語系:
繁體中文
English
說明(常見問題)
回圖書館首頁
手機版館藏查詢
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
The Divergence theorem and sets of f...
~
Pfeffer, Washek F.
FindBook
Google Book
Amazon
博客來
The Divergence theorem and sets of finite perimeter /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
The Divergence theorem and sets of finite perimeter // Washek F. Pfeffer.
作者:
Pfeffer, Washek F.
出版者:
Boca Raton :CRC Press, : c2012.,
面頁冊數:
xv, 242 p. :ill ;25 cm.
標題:
Differential calculus. -
ISBN:
9781466507197 (hbk.) :
The Divergence theorem and sets of finite perimeter /
Pfeffer, Washek F.
The Divergence theorem and sets of finite perimeter /
Washek F. Pfeffer. - Boca Raton :CRC Press,c2012. - xv, 242 p. :ill ;25 cm. - Monographs and textbooks in pure and applied mathematics.
Includes bibliographical references (p. 231-233) and index.
"Preface The divergence theorem and the resulting integration by parts formula belong to the most frequently used tools of mathematical analysis. In its elementary form, that is for smooth vector fields defined in a neighborhood of some simple geometric object such as rectangle, cylinder, ball, etc., the divergence theorem is presented in many calculus books. Its proof is obtained by a simple application of the one-dimensional fundamental theorem of calculus and iterated Riemann integration. Appreciable difficulties arise when we consider a more general situation. Employing the Lebesgue integral is essential, but it is only the first step in a long struggle. We divide the problem into three parts. (1) Extending the family of vector fields for which the divergence theorem holds on simple sets. (2) Extending the the family of sets for which the divergence theorem holds for Lipschitz vector fields. (3) Proving the divergence theorem when the vector fields and sets are extended simultaneously. Of these problems, part (2) is unquestionably the most complicated. While many mathematicians contributed to it, the Italian school represented by Caccioppoli, De Giorgi, and others, obtained a complete solution by defining the sets of bounded variation (BV sets). A major contribution to part (3) is due to Federer, who proved the divergence theorem for BV sets and Lipschitz vector fields. While parts (1)-(3) can be combined, treating them separately illuminates the exposition. We begin with sets that are locally simple: finite unions of dyadic cubes, called dyadic figures. Combining ideas of Henstock and McShane with a combinatorial argument of Jurkat, we establish the divergence theorem for very general vector fields defined on dyadic figures"--
ISBN: 9781466507197 (hbk.) :UK63.99
LCCN: 2012005948Subjects--Topical Terms:
648417
Differential calculus.
LC Class. No.: QA433 / .P493 2012
Dewey Class. No.: 515/.4
The Divergence theorem and sets of finite perimeter /
LDR
:02543cam a22002294a 450
001
1875167
005
20131223133522.0
008
130828s2012 flu b 001 0 eng
010
$a
2012005948
020
$a
9781466507197 (hbk.) :
$c
UK63.99
020
$a
1466507195 (hbk.)
020
$a
9781466507210 (ebk.- PDF)
020
$a
1466507217 (ebk.-PDF)
035
$a
AS-BW-102-N-03
040
$a
DLC
$c
DLC
$d
DLC
050
0 0
$a
QA433
$b
.P493 2012
082
0 0
$a
515/.4
$2
23
100
1
$a
Pfeffer, Washek F.
$3
604844
245
1 0
$a
The Divergence theorem and sets of finite perimeter /
$c
Washek F. Pfeffer.
260
#
$a
Boca Raton :
$b
CRC Press,
$c
c2012.
300
$a
xv, 242 p. :
$b
ill ;
$c
25 cm.
490
0
$a
Monographs and textbooks in pure and applied mathematics
504
$a
Includes bibliographical references (p. 231-233) and index.
520
#
$a
"Preface The divergence theorem and the resulting integration by parts formula belong to the most frequently used tools of mathematical analysis. In its elementary form, that is for smooth vector fields defined in a neighborhood of some simple geometric object such as rectangle, cylinder, ball, etc., the divergence theorem is presented in many calculus books. Its proof is obtained by a simple application of the one-dimensional fundamental theorem of calculus and iterated Riemann integration. Appreciable difficulties arise when we consider a more general situation. Employing the Lebesgue integral is essential, but it is only the first step in a long struggle. We divide the problem into three parts. (1) Extending the family of vector fields for which the divergence theorem holds on simple sets. (2) Extending the the family of sets for which the divergence theorem holds for Lipschitz vector fields. (3) Proving the divergence theorem when the vector fields and sets are extended simultaneously. Of these problems, part (2) is unquestionably the most complicated. While many mathematicians contributed to it, the Italian school represented by Caccioppoli, De Giorgi, and others, obtained a complete solution by defining the sets of bounded variation (BV sets). A major contribution to part (3) is due to Federer, who proved the divergence theorem for BV sets and Lipschitz vector fields. While parts (1)-(3) can be combined, treating them separately illuminates the exposition. We begin with sets that are locally simple: finite unions of dyadic cubes, called dyadic figures. Combining ideas of Henstock and McShane with a combinatorial argument of Jurkat, we establish the divergence theorem for very general vector fields defined on dyadic figures"--
$c
Provided by publisher.
650
# 0
$a
Differential calculus.
$3
648417
650
# 0
$a
Divergence theorem.
$3
2012535
筆 0 讀者評論
採購/卷期登收資訊
壽豐校區(SF Campus)
-
最近登收卷期:
1 (2013/12/30)
明細
館藏地:
全部
六樓西文書區HC-Z(6F Western Language Books)
出版年:
卷號:
館藏
1 筆 • 頁數 1 •
1
條碼號
典藏地名稱
館藏流通類別
資料類型
索書號
使用類型
借閱狀態
預約狀態
備註欄
附件
W0181072
六樓西文書區HC-Z(6F Western Language Books)
01.外借(書)_YB
一般圖書
QA433 P493 2012
一般使用(Normal)
在架
0
預約
1 筆 • 頁數 1 •
1
評論
新增評論
分享你的心得
Export
取書館
處理中
...
變更密碼
登入