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# ðŸ“™ 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:
**BirkhÃ¤user Boston** - Language:
**English** - ISBN:
**9780817642853,0-8176-4285-4**

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

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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...

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...

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...

This book is aimed at mathematics students, typically in the second year of a university course. The first chapter, however, is suitable for first-year students. Differentiable functions are treated initially from the standpoint of approximating a curved ...

This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on ChoquetÂ´s theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay b...

This book provides a rigorous treatment of multivariable differential and integral calculus. Inverse and implicit function theorems based on total derivatives are given and the connection with solving systems of equations is included. There is an extensiv...

Designed for use in a two-semester course on abstract analysis, REAL ANALYSIS: An Introduction to the Theory of Real Functions and Integration illuminates the principle topics that constitute real analysis. Self-contained, with coverage of topology, meas...

The featured review of the AMS describes the authorâ€™s earlier work in the field of approach spaces as, â€˜A landmark in the history of general topologyâ€™. In this book, the author has expanded this study further and taken it in a new and exciting direction.T...

Insect parasitoids are a fascinating group of animals in many respects. Perhaps the most fascinating point is that these insects, in the course of the evolutionary time, have developed an impressive way to use chemical compounds to dialogue with the diffe...

In this book, the reader is guided through the complex study of dynamic chemical engineering systems by the unique combination of a simplified presentation of the fundamental theory (Part 1) and direct hands-on computer experimentation with the provision ...

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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 ...