Name: derivatives and integrals of multivariable functions
Price: 57.84 GBP
Availability: InStock
Author: guzman
ISBN: 9780817642747

portada derivatives and integrals of multivariable functions

Type

Physical Book

Publisher

springer publishing map

Author

guzman

Language

English

Pages

319

ISBN

0817642749

ISBN13

9780817642747

Synopsis "derivatives and integrals of multivariable functions"

this work provides a systematic examination of derivatives and integrals of multivariable functions; it is suitable for a one-semester course in what is usually called advanced calculus of several variables. 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. the elementary material in the single- and several-variable case leads naturally to significant advanced theorems about functions of multiple variables. topics covered include differentiability and its relation to 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. the development of the vector-field theorems ties together material from many of the chapters and emphasizes the physical applications of the theory. prerequisites for the reader include background in theoretical 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, derivatives and integrals of multivariable functions has a conversational style and is replete with historical comments, questions, and discussions about strategy, difficulties, and alternate paths. ideal for upper-level undergraduates whose next course will be real analysis, this book is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations in analysis and differential geometry.