The Cauchy Method Of Residues
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| Author | : Dragoslav S. Mitrinovic |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 218 |
| Release | : 1984-04-30 |
| Genre | : Mathematics |
| ISBN | : 9789027716231 |
Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not' grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory arid the struc ture of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-5cale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics. This program, Mathematics and Its Applications, is devoted to such (new) interrelations as exampla gratia: - a central concept which plays an important role in several different mathe matical and/or scientific specialized areas; - new applications of the results and ideas from one area of scientific en deavor into another; - influences which the results, problems and concepts of one field of enquiry have and have had on the development of another.
| Author | : Dragoslav S. Mitrinovic |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 206 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 9401120005 |
Volume 1, i. e. the monograph The Cauchy Method of Residues - Theory and Applications published by D. Reidel Publishing Company in 1984 is the only book that covers all known applications of the calculus of residues. They range from the theory of equations, theory of numbers, matrix analysis, evaluation of real definite integrals, summation of finite and infinite series, expansions of functions into infinite series and products, ordinary and partial differential equations, mathematical and theoretical physics, to the calculus of finite differences and difference equations. The appearance of Volume 1 was acknowledged by the mathematical community. Favourable reviews and many private communications encouraged the authors to continue their work, the result being the present book, Volume 2, a sequel to Volume 1. We mention that Volume 1 is a revised, extended and updated translation of the book Cauchyjev raeun ostataka sa primenama published in Serbian by Nau~na knjiga, Belgrade in 1978, whereas the greater part of Volume 2 is based upon the second Serbian edition of the mentioned book from 1991. Chapter 1 is introductory while Chapters 2 - 6 are supplements to the corresponding chapters of Volume 1. They mainly contain results missed during the preparation of Volume 1 and also some new results published after 1982. Besides, certain topics which were only briefly mentioned in Volume 1 are treated here in more detail.
| Author | : Frank C. Hoppensteadt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 331 |
| Release | : 2000-01-21 |
| Genre | : Mathematics |
| ISBN | : 0387989439 |
Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable models for further mathematical analysis or computer simulations. For the most part, derivations are based on perturbation methods, and the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances. Relevant topics about linear systems, nonlinear oscillations, and stability methods for difference, differential-delay, integro-differential and ordinary and partial differential equations are developed throughout the book. For the second edition, the author has restructured the chapters, placing special emphasis on introductory materials in Chapters 1 and 2 as distinct from presentation materials in Chapters 3 through 8. In addition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added.
| Author | : Robert Splinter |
| Publisher | : CRC Press |
| Total Pages | : 2045 |
| Release | : 2017-04-07 |
| Genre | : Science |
| ISBN | : 1351625632 |
This resource provides a single, concise reference containing terms and expressions used in the study, practice, and application of physical sciences. The reader will be able to identify quickly critical information about professional jargon, important people, and events. The encyclopedia gives self-contained definitions with essentials regarding the meaning of technical terms and their usage, as well as about important people within various fields of physics and engineering, with highlights of technical and practical aspects related to cross-functional integration. It will be indispensable for anyone working on applications in biomedicine, materials science, chemical engineering, electrical engineering, mechanical engineering, geology, astronomy, and energy. It also includes handy tables and chronological timelines organized by subject area and giving an overview on the historical development of ideas and discovery.
| Author | : Dean G. Duffy |
| Publisher | : CRC Press |
| Total Pages | : 727 |
| Release | : 2004-07-15 |
| Genre | : Mathematics |
| ISBN | : 1420035142 |
Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found ana
| Author | : Dean G. Duffy |
| Publisher | : CRC Press |
| Total Pages | : 1107 |
| Release | : 2010-10-26 |
| Genre | : Mathematics |
| ISBN | : 1439816247 |
Taking a practical approach to the subject, Advanced Engineering Mathematics with MATLAB®, Third Edition continues to integrate technology into the conventional topics of engineering mathematics. The author employs MATLAB to reinforce concepts and solve problems that require heavy computation. MATLAB scripts are available for download at www.crcpress.com Along with new examples, problems, and projects, this updated and expanded edition incorporates several significant improvements. New to the Third Edition New chapter on Green’s functions New section that uses the matrix exponential to solve systems of differential equations More numerical methods for solving differential equations, including Adams–Bashforth and finite element methods New chapter on probability that presents basic concepts, such as mean, variance, and probability density functions New chapter on random processes that focuses on noise and other random fluctuations Suitable for a differential equations course or a variety of engineering mathematics courses, the text covers fundamental techniques and concepts as well as Laplace transforms, separation of variable solutions to partial differential equations, the z-transform, the Hilbert transform, vector calculus, and linear algebra. It also highlights many modern applications in engineering to show how these topics are used in practice. A solutions manual is available for qualifying instructors.
