Steven G. Krantz, Harold R. Parks

The Implicit Function Theorem (eBook, PDF)

History, Theory, and Applications

• Format: PDF

Produktbeschreibung

The implicit function theorem, part of the bedrock of mathematical analysis and geometry, has important implications in the theories of partial differential equations, differential geometry, and geometric analysis. Its history is lively and complex, 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 will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 163
• Erscheinungstermin: 26. November 2012
• Englisch
• ISBN-13: 9781461200598
• Artikelnr.: 44198987

Inhaltsangabe

Preface.- Introduction to the Implicit Function Theorem.- History.- Basic Ideas.- Applications.- Variations and Generalizations.- Advanced Implicit Function Theorems.- Glossary.- Bibliography.- Index.

Rezensionen

From the reviews:

"The book under review balances the historical analyses with presentations and discussions of the proofs of some formulations of the implicit function theorem. ... The authors have taken some care to make the book self-contained, and as such a well-motivated undergraduate student can profitably read many parts of it, and the whole book is within the reach of a first-year graduate student." (Felipe Zaldivar, MAA Reviews, March, 2013)

The authors offer a useful and fascinating manuscript which should be of interest and useful to graduate and postgraduate students, professional mathematicians, teachers as well as researchers. Most of them will be able to find all fundamental ideas in the field and simple and transparent proofs of all main implicit function theorems and theorems closely related to these. -Zentralblatt MATH¿