MARC 主機 00000cam 2200697Ka 4500
001 806179181
003 OCoLC
005 20140513031111.0
006 m o d
007 cr bn||||abp||
007 cr bn||||ada||
008 120814s2002 maua ob 001 0 eng d
020 9781461200833 (electronic bk.)
020 1461200830 (electronic bk.)
035 (OCoLC)806179181|z(OCoLC)853269668
040 OCLCE|beng|epn|cOCLCE|dOCLCO|dOCLCQ|dAU@|dGW5XE|dOCLCQ
|dOCLCF|dAS|dMATH
042 dlr
050 4 QA331.5|b.G89 2002
082 04 515/.73|221
100 1 Guzman, Alberto,|d1947-
245 10 Continuous functions of vector variables|h[electronic
resource] /|cAlberto Guzman
260 Boston :|bBirkhäuser,|c©2002
300 1 online resource (x, 207 pages) :|billustrations
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
504 Includes bibliographical references (p. [203]-204) and
index
505 00 |g1.|tEuclidean Space --|g2.|tSequences in Normed Spaces -
-|g3.|tLimits and Continuity in Normed Spaces --|g4.
|tCharacteristics of Continuous Functions --|g5.|tTopology
in Normed Spaces
506 |3Use copy|fRestrictions unspecified|2star|5MiAaHDL
520 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 definition-
theorem-proof 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 single-variable
calculus and the elements of linear algebra. Also by the
author: 'Derivatives and Integrals of Multivariable
Functions, ' ISBN 0-8176-4274-9
533 Electronic reproduction.|b[S.l.] :|cHathiTrust Digital
Library,|d2011.|5MiAaHDL
538 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.|uhttp://purl.oclc.org/DLF/benchrepro0212
|5MiAaHDL
583 1 digitized|c2011|hHathiTrust Digital Library|lcommitted to
preserve|2pda|5MiAaHDL
588 Description based on print version record
650 0 Functions, Continuous
650 0 Normed linear spaces
650 0 Vector spaces
650 7 Funktion <Mathematik>|xMehrere reelle Variable
|xVektorraum.|2swd
650 7 Vektorraum|xMehrere reelle Variable|xFunktion <Mathematik>
.|2swd
650 7 Functions, Continuous.|2fast|0(OCoLC)fst00936126
650 7 Normed linear spaces.|2fast|0(OCoLC)fst01039141
650 7 Vector spaces.|2fast|0(OCoLC)fst01164670
655 4 Electronic books
776 08 |iPrint version:|w(DLC) 2002018232|w(OCoLC)48851302
856 40 |3SpringerLink|uhttp://dx.doi.org/10.1007/978-1-4612-0083-
3