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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
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Innovative Integrals and Their Applications I (Hardcover, 1st ed. 2022)
Loot Price: R3,652
Discovery Miles 36 520
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Innovative Integrals and Their Applications I (Hardcover, 1st ed. 2022)
Series: STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health
Expected to ship within 10 - 15 working days
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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.
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