Laurent Series Expansion And Its Applications
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Laurent Series Expansion And Its Applications
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Author :
language : en
Publisher:
Release Date : 2020
Laurent Series Expansion And Its Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Curves categories.
The Laurent expansion is a well-known topic in complex analysis for its application in obtaining residues of complex functions around their singularities. Computing the Laurent series of a function around its singularities turns out to be an efficient way to determine the residue of the function as well as to compute the integral of the function along any closed curves around its singularities. Based on the theory of the Laurent series, this paper provides several working examples where the Laurent series of a function is determined and then used to calculate the integral of the function along any closed curve around the singularities of the function. A brief description of the Frobenius method in solving ordinary differential equations is also provided.
Analytic Perturbation Theory And Its Applications
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Author : Konstantin E. Avrachenkov
language : en
Publisher: SIAM
Release Date : 2013-12-11
Analytic Perturbation Theory And Its Applications written by Konstantin E. Avrachenkov and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter deviations provides a natural starting point for this analysis in many special settings in the sciences, engineering, and economics. The difference between the actual and nominal values of the perturbation parameter is small but unknown, and it is important to understand the asymptotic behavior of the system as the perturbation tends to zero. This is particularly true in applications with an apparent discontinuity in the limiting behavior?the so-called singularly perturbed problems. Analytic Perturbation Theory and Its Applications includes a comprehensive treatment of analytic perturbations of matrices, linear operators, and polynomial systems, particularly the singular perturbation of inverses and generalized inverses. It also offers original applications in Markov chains, Markov decision processes, optimization, and applications to Google PageRank? and the Hamiltonian cycle problem as well as input retrieval in linear control systems and a problem section in every chapter to aid in course preparation.
Complex Analysis And Applications Second Edition
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Author : Alan Jeffrey
language : en
Publisher: CRC Press
Release Date : 2005-11-10
Complex Analysis And Applications Second Edition written by Alan Jeffrey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-10 with Mathematics categories.
Complex Analysis and Applications, Second Edition explains complex analysis for students of applied mathematics and engineering. Restructured and completely revised, this textbook first develops the theory of complex analysis, and then examines its geometrical interpretation and application to Dirichlet and Neumann boundary value problems. A discussion of complex analysis now forms the first three chapters of the book, with a description of conformal mapping and its application to boundary value problems for the two-dimensional Laplace equation forming the final two chapters. This new structure enables students to study theory and applications separately, as needed. In order to maintain brevity and clarity, the text limits the application of complex analysis to two-dimensional boundary value problems related to temperature distribution, fluid flow, and electrostatics. In each case, in order to show the relevance of complex analysis, each application is preceded by mathematical background that demonstrates how a real valued potential function and its related complex potential can be derived from the mathematics that describes the physical situation.
Laurent Series And Their Pad Approximations
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Author : A. Bultheel
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Laurent Series And Their Pad Approximations written by A. Bultheel and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The Pade approximation problem is, roughly speaking, the local approximation of analytic or meromorphic functions by rational ones. It is known to be important to solve a large scale of problems in numerical analysis, linear system theory, stochastics and other fields. There exists a vast literature on the classical Pade problem. However, these papers mostly treat the problem for functions analytic at 0 or, in a purely algebraic sense, they treat the approximation of formal power series. For certain problems however, the Pade approximation problem for formal Laurent series, rather than for formal power series seems to be a more natural basis. In this monograph, the problem of Laurent-Pade approximation is central. In this problem a ratio of two Laurent polynomials in sought which approximates the two directions of the Laurent series simultaneously. As a side result the two-point Pade approximation problem can be solved. In that case, two series are approximated, one is a power series in z and the other is a power series in z-l. So we can approximate two, not necessarily different functions one at zero and the other at infinity.
