Results 11 to 20 of about 271 (172)

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.
openaire   +1 more source

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
openaire   +1 more source

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.
openaire   +1 more source

Non-Integer Valued Winding Numbers and a Generalized Residue Theorem

Journal of Mathematics, 2019
We define a generalization of the winding number of a piecewise C1 cycle in the complex plane which has a geometric meaning also for points which lie on the cycle.
Norbert Hungerbühler, Micha Wasem
doaj   +1 more source

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.
openaire   +1 more source

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.
openaire   +1 more source

Application of Cauchy’s Residue Theorem in Several Improper Integrals

Highlights in Science, Engineering and Technology, 2023
Calculating definite integrals in complex functions requires the Cauchy's residue theorem, which is a key concept in the complex variables. It is based on several ideas, including the isolated singular points theory, the Laurent theorem, and the Cauchy integral theorem.
openaire   +1 more source

Analytical Solution for the Problem of Point Location in Arbitrary Planar Domains

Algorithms
This paper presents a general analytical solution for the problem of locating points in planar regions with an arbitrary geometry at the boundary. The proposed methodology overcomes the traditional solutions used for polygonal regions.
Vitor Santos
doaj   +1 more source

Comparison of the Cauchy Integral Formula and Residue Theorem on the Calculation of Definite Integrals

Highlights in Science, Engineering and Technology, 2023
Integration is a useful mathematical tool which is applied in a wide range of studies and assists people to solve many problems. Despite methods of real analysis, complex integrations in complex analysis are more beneficial and more convenient than real integrations under certain circumstances.
openaire   +1 more source

Revisiting stress propagation in a three-dimensional elastic sphere under diametric loading

Nihon Kikai Gakkai ronbunshu
The stress propagation for a three-dimensional elastic sphere under a diametric loading condition in the framework of the linear elastodynamics is revisited. By describing displacements in terms of scalar and vector potentials using the Helmholtz theorem,
Yosuke SATO, Satoshi TAKADA
doaj   +1 more source