國立虎尾科技大學 |

Innovative integrals and their applications II

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 II/ by Anthony A. Ruffa, Bourama Toni.
其他題名:	Innovative integrals and their applications 2
作者:	Ruffa, Anthony A.
其他作者:	Toni, Bourama.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	xiii, 305 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Integral Transforms and Operational Calculus. -
電子資源:	https://doi.org/10.1007/978-3-031-62123-9
ISBN:	9783031621239

Innovative integrals and their applications II
Ruffa, Anthony A.

Innovative integrals and their applications II[electronic resource] /Innovative integrals and their applications 2by Anthony A. Ruffa, Bourama Toni. - Cham :Springer Nature Switzerland :2024. - xiii, 305 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 An Overview of the Methods -- Chapter 2 Warm-up Interchanging the Order of Integration -- Chapter 3 Permutation Symmetry -- Chapter 4 Identities Involving the Laplace Transform and the Fourier Transform -- Chapter 5 A Potpourri of Methods and Results -- Chapter 6 Applications in the Sciences Technology and Engineering -- Bibliography -- Index.

In its second installment, Innovative Integrals and Their Applications II explores multidimensional integral identities, unveiling powerful techniques for attacking otherwise intractable integrals, thus demanding ingenuity and novel approaches. This volume focuses on novel approaches for evaluating definite integrals, with the aid of tools such as Mathematica as a means of obtaining useful results. Building upon the previous methodologies, this volume introduces additional concepts such as interchanging the order of integration, permutation symmetry, and the use of pairs of Laplace transforms and Fourier transforms, offering readers a comprehensive array of integral identities. The content further elucidates the techniques of permutation symmetry and extends the multivariate substitution approach to integrals with finite limits of integration. These insights culminate in a collection of integral identities involving gamma functions, incomplete beta functions, Bessel functions, polylogarithms, and the Meijer G-function. Additionally, readers will encounter applications of error functions, inverse error functions, hypergeometric functions, the Lambert W-function, elliptic integrals, Jacobi elliptic functions, and the Riemann zeta function, among many others, with a focus on their relevance in various scientific disciplines and cutting-edge technologies. Each chapter in this volume concludes with many interesting exercises for the reader to practice. 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, lead to no result at all, or 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, lead to new and useful results, and can also enable the reader to generate other new results that do not appear in the book. The intended readership includes science, technology, engineering, and mathematics (STEM) undergraduates and graduates, as well as STEM researchers and the community of engineers, scientists, and physicists; most of these potential readers have experienced the importance and/or the applications of integration from finding areas, volumes, lengths, and velocities to more advanced applications. The pedagogical approach of the exposition empowers students to comprehend and efficiently wield multidimensional integrals from their foundations, fostering a deeper understanding of advanced mathematical concepts.

ISBN: 9783031621239

Standard No.: 10.1007/978-3-031-62123-9doiSubjects--Topical Terms:

1366597
Integral Transforms and Operational Calculus.

LC Class. No.: QA351

Dewey Class. No.: 515.5

Innovative integrals and their applications II
LDR:04073nam a2200349 a 4500 001 1134283
003 DE-He213
005 20240731125702.0
006 m d
007 cr nn 008maaau
008 241213s2024 sz s 0 eng d
020 $a 9783031621239 $q (electronic bk.)
020 $a 9783031621222 $q (paper)
024 7 $a 10.1007/978-3-031-62123-9 $2 doi
035 $a 978-3-031-62123-9
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 2024
100 1 $a Ruffa, Anthony A. $3 1210567
245 1 0 $a Innovative integrals and their applications II $h [electronic resource] / $c by Anthony A. Ruffa, Bourama Toni.
246 3 $a Innovative integrals and their applications 2
260 $a Cham : $c 2024. $b Springer Nature Switzerland : $b Imprint: Springer,
300 $a xiii, 305 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 An Overview of the Methods -- Chapter 2 Warm-up Interchanging the Order of Integration -- Chapter 3 Permutation Symmetry -- Chapter 4 Identities Involving the Laplace Transform and the Fourier Transform -- Chapter 5 A Potpourri of Methods and Results -- Chapter 6 Applications in the Sciences Technology and Engineering -- Bibliography -- Index.
520 $a In its second installment, Innovative Integrals and Their Applications II explores multidimensional integral identities, unveiling powerful techniques for attacking otherwise intractable integrals, thus demanding ingenuity and novel approaches. This volume focuses on novel approaches for evaluating definite integrals, with the aid of tools such as Mathematica as a means of obtaining useful results. Building upon the previous methodologies, this volume introduces additional concepts such as interchanging the order of integration, permutation symmetry, and the use of pairs of Laplace transforms and Fourier transforms, offering readers a comprehensive array of integral identities. The content further elucidates the techniques of permutation symmetry and extends the multivariate substitution approach to integrals with finite limits of integration. These insights culminate in a collection of integral identities involving gamma functions, incomplete beta functions, Bessel functions, polylogarithms, and the Meijer G-function. Additionally, readers will encounter applications of error functions, inverse error functions, hypergeometric functions, the Lambert W-function, elliptic integrals, Jacobi elliptic functions, and the Riemann zeta function, among many others, with a focus on their relevance in various scientific disciplines and cutting-edge technologies. Each chapter in this volume concludes with many interesting exercises for the reader to practice. 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, lead to no result at all, or 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, lead to new and useful results, and can also enable the reader to generate other new results that do not appear in the book. The intended readership includes science, technology, engineering, and mathematics (STEM) undergraduates and graduates, as well as STEM researchers and the community of engineers, scientists, and physicists; most of these potential readers have experienced the importance and/or the applications of integration from finding areas, volumes, lengths, and velocities to more advanced applications. The pedagogical approach of the exposition empowers students to comprehend and efficiently wield multidimensional integrals from their foundations, fostering a deeper understanding of advanced mathematical concepts.
650 2 4 $a Integral Transforms and Operational Calculus. $3 1366597
650 2 4 $a Integral Equations. $3 672359
650 1 4 $a Special Functions. $3 672152
650 0 $a Integral equations. $3 527971
650 0 $a Functions, Special. $3 527750
700 1 $a Toni, Bourama. $3 883337
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a STEAM-H: science, technology, engineering, agriculture, mathematics & health. $3 1206408
856 4 0 $u https://doi.org/10.1007/978-3-031-62123-9
950 $a Mathematics and Statistics (SpringerNature-11649)