Guzman Derivatives and Integrals of Multivariable Functions

2003
ISBN: 978-1-4612-0035-2
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 319 Seiten, eBook

This work provides a systematic examination of derivatives and integrals of multivariable functions. The approach taken here is similar to that of the author’s previous text, "Continuous Functions of Vector Variables": specifically, elementary results from single-variable calculus are extended to functions in several-variable Euclidean space. Topics encompass differentiability, partial derivatives, directional derivatives and the gradient; curves, surfaces, and vector fields; the inverse and implicit function theorems; integrability and properties of integrals; and the theorems of Fubini, Stokes, and Gauss. Prerequisites include background in linear algebra, one-variable calculus, and some acquaintance with continuous functions and the topology of the real line.

Written in a definition-theorem-proof format, the book is replete with historical comments, questions, and discussions about strategy, difficulties, and alternate paths.  "Derivatives and Integrals of Multivariable Functions" is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations in analysis and differential geometry.

Zielgruppe

Graduate

Autoren/Hrsg.

Guzman, Alberto

Inhaltsverzeichnis

Preface * Differentiability of Multivariable Functions * Derivatives of Scalar Functions * Derivatives of Vector Functions * Integrability of Multivariable Functions * Integrals of Scalar Functions * Vector Integrals and the Vector-Field Theorems * Solutions to Exercises * References * Index