國立虎尾科技大學 |

Real analysis = series, functions of several variables, and applications /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Real analysis/ by Miklos Laczkovich, Vera T. Sos.
Reminder of title:	series, functions of several variables, and applications /
Author:	Laczkovich, Miklos.
other author:	Sos, Vera T.
Published:	New York, NY :Springer New York : : 2017.,
Description:	ix, 392 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Mathematical analysis. -
Online resource:	http://dx.doi.org/10.1007/978-1-4939-7369-9
ISBN:	9781493973699

Real analysis = series, functions of several variables, and applications /
Laczkovich, Miklos.

Real analysisseries, functions of several variables, and applications /[electronic resource] :by Miklos Laczkovich, Vera T. Sos. - New York, NY :Springer New York :2017. - ix, 392 p. :ill., digital ;24 cm. - Undergraduate texts in mathematics,30172-6056 ;. - Undergraduate texts in mathematics ;3..

Functions of Several Variables -- 1. R^p → R functions -- 2. R^p → R^q functions -- 3. The Jordan Measure -- 4. The Integral of Multivariable Functions I -- 5. The Integral of Multivariable Functions II -- 6. Infinite Series -- 7. Sequences and Series of Functions -- 8. Miscellaneous Topics -- 9. Hint, Solutions -- References -- Index -- Notation.

This book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable. Together, these volumes form the first English edition of the popular Hungarian original, Valos Analizis I & II, based on courses taught by the authors at Eotvos Lorand University, Hungary, for more than 30 years. Numerous exercises are included throughout, offering ample opportunities to master topics by progressing from routine to difficult problems. Hints or solutions to many of the more challenging exercises make this book ideal for independent study, or further reading. Intended as a sequel to a course in single variable analysis, this book builds upon and expands these ideas into higher dimensions. The modular organization makes this text adaptable for either a semester or year-long introductory course. Topics include: differentiation and integration of functions of several variables; infinite numerical series; sequences and series of functions; and applications to other areas of mathematics. Many historical notes are given and there is an emphasis on conceptual understanding and context, be it within mathematics itself or more broadly in applications, such as physics. By developing the student's intuition throughout, many definitions and results become motivated by insights from their context.

ISBN: 9781493973699

Standard No.: 10.1007/978-1-4939-7369-9doiSubjects--Topical Terms:

527926
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

Real analysis = series, functions of several variables, and applications /
LDR:02813nam a2200325 a 4500 001 922434
003 DE-He213
005 20171215025426.0
006 m d
007 cr nn 008maaau
008 190624s2017 nyu s 0 eng d
020 $a 9781493973699 $q (electronic bk.)
020 $a 9781493973675 $q (paper)
024 7 $a 10.1007/978-1-4939-7369-9 $2 doi
035 $a 978-1-4939-7369-9
040 $a GP $c GP
041 1 $a eng $h hun
050 4 $a QA300
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515 $2 23
090 $a QA300 $b .L152 2017
100 1 $a Laczkovich, Miklos. $3 1069766
245 1 0 $a Real analysis $h [electronic resource] : $b series, functions of several variables, and applications / $c by Miklos Laczkovich, Vera T. Sos.
260 $a New York, NY : $b Springer New York : $b Imprint: Springer, $c 2017.
300 $a ix, 392 p. : $b ill., digital ; $c 24 cm.
490 1 $a Undergraduate texts in mathematics, $x 0172-6056 ; $v 3
505 0 $a Functions of Several Variables -- 1. R^p → R functions -- 2. R^p → R^q functions -- 3. The Jordan Measure -- 4. The Integral of Multivariable Functions I -- 5. The Integral of Multivariable Functions II -- 6. Infinite Series -- 7. Sequences and Series of Functions -- 8. Miscellaneous Topics -- 9. Hint, Solutions -- References -- Index -- Notation.
520 $a This book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable. Together, these volumes form the first English edition of the popular Hungarian original, Valos Analizis I & II, based on courses taught by the authors at Eotvos Lorand University, Hungary, for more than 30 years. Numerous exercises are included throughout, offering ample opportunities to master topics by progressing from routine to difficult problems. Hints or solutions to many of the more challenging exercises make this book ideal for independent study, or further reading. Intended as a sequel to a course in single variable analysis, this book builds upon and expands these ideas into higher dimensions. The modular organization makes this text adaptable for either a semester or year-long introductory course. Topics include: differentiation and integration of functions of several variables; infinite numerical series; sequences and series of functions; and applications to other areas of mathematics. Many historical notes are given and there is an emphasis on conceptual understanding and context, be it within mathematics itself or more broadly in applications, such as physics. By developing the student's intuition throughout, many definitions and results become motivated by insights from their context.
650 0 $a Mathematical analysis. $3 527926
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Analysis. $3 669490
700 1 $a Sos, Vera T. $3 1069767
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Undergraduate texts in mathematics ; $v 3. $3 1198021
856 4 0 $u http://dx.doi.org/10.1007/978-1-4939-7369-9
950 $a Mathematics and Statistics (Springer-11649)