Description
BIRKHAUSER Derivatives And Integrals Of Multivariable Functions 2003 Edition by Alberto Guzman
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. Table of contents : 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