Results 11 to 20 of about 341 (205)
New Theorems in Solving Families of Improper Integrals
Axioms, 2022 Many improper integrals appear in the classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik. It is a challenge for some researchers to determine the method in which these integrations are formed or solved. In this article, we present some new
Mohammad Abu Ghuwaleh +2 more
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Mathematical and Computational Applications, 2022 In this paper, we focus on investigating the performance of the mathematical software program Maple and the programming language MATLAB when using these respective platforms to compute the method of steps (MoS) and the Laplace transform (LT) solutions ...
Michelle Sherman +2 more
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Relationship Between Cauchy Integral Theorem and Residue Theorems
Highlights in Science, Engineering and Technology, 2023 Cauchy integral theorem belongs to an extremely important part of complex functions, which is a fundamental bridge, and people can derive Cauchy integral theorem from the residue theorem. Cauchy's integral theorem is generally applied in many higher mathematics, is an important theorem concerning path integrals of fully pure functions.
Jiaming Guo, Biran Song
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Cauchy Theorem and Cauchy Residue Theorem
Highlights in Science, Engineering and Technology, 2023 Cauchy theorem is widely used in solving analytic function problems in complex variables. It is an important theorem on path integrals of holomorphic functions in the complex plane. In this paper, the main work is about the application of the Cauchy theorem on the integrals which have singularities.
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On the Cauchy-Goursat Theorem [PDF]
, 2010 : In this study, we have presented a simple and un-conventional proof of a basic but important Cauchy-Goursat theorem of complex integral calculus. The pivotal idea is to sub-divide the region bounded by the simple closed curve by infinitely large number
Faiz A.M. Elfak +5 more
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Cauchy Residue Theorem and K-residue Theorem
Highlights in Science, Engineering and Technology, 2023 Due to negative numbers do not have square roots, scientists introduced complex numbers, which are more abstract compared with real numbers. Residue Theorem has a very significant status in complex analysis – it can be used to simplify difficult integrals. In this article, Cauchy’s Residue Theorem is first introduced with definition and proof. Then the
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, 2021 Riemann Hypothesis simple proof using Cauchy Residue theorem and Schwarz Reflection ...
SHEKHAR SUMAN (9370913)
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Proof and Application of Cauchy’s Residue Theorem
Highlights in Science, Engineering and Technology, 2023 Complex analysis is a major subfield of mathematics that is concerned with investigating complex functions and their behaviors. The Cauchy’s residue theorem plays an important role in complex analysis. It is also the main focus for this paper. The residue theorem connects complex integrals of functions with their residues at singular points.
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Cauchy Residue Theorem’s Application in Improper integrals
Highlights in Science, Engineering and Technology, 2023 Definite integrals are an essential tool for understanding and calculating many aspects of the natural world. An improper integral, one type of definite integral, has either an infinite interval or an integrand that is not defined at one or more points within the interval of integration.
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Applications of Cauchy’s Residue Theorem in Computing Improper Integral
Highlights in Science, Engineering and Technology, 2023 An improper integral is a definite integral that either has an infinite interval or has the integrand that is not defined on some points in the interval. Many improper integrals are difficult to compute by using real analysis methods, especially those containing infinity.
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