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
到查詢結果
[ subject:"Integral equations." ]
切換:
標籤
|
MARC模式
|
ISBD
Innovative integrals and their Appli...
~
Ruffa, Anthony A.
FindBook
Google Book
Amazon
博客來
Innovative integrals and their Applications.. I
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Innovative integrals and their Applications./ by Anthony A. Ruffa, Bourama Toni.
作者:
Ruffa, Anthony A.
其他作者:
Toni, Bourama.
出版者:
Cham :Springer International Publishing : : 2022.,
面頁冊數:
x, 319 p. :ill., digital ;24 cm.
內容註:
Preface -- Chapter. 1. The Generalized Method of Exhaustion -- Chapter. 2. The Multivariate Power Substitution and its Variants -- Chapter. 3. Additional Multivariate Substitution Variants -- Chapter. 4. Miscellaneous Integral Identities -- Chapter. 5. The Exponential Integral Function, the Sine Integral and Cosine Integrals -- Chapter. 6. The Riemann Zeta Function and the Hurwitz Zeta Function -- Chapter. 7. Engineering Applications -- Bibliography -- Index.
Contained By:
Springer Nature eBook
標題:
Functions, Special. -
電子資源:
https://doi.org/10.1007/978-3-031-17871-9
ISBN:
9783031178719
Innovative integrals and their Applications.. I
Ruffa, Anthony A.
Innovative integrals and their Applications.
I[electronic resource] /by Anthony A. Ruffa, Bourama Toni. - Cham :Springer International Publishing :2022. - x, 319 p. :ill., digital ;24 cm. - STEAM-H: science, technology, engineering, agriculture, mathematics & health,2520-1948. - STEAM-H: science, technology, engineering, agriculture, mathematics & health..
Preface -- Chapter. 1. The Generalized Method of Exhaustion -- Chapter. 2. The Multivariate Power Substitution and its Variants -- Chapter. 3. Additional Multivariate Substitution Variants -- Chapter. 4. Miscellaneous Integral Identities -- Chapter. 5. The Exponential Integral Function, the Sine Integral and Cosine Integrals -- Chapter. 6. The Riemann Zeta Function and the Hurwitz Zeta Function -- Chapter. 7. Engineering Applications -- Bibliography -- Index.
This book develops integral identities, mostly involving multidimensional functions and infinite limits of integration, whose evaluations are intractable by common means. It exposes a methodology based on the multivariate power substitution and its variants, assisted by the software tool Mathematica. The approaches introduced comprise the generalized method of exhaustion, the multivariate power substitution and its variants, and the use of permutation symmetry to evaluate definite integrals, which are very important both in their own right, and as necessary intermediate steps towards more involved computation. A key tenet is that such approaches work best when applied to integrals having certain characteristics as a starting point. Most integrals, if used as a starting point, will lead to no result at all, or will lead to a known result. However, there is a special class of integrals (i.e., innovative integrals) which, if used as a starting point for such approaches, will lead to new and useful results, and can also enable the reader to generate many other new results that are not in the book. The reader will find a myriad of novel approaches for evaluating integrals, with a focus on tools such as Mathematica as a means of obtaining useful results, and also checking whether they are already known. Results presented involve the gamma function, the hypergeometric functions, the complementary error function, the exponential integral function, the Riemann zeta function, and others that will be introduced as they arise. The book concludes with selected engineering applications, e.g., involving wave propagation, antenna theory, non-Gaussian and weighted Gaussian distributions, and other areas. The intended audience comprises junior and senior sciences majors planning to continue in the pure and applied sciences at the graduate level, graduate students in mathematics and the sciences, and junior and established researchers in mathematical physics, engineering, and mathematics. Indeed, the pedagogical inclination of the exposition will have students work out, understand, and efficiently use multidimensional integrals from first principles.
ISBN: 9783031178719
Standard No.: 10.1007/978-3-031-17871-9doiSubjects--Topical Terms:
606076
Functions, Special.
