說明 
1 online resource (x, 207 pages) : illustrations 

text txt rdacontent 

computer c rdamedia 

online resource cr rdacarrier 
附註 
Includes bibliographical references (p. [203]204) and index 

1. Euclidean Space  2. Sequences in Normed Spaces  3. Limits and Continuity in Normed Spaces  4. Characteristics of Continuous Functions  5. Topology in Normed Spaces 

Use copy Restrictions unspecified star MiAaHDL 

Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2011. MiAaHDL 

Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL 

digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL 

This text is an axiomatic treatment of the properties of continuous multivariable functions and related results from topology. In the context of normed vector spaces, the author covers boundedness, extreme values, and uniform continuity of functions, along with the connections between continuity and topological concepts such as connectedness and compactness. The order of topics deliberately mimics the order of development in elementary calculus. This sequencing allows for an elementary approach, with analogies to and generalizations from such familiar ideas as the Pythagorean theorem. The reader is frequently reminded that the pictures suggested by geometry are powerful guides and tools. The definitiontheoremproof format resides within an informal exposition, containing numerous historical comments and questions within and between the proofs. The objective is to present precise proofs, but in a structure and tone that teach the student to plan and write proofs, both in general and specifically for the real analysis course that will follow this one. Applications are included where they provide interesting illustrations of the principles and theorems presented. Problems, solutions, bibliography and index complete this book. ̀Continuous Functions of Vector Variables' is suitable for a course in multivariable calculus aimed at advanced undergraduates preparing for graduate programs in pure mathematics. Required background includes a course in the theory of singlevariable calculus and the elements of linear algebra. Also by the author: 'Derivatives and Integrals of Multivariable Functions, ' ISBN 0817642749 

Description based on print version record 
鏈接 
Print version: (DLC) 2002018232 (OCoLC)48851302 
主題 
Functions, Continuous


Normed linear spaces


Vector spaces


Funktion <Mathematik>  Mehrere reelle Variable  Vektorraum.
swd


Vektorraum  Mehrere reelle Variable  Funktion <Mathematik>.
swd


Functions, Continuous. fast (OCoLC)fst00936126


Normed linear spaces. fast (OCoLC)fst01039141


Vector spaces. fast (OCoLC)fst01164670


Electronic books