Analyzable Functions And Applications
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Author : Ovidiu Costin
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Analyzable Functions And Applications written by Ovidiu Costin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The theory of analyzable functions is a technique used to study a wide class of asymptotic expansion methods and their applications in analysis, difference and differential equations, partial differential equations and other areas of mathematics. Key ideas in the theory of analyzable functions were laid out by Euler, Cauchy, Stokes, Hardy, E. Borel, and others. Then in the early 1980s, this theory took a great leap forward with the work of J. Ecalle. Similar techniques and conceptsin analysis, logic, applied mathematics and surreal number theory emerged at essentially the same time and developed rapidly through the 1990s. The links among various approaches soon became apparent and this body of ideas is now recognized as a field of its own with numerous applications. Thisvolume stemmed from the International Workshop on Analyzable Functions and Applications held in Edinburgh (Scotland). The contributed articles, written by many leading experts, are suitable for graduate students and researchers interested in asymptotic methods.
Applied Complex Variables For Scientists And Engineers
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Author : Yue Kuen Kwok
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24
Applied Complex Variables For Scientists And Engineers written by Yue Kuen Kwok and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.
This introduction to complex variable methods begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. Throughout the text, many of the important theoretical results in complex function theory are followed by relevant and vivid examples in physical sciences. This second edition now contains 350 stimulating exercises of high quality, with solutions given to many of them. Material has been updated and additional proofs on some of the important theorems in complex function theory are now included, e.g. the Weierstrass–Casorati theorem. The book is highly suitable for students wishing to learn the elements of complex analysis in an applied context.
Complex Analysis And Applications
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Author : Alan Jeffrey
language : en
Publisher: CRC Press
Release Date : 2005-11-10
Complex Analysis And Applications written by Alan Jeffrey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-10 with Mathematics categories.
Complex Analysis and Applications, Second Edition explains complex analysis for students of applied mathematics and engineering. Restructured and completely revised, this textbook first develops the theory of complex analysis, and then examines its geometrical interpretation and application to Dirichlet and Neumann boundary value problems.
Handbook Of Conformal Mappings And Applications
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Author : Prem K. Kythe
language : en
Publisher: CRC Press
Release Date : 2019-03-04
Handbook Of Conformal Mappings And Applications written by Prem K. Kythe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-04 with Mathematics categories.
The subject of conformal mappings is a major part of geometric function theory that gained prominence after the publication of the Riemann mapping theorem — for every simply connected domain of the extended complex plane there is a univalent and meromorphic function that maps such a domain conformally onto the unit disk. The Handbook of Conformal Mappings and Applications is a compendium of at least all known conformal maps to date, with diagrams and description, and all possible applications in different scientific disciplines, such as: fluid flows, heat transfer, acoustics, electromagnetic fields as static fields in electricity and magnetism, various mathematical models and methods, including solutions of certain integral equations.
Advances On Computer Mathematics And Its Applications
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Author : Elias A. Lipitakis
language : en
Publisher: World Scientific
Release Date : 1993
Advances On Computer Mathematics And Its Applications written by Elias A. Lipitakis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Computers categories.
This volume contains selected papers of the proceedings of the first Hellenic Conference on Mathematics and Informatics (HERMIS '92). The main theme for HERMIS '92 Conference was Computer Mathematics, with special emphasis on Computational Mathematics, Operational Research and Statistics, and Mathematics in Economic Science. The presented papers of the HERMIS Conference have been classified into the following technical sessions: Numerical solution of Differential Equations, Parallel Processing and Parallel Algorithms, Optimization and Approximation, Algorithms in Operational Research and Control Theory, Statistical Methods and Analysis, Mathematics in Economic Science, Artificial Intelligence and Data Bases Technology.In addition, a number of selected research articles published recently in the Hellenic Mathematical Society Bulletin in the form of special issues on Computer Mathematics (Volumes 31 and 32) are also included.
The Mass Gap And Its Applications
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Author : Gogokhia Vakhtang
language : en
Publisher: World Scientific
Release Date : 2013
The Mass Gap And Its Applications written by Gogokhia Vakhtang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Science categories.
Quantum Chromodynamics (QCD) is the most up-to-date theory of the strong interaction. Its predictions have been verified experimentally, and it is a cornerstone of the Standard Model of particle physics. This book not only presents the new QCD mass gap method, but also details its applications and outlook. A detailed summary of references and problems are included as well.