國立虎尾科技大學 |

Innovative Integrals and Their Applications I

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Innovative Integrals and Their Applications I/ by Anthony A. Ruffa, Bourama Toni.
作者:	Ruffa, Anthony A.
其他作者:	Toni, Bourama.
面頁冊數:	X, 319 p. 10 illus., 9 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Special functions. -
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. - 1st ed. 2022. - X, 319 p. 10 illus., 9 illus. in color.online resource. - 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:

1257411
Special functions.

LC Class. No.: QA351

Dewey Class. No.: 515.5

Innovative Integrals and Their Applications I
LDR:04101nam a22004095i 4500 001 1085486
003 DE-He213
005 20221114095310.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783031178719 $9 978-3-031-17871-9
024 7 $a 10.1007/978-3-031-17871-9 $2 doi
035 $a 978-3-031-17871-9
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
100 1 $a Ruffa, Anthony A. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1210567
245 1 0 $a Innovative Integrals and Their Applications I $h [electronic resource] / $c by Anthony A. Ruffa, Bourama Toni.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a X, 319 p. 10 illus., 9 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 Special functions. $3 1257411
650 0 $a Integral equations. $3 527971
650 0 $a Algebraic fields. $3 672441
650 0 $a Polynomials. $3 528565
650 0 $a Mathematical analysis. $3 527926
650 1 4 $a Special Functions. $3 672152
650 2 4 $a Integral Equations. $3 672359
650 2 4 $a Field Theory and Polynomials. $3 672025
650 2 4 $a Integral Transforms and Operational Calculus. $3 1366597
700 1 $a Toni, Bourama. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 883337
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783031178702
776 0 8 $i Printed edition: $z 9783031178726
776 0 8 $i Printed edition: $z 9783031178733
830 0 $a STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, $x 2520-193X $3 1281218
856 4 0 $u https://doi.org/10.1007/978-3-031-17871-9
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)