東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

A concise introduction to analysis

Stroock, Daniel W.

Linked to FindBook

Google Book

Amazon

博客來

A concise introduction to analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	A concise introduction to analysis/ by Daniel W. Stroock.
Author:	Stroock, Daniel W.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xii, 218 p. :ill., digital ;24 cm.
[NT 15003449]:	Analysis on The Real Line -- Elements of Complex Analysis -- Integration -- Higher Dimensions -- Integration in Higher Dimensions -- A Little Bit of Analytic Function Theory.
Contained By:	Springer eBooks
Subject:	Mathematical analysis. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-24469-3
ISBN:	9783319244693

A concise introduction to analysis
Stroock, Daniel W.

A concise introduction to analysis[electronic resource] /by Daniel W. Stroock. - Cham :Springer International Publishing :2015. - xii, 218 p. :ill., digital ;24 cm.

Analysis on The Real Line -- Elements of Complex Analysis -- Integration -- Higher Dimensions -- Integration in Higher Dimensions -- A Little Bit of Analytic Function Theory.

This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions. Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text. A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them.

ISBN: 9783319244693

Standard No.: 10.1007/978-3-319-24469-3doiSubjects--Topical Terms:

516833
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

A concise introduction to analysis
LDR:02438nmm a2200313 a 4500 001 2013558
003 DE-He213
005 20160415152118.0
006 m d
007 cr nn 008maaau
008 160518s2015 gw s 0 eng d
020 $a 9783319244693 $q (electronic bk.)
020 $a 9783319244679 $q (paper)
024 7 $a 10.1007/978-3-319-24469-3 $2 doi
035 $a 978-3-319-24469-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA300
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 515 $2 23
090 $a QA300 $b .S924 2015
100 1 $a Stroock, Daniel W. $3 697134
245 1 2 $a A concise introduction to analysis $h [electronic resource] / $c by Daniel W. Stroock.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xii, 218 p. : $b ill., digital ; $c 24 cm.
505 0 $a Analysis on The Real Line -- Elements of Complex Analysis -- Integration -- Higher Dimensions -- Integration in Higher Dimensions -- A Little Bit of Analytic Function Theory.
520 $a This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions. Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text. A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them.
650 0 $a Mathematical analysis. $3 516833
650 0 $a Mathematics. $3 515831
650 0 $a Associative rings. $3 668071
650 0 $a Rings (Algebra) $3 540500
650 2 4 $a Associative Rings and Algebras. $3 897405
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-24469-3
950 $a Mathematics and Statistics (Springer-11649)