The Implicit Function Theorem
The Implicit Function Theorem
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DOI：
10.1007/978-1-4612-0059-8
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
S. Krantz;H. Parks
中科院分区：
文献类型：
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作者：
S. Krantz;H. Parks
隐函数定理是数学分析和几何的基石的一部分。隐函数定理和反函数定理起源于 18 世纪对实解析函数和力学的研究，现已发展成为偏微分方程、微分几何和几何分析理论中的强大工具。隐函数定理的历史是一个生动而复杂的故事，与发展密切相关。 分析和几何的基本思想。这里首次叙述了整个发展过程以及数学示例和证明。这是一个激动人心的故事，而且还在不断发展。” 《隐函数定理》是对隐函数定理和反函数定理及其应用的深入浅出的阐述。数学家、研究生/高年级本科生以及应用数学的人都会对此感兴趣。这本书统一了在现代数学中发挥重要作用的不同思想。它用于记录大量数学思想并将其置于上下文中。隐函数定理有许多不同形式，包括 (i) Ck 函数的经典公式，(ii) 其他函数空间中的公式，(iii) 非光滑函数的公式，(iv) 具有简并雅可比行列式的函数公式。特别强大的隐函数定理，例如纳什定理、莫泽定理，已经针对特定应用（例如黎曼流形的嵌入）而开发。所有这些主题以及更多主题都得到了处理 在本卷中。”——出版商。
" The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. ThereThe history of the implicit function theorem is a lively and complex story, and is intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples and proofs, is recounted for the first time here. It is an exciting tale, and it continues to evolve." The Implicit Function Theorem" is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas. are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions,(ii) formulations in other function spaces,(iii) formulations for non-smooth functions,(iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash, Moser theorem, have been developed for specific applications (eg, the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume."--Publisher.