國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

A concise introduction to analysis

SpringerLink (Online service)

A concise introduction to analysis

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A concise introduction to analysisby Daniel W. Stroock.
作者:	Stroock, Daniel W.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xii, 218 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Mathematical analysis.
電子資源:	http://dx.doi.org/10.1007/978-3-319-24469-3
ISBN:	9783319244693$q(electronic bk.)

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$q(electronic bk.)

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

186133
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

A concise introduction to analysis
LDR:02438nmm a2200313 a 4500 001 476980
003 DE-He213
005 20160415152118.0
006 m d
007 cr nn 008maaau
008 160526s2015 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 229648
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 186133
650 0 $a Mathematics. $3 184409
650 0 $a Associative rings. $3 345364
650 0 $a Rings (Algebra) $3 190979
650 2 4 $a Associative Rings and Algebras. $3 274818
710 2 $a SpringerLink (Online service) $3 273601
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)