| Author | : G. B. GURUNG |
| Publisher | : PHI Learning Pvt. Ltd. |
| Total Pages | : 632 |
| Release | : 2009-01-30 |
| Genre | : Technology & Engineering |
| ISBN | : 8120334221 |
A valuable introduction to Signals and Systems, this textbook has been developed by the author from his experience of teaching this particular subject to undergraduate students. It is suitable for B.E./B.Tech students in such disciplines as Electrical Engineering, Electronics and Communication Engineering, Computer Science and Engineering, Information Technology, and Biomedical Engineering. The book provides a clear understanding of the issues that students face in assimilating this highly mathematical subject. It is a comprehensive analytical treatment of signals and systems with a strong emphasis on solving problems. Each topic is supported by sufficient numbers of solved examples. Besides, a variety of tricky objective type questions have been included at the end of every chapter. Emphasizing systems approach, the book offers a unified treatment of both continuous-time and discrete-time signals and systems. The analysis tools such as Fourier transform, Laplace transform, sampling theorem and Z-transform are presented elaborately. Conceptual understanding is reinforced through plenty of worked examples. The book concludes with a chapter focused on realization of Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters. Several appendices provide the requisite background mathematical material for ease of reference by the students
| Author | : Dean G. Duffy |
| Publisher | : CRC Press |
| Total Pages | : 466 |
| Release | : 2022-03-23 |
| Genre | : Mathematics |
| ISBN | : 1000551253 |
Through four previous editions of Advanced Engineering Mathematics with MATLAB, the author presented a wide variety of topics needed by today's engineers. The fifth edition of that book, available now, has been broken into two parts: topics currently needed in mathematics courses and a new stand-alone volume presenting topics not often included in these courses and consequently unknown to engineering students and many professionals. The overall structure of this new book consists of two parts: transform methods and random processes. Built upon a foundation of applied complex variables, the first part covers advanced transform methods, as well as z-transforms and Hilbert transforms--transforms of particular interest to systems, communication, and electrical engineers. This portion concludes with Green's function, a powerful method of analyzing systems. The second portion presents random processes--processes that more accurately model physical and biological engineering. Of particular interest is the inclusion of stochastic calculus. The author continues to offer a wealth of examples and applications from the scientific and engineering literature, a highlight of his previous books. As before, theory is presented first, then examples, and then drill problems. Answers are given in the back of the book. This book is all about the future: The purpose of this book is not only to educate the present generation of engineers but also the next. "The main strength is the text is written from an engineering perspective. The majority of my students are engineers. The physical examples are related to problems of interest to the engineering students." --Lea Jenkins, Clemson University
| Author | : E.G. Phillips |
| Publisher | : Courier Dover Publications |
| Total Pages | : 163 |
| Release | : 2020-04-15 |
| Genre | : Mathematics |
| ISBN | : 0486841944 |
This concise text on the functions of a complex variable provides the basics on a number of important topics, including conformal representation, complex integral calculus, and calculus of residues. 1957 edition.
| Author | : Miodrag Petković |
| Publisher | : John Wiley & Sons |
| Total Pages | : 296 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 9783527401345 |
The aim of this book is to present formulas and methods developed using complex interval arithmetic. While most of numerical methods described in the literature deal with real intervals and real vectors, there is no systematic study of methods in complex interval arithmetic. The book fills this gap. Several main subjects are considered: outer estimates for the range of complex functions, especially complex centered forms, the best approximations of elementary complex functions by disks, iterative methods for the inclusion by polynomial zeros including their implementation on parallel computers, the analysis of numerical stability of iterative methods by using complex interval arithmetic and numerical computation of curvilinear integrals with error bounds. Mainly new methods are presented developed over the last years, including a lot of very recent results by the authors some of which have not been published before.
