Articles liés à Multivariable Analysis

Multivariable Analysis - Couverture souple

Shirali, Satish; Vasudeva, Harkrishan Lal

 
9780857291912: Multivariable Analysis
Couverture souple
ISBN 10 : 0857291912 ISBN 13 : 9780857291912
Editeur : Springer, 2010

Synopsis

This book provides a rigorous treatment of multivariable differential and integral calculus. Implicit function theorem and the inverse function theorem based on total derivatives is explained along with the results and the connection to solving systems of equations. There is an extensive treatment of extrema, including constrained extrema and Lagrange multipliers, covering both first order necessary conditions and second order sufficient conditions. The material on Riemann integration in n dimensions, being delicate by its very nature, is discussed in detail. Differential forms and the general Stokes' Theorem are expounded in the last chapter. With a focus on clarity rather than brevity, this text gives clear motivation, definitions and examples with transparent proofs. Much of the material included is published for the first time in textbook form, for example Schwarz' Theorem in Chapter 2 and double sequences and sufficient conditions for constrained extrema in Chapter 4. A wide selection of problems, ranging from simple to more challenging, are included with carefully formed solutions. Ideal as a classroom text or a self study resource for students, this book will appeal to higher level undergraduates in Mathematics.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

This book provides a rigorous treatment of multivariable differential and integral calculus. Implicit function theorem and the inverse function theorem based on total derivatives is explained along with the results and the connection to solving systems of equations. There is an extensive treatment of extrema, including constrained extrema and Lagrange multipliers, covering both first order necessary conditions and second order sufficient conditions. The material on Riemann integration in n dimensions, being delicate by its very nature, is discussed in detail. Differential forms and the general Stokes' Theorem are expounded in the last chapter. With a focus on clarity rather than brevity, this text gives clear motivation, definitions and examples with transparent proofs. Much of the material included is published for the first time in textbook form, for example Schwarz' Theorem in Chapter 2 and double sequences and sufficient conditions for constrained extrema in Chapter 4. A wide selection of problems, ranging from simple to more challenging, are included with carefully formed solutions. Ideal as a classroom text or a self study resource for students, this book will appeal to higher level undergraduates in Mathematics.

Présentation de l'éditeur

In what is a rigorous treatment of multivariable differential and integral calculus, this book explains key theorems including Stokes’s as well as covering extrema such as Lagrange multipliers. It explores Riemann integration in n dimensions in detail.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer
Date d'édition
2010
Langue
anglais
ISBN 10 
0857291912
ISBN 13 
9780857291912
Reliure
Broché
Nombre de pages
404
Coordonnées du fabricant
Springer-Verlag GmbH
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