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020 _a9783031621239
_9978-3-031-62123-9
024 7 _a10.1007/978-3-031-62123-9
_2doi
050 4 _aQA351
072 7 _aPBKF
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKF
_2thema
100 1 _aRuffa, Anthony A.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981615
245 1 0 _aInnovative Integrals and Their Applications II
_h[electronic resource] /
_cby Anthony A. Ruffa, Bourama Toni.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXIII, 305 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSTEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health,
_x2520-1948
505 0 _aPreface -- 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 _aIn 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 0 _aSpecial functions.
650 0 _aIntegral equations.
650 0 _aMathematical analysis.
_964178
650 1 4 _aSpecial Functions.
650 2 4 _aIntegral Equations.
650 2 4 _aIntegral Transforms and Operational Calculus.
_967269
700 1 _aToni, Bourama.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981616
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031621222
776 0 8 _iPrinted edition:
_z9783031621246
776 0 8 _iPrinted edition:
_z9783031621253
830 0 _aSTEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health,
_x2520-1948
_981617
856 4 0 _uhttps://doi.org/10.1007/978-3-031-62123-9
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
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