quartonews.it » Math and Science » The Implicit Function Theorem: History, Theory, and Applications (Modern Birkhäuser Classics)

Author: | Steven G. G. Krantz,Harold R. Parks |

Subcategory: | Mathematics |

Language: | English |

Publisher: | Birkhäuser; 2013 edition (November 9, 2012) |

Pages: | 180 pages |

Category: | Math and Science |

Rating: | 4.4 |

Other formats: | rtf lit docx mobi |

The implicit function theorem is part of the bedrock of mathematical analysis and geometry.

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. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. Particularly powerful implicit function theorems, such as the Nash-Moser theorem, have been developed for specific applications (. the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The 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.

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Электронная книга "The Implicit Function Theorem: History, Theory, and Applications", Steven G. Krantz, Harold R. Parks

Электронная книга "The Implicit Function Theorem: History, Theory, and Applications", Steven G. Parks. Эту книгу можно прочитать в Google Play Книгах на компьютере, а также на устройствах Android и iOS. Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "The Implicit Function Theorem: History, Theory, and Applications" для чтения в офлайн-режиме.

Автор: Steven G. Krantz; Harold R. Parks Название: The Implicit .

The book documents and places in context a substantial body of concepts that have played an role in modern mathematics.

Steven G. Krantz Harold R. 1 Introduction to the Implicit Function Theorem.

There are many sophisticated applications of implicit function theorems, particularly the Nash- Moser theorem, in modern mathematics. The imbedding theorem for Riemannian manifolds, the imbedding theorem for CR manifo lds, and the deformation theory of complex structures are just a few of them. Steven G.

Krantz's monographs include Function Theory of Several Complex Variables, Complex Analysis: The Geometric Viewpoint, A Primer of Real Analytic Functions (joint with Harold R. Parks), The Implicit Function Theorem (joint with Harold Parks), Geometric Integration Theory (joint with. Parks), The Implicit Function Theorem (joint with Harold Parks), Geometric Integration Theory (joint with Harold Parks), and The Geometry of Complex Domains (joint with Kang-Tae Kim and Robert E. Greene). His book The Proof is in the Pudding: A Look at the Changing Nature of Mathematical Proof looks at the history and evolving nature of the proof concept

The history of the implicit function theorem is a lively and complex story . oceedings{Krantz2002TheIF, title {The Implicit Function Theorem: History, Theory, and Applications}, author {Steven . .

The 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. 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. oceedings{Krantz2002TheIF, title {The Implicit Function Theorem: History, Theory, and Applications}, author {Steven G. Krantz and Harold R. Parks}, year {2002} }. Parks - Implicit Function Theorem: History, Theory, and Applications. Parks - The Geometry of Domains in Space (Birkhäuser Advanced Texts Basler Lehrbücher). Parks - A primer of real analytic functions. Читать pdf. Parks - Geometric Integration Theory (Cornerstones).

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.

There 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 function, and (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash–Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present uncorrected reprint of this classic monograph.

Originally published in 2002, *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.** **

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