LC Class. No.: QA351
Dewey Class. No.: 515.5
Innovative integrals and their Applications.. I
LDR
:03713nmm a2200337 a 4500
001
2305797
003
DE-He213
005
20221114095310.0
006
m d
007
cr nn 008maaau
008
230409s2022 sz s 0 eng d
020
$a
9783031178719
$q
(electronic bk.)
020
$a
9783031178702
$q
(paper)
024
7
$a
10.1007/978-3-031-17871-9
$2
doi
035
$a
978-3-031-17871-9
040
$a
GP
$c
GP
041
0
$a
eng
050
4
$a
QA351
072
7
$a
PBKF
$2
bicssc
072
7
$a
MAT034000
$2
bisacsh
072
7
$a
PBKF
$2
thema
082
0 4
$a
515.5
$2
23
090
$a
QA351
$b
.R922 2022
100
1
$a
Ruffa, Anthony A.
$3
3506123
245
1 0
$a
Innovative integrals and their Applications.
$n
I
$h
[electronic resource] /
$c
by Anthony A. Ruffa, Bourama Toni.
260
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2022.
300
$a
x, 319 p. :
$b
ill., digital ;
$c
24 cm.
490
1
$a
STEAM-H: science, technology, engineering, agriculture, mathematics & health,
$x
2520-1948
505
0
$a
Preface -- Chapter. 1. The Generalized Method of Exhaustion -- Chapter. 2. The Multivariate Power Substitution and its Variants -- Chapter. 3. Additional Multivariate Substitution Variants -- Chapter. 4. Miscellaneous Integral Identities -- Chapter. 5. The Exponential Integral Function, the Sine Integral and Cosine Integrals -- Chapter. 6. The Riemann Zeta Function and the Hurwitz Zeta Function -- Chapter. 7. Engineering Applications -- Bibliography -- Index.
520
$a
This book develops integral identities, mostly involving multidimensional functions and infinite limits of integration, whose evaluations are intractable by common means. It exposes a methodology based on the multivariate power substitution and its variants, assisted by the software tool Mathematica. The approaches introduced comprise the generalized method of exhaustion, the multivariate power substitution and its variants, and the use of permutation symmetry to evaluate definite integrals, which are very important both in their own right, and as necessary intermediate steps towards more involved computation. A key tenet is that such approaches work best when applied to integrals having certain characteristics as a starting point. Most integrals, if used as a starting point, will lead to no result at all, or will lead to a known result. However, there is a special class of integrals (i.e., innovative integrals) which, if used as a starting point for such approaches, will lead to new and useful results, and can also enable the reader to generate many other new results that are not in the book. The reader will find a myriad of novel approaches for evaluating integrals, with a focus on tools such as Mathematica as a means of obtaining useful results, and also checking whether they are already known. Results presented involve the gamma function, the hypergeometric functions, the complementary error function, the exponential integral function, the Riemann zeta function, and others that will be introduced as they arise. The book concludes with selected engineering applications, e.g., involving wave propagation, antenna theory, non-Gaussian and weighted Gaussian distributions, and other areas. The intended audience comprises junior and senior sciences majors planning to continue in the pure and applied sciences at the graduate level, graduate students in mathematics and the sciences, and junior and established researchers in mathematical physics, engineering, and mathematics. Indeed, the pedagogical inclination of the exposition will have students work out, understand, and efficiently use multidimensional integrals from first principles.
650
0
$a
Functions, Special.
$3
606076
650
0
$a
Integral equations.
$3
589037
700
1
$a
Toni, Bourama.
$3
1620789
710
2
$a
SpringerLink (Online service)
$3
836513
773
0
$t
Springer Nature eBook
830
0
$a
STEAM-H: science, technology, engineering, agriculture, mathematics & health.
$3
3453963
856
4 0
$u
https://doi.org/10.1007/978-3-031-17871-9
950
$a
Mathematics and Statistics (SpringerNature-11649)
筆 0 讀者評論
館藏地:
全部
電子資源
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
W9447346
電子資源
11.線上閱覽_V
電子書
EB QA351
一般使用(Normal)
在架
0
1 筆 • 頁數 1 •
1
多媒體
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