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# đź“™ Implicit Function Theorem: History, Theory, and Applications by Steven G. Krantz, Harold R. Parks â€” download pdf

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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 C^k 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 (e.g., 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. 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.

## About book:

## About file:

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- Author:
**Steven G. Krantz, Harold R. Parks** - Year:
**2002** - Publisher:
**BirkhĂ¤user Boston** - Language:
**English** - ISBN:
**9780817642853,0-8176-4285-4**

- File size:
**2 553 808** - Format:
**djvu**

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The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This book treats the implicit function paradigm in the classical framework and ...

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of functi...

The subject of real analytic functions is one of the oldest in modern mathematics and is the wellspring of the theory of analysis, both real and complex. To date, there is no comprehensive book on the subject, yet the tools of the theory are widely used b...

Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second ...

Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of th...

Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equatio...

In the early fifties, applied mathematicians, engineers and economists started to pay c10se attention to the optimization problems in which another (lower-Ievel) optimization problem arises as a side constraint. One of the motivating factors was the conce...

This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective th...

A distinguishing feature of video games is their interactivity, and sound plays an important role in this: a playerâ€™s actions can trigger dialogue, sound effects, ambient sound, and music. And yet game sound has been neglected in the growing literature on...

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Considerable recent research has focused on the topic of chemical speciation in the environment. It is increasingly realised that the distribution, mobility and biological availability of chemical elements depend not simply on their concentrations but, cr...

Properties and Reactions of Thiazole (J. Metzger and E. Vincent). General Synthetic Methods for Thiazole and Thiazolium Salts (G. Vernin). Alkyl, Aryl, Aralkyl, and Related Thiazole Derivatives (J. Aune et al.). Thiazolecarboxylic Acids, Thiazolecarboxald...

Isoquinolines Bearing Basic Side Chains (H. Schuster & F. Kathawala). Isoquinolines and Their Hydrogenated Derivatives (O. Hoshino, et al.). Index.Content: Chapter I Isoquinolines Bearing Basic Side Chains (pages 1â€“224): H. F. Schuster and F. KathawalaCha...

Content: Chapter I General Discussion (pages 1â€“28): Chapter II Biological and Pharmacological Activity of Thiophene and its Derivatives (pages 29â€“46): F. F. BlickeChapter III Synthesis and Physical Properties of Thiophene and its Homologs (pages 47â€“80): C...

Few topics have attracted as much attention worldwide in recent years as the RMB. These debates have gained added urgency in light of the financial crisis and the topic of RMB revaluation is now being actively debated in countries all over the world from ...

Content: Chapter 1 Overview of Chiral Separations (pages 1â€“8): Satinder AhujaChapter 2 Regulatory and Development Considerations of Chiral Compounds (pages 9â€“34): Robert L. ZeidChapter 3 Basic Considerations in HPLC Method Development of Chiral Compounds ...