The Mathematics of Soap Films

The Mathematics of Soap Films pdf epub mobi txt 电子书 下载 2025

John Oprea: Cleveland State University, Cleveland, OH

出版者:Amer Mathematical Society
作者:Oprea, John
出品人:
页数:266
译者:
出版时间:2000-9
价格:247.00 元
装帧:Pap
isbn号码:9780821821183
丛书系列:Student Mathematical Library
图书标签:
  • 数学-极小曲面 
  • 数学-数学软件 
  • 数学 
  • 微分拓扑7 
  •  
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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.

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