• Erscheinungsdatum: 2000
• ISBN 10: 0821821180
• ISBN 13: 9780821821183
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 266