The Geometry of Domains in Space (Birkhäuser Advanced Texts / Basler Lehrbücher) pdf epub mobi txt 电子书 下载 2025
- 几何分析
- 几何
- Geometry
- Geometrical_Analysis
Traditionally, analysis on Euclidean space is based on the study of the classical groups that act on the space. The classical treatises focus on rotations, dilations, and especially translations; all of these tools and techniques have shaped the way in which classical analysis on Euclidean space has developed.
On the other hand, a modern analytical treatment, such as the one presented here, often focuses on domains in space. A domain is the natural venue for various problems arising from physics, as well as the natural setting for the study of boundary value problems. Instead of considering group actions (inappropriate since a typical domain has on natural symmetries), one considers properties that arise from the intrinsic geometry of the domain and from the geometry of the boundary as a codimension one manifold in space.
Contributing to part of the new "toolkit" that should be at hand for every analyst, the authors cover a wide array of topics: imbedded manifolds, curvature, positive reach, Sard's theorem, Sobolev spaces, the isoperimetric inequality, Weyl's theorem, covering theorems, convex functions, and Stokes's theorem in all of its many formulations, to name just several. All geometric ideas are treated in a self-contained manner.
This comprehensive treatment of domains (in space) emphasizes the growing interaction between analysis and geometry. Geometric analysis, as it is known, is currently an important area of study for both pure and applied mathematicians, physicists, and engineers. Aimed at graduate students of the field, this monograph will be useful in the classroom or as a resource for self-study. The prerequisites are minimal; a good understanding of multivariate calculus and linear algebra will suffice for most purposes.
具体描述
读后感
评分
评分
评分
评分
用户评价
相关图书
本站所有内容均为互联网搜索引擎提供的公开搜索信息，本站不存储任何数据与内容，任何内容与数据均与本站无关，如有需要请联系相关搜索引擎包括但不限于百度，google,bing,sogou 等
© 2025 book.wenda123.org All Rights Reserved. 图书目录大全 版权所有