Download or read book The Cauchy Method of Residues written by Dragoslav S. Mitrinovic and published by Springer Science & Business Media. This book was released on 1984-04-30 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Certain Applications of the Cauchy Residue Theorem written by William Henry Gordon (Jr.) and published by . This book was released on 1949 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Cauchy Residue Theorem with Applications written by Augustin Cauchy and published by . This book was released on 2019-09-28 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a translation of "Mémoir sur les Intégrales Définies, prises entre des Limites Imaginaires." by Augustin Louis Cauchy, available from www.e-rara.ch. You will need to be well versed in Integral Calculus and the theory of complex variables to be able to understand this memoir. It will also help if you are already familiar with the Residue Theorem. This memoir contains a plentiful number of applications of the Residue Theorem to real definite integrals.
Download or read book On the Theory and Applications of Cauchy s Residue Theorem written by Francis G. Olbert and published by . This book was released on 1960 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cauchy s Residue Theorem and Application written by Bernard D. Seckler and published by . This book was released on 1948 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Cauchy Method of Residues written by Dragoslav S. Mitrinovic and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Complex Variables with Applications written by Saminathan Ponnusamy and published by Springer Science & Business Media. This book was released on 2007-05-26 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores the interrelations between real and complex numbers by adopting both generalization and specialization methods to move between them, while simultaneously examining their analytic and geometric characteristics Engaging exposition with discussions, remarks, questions, and exercises to motivate understanding and critical thinking skills Encludes numerous examples and applications relevant to science and engineering students
Download or read book Complex Analysis with Applications in Science and Engineering written by Harold Cohen and published by Springer Science & Business Media. This book was released on 2010-04-23 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second Edition of this acclaimed text helps you apply theory to real-world applications in mathematics, physics, and engineering. It easily guides you through complex analysis with its excellent coverage of topics such as series, residues, and the evaluation of integrals; multi-valued functions; conformal mapping; dispersion relations; and analytic continuation. Worked examples plus a large number of assigned problems help you understand how to apply complex concepts and build your own skills by putting them into practice. This edition features many new problems, revised sections, and an entirely new chapter on analytic continuation.
Download or read book Complex Integration and Cauchy s Theorem written by G. N. Watson and published by . This book was released on 1914 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1914, this book provides a concise proof of Cauchy's Theorem, with applications of the theorem to the evaluation of definite integrals.
Download or read book Applications of the Residue Theorem written by Dennis R. Daluge and published by . This book was released on 1964 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Calculus of Residues and Its Application to the Evaluation of Definite Integrals written by Viola Woodward and published by . This book was released on 1947 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introductory Complex and Analysis Applications written by William R. Derrick and published by Academic Press. This book was released on 2014-05-10 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory Complex and Analysis Applications provides an introduction to the functions of a complex variable, emphasizing applications. This book covers a variety of topics, including integral transforms, asymptotic expansions, harmonic functions, Fourier transformation, and infinite series. Organized into eight chapters, this book begins with an overview of the theory of functions of a complex variable. This text then examines the properties of analytical functions, which are all consequences of the differentiability of the function. Other chapters consider the converse of Taylor's Theorem, namely that convergent power series are analytical functions in their domain of convergence. This book discusses as well the Residue Theorem, which is of fundamental significance in complex analysis and is the core concept in the development of the techniques. The final chapter deals with the method of steepest descent, which is useful in determining the asymptotic behavior of integral representations of analytic functions. This book is a valuable resource for undergraduate students in engineering and mathematics.
Download or read book Applications of the Residue Theorem written by Sunshine Marie Gibbons and published by . This book was released on 2002 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fundamentals and Applications of Complex Analysis written by Harold Cohen and published by Springer Science & Business Media. This book was released on 2003-07-31 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to serve as a text for first and second year courses in single variable complex analysis. The material that is appropriate for more advanced study is developed from elementary material. The concepts are illustrated with large numbers of examples, many of which involve problems students encounter in other courses. For example, students who have taken an introductory physics course will have encountered analysis of simple AC circuits. This text revisits such analysis using complex numbers. Cauchy's residue theorem is used to evaluate many types of definite integrals that students are introduced to in the beginning calculus sequence. Methods of conformal mapping are used to solve problems in electrostatics. The book contains material that is not considered in other popular complex analysis texts.
Download or read book Cauchy and the Creation of Complex Function Theory written by Frank Smithies and published by Cambridge University Press. This book was released on 1997-11-20 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dr Smithies' analysis of the process whereby Cauchy created the basic structure of complex analysis, begins by describing the 18th century background. He then proceeds to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem. Controversies associated with the the birth of the subject are also considered in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This authoritative book is the first to make use of the whole spectrum of available original sources.
Download or read book Functions of a Complex Variable and Some of Their Applications written by B. A. Fuchs and published by Elsevier. This book was released on 2014-08-01 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functions of a Complex Variable and Some of Their Applications, Volume 1, discusses the fundamental ideas of the theory of functions of a complex variable. The book is the result of a complete rewriting and revision of a translation of the second (1957) Russian edition. Numerous changes and additions have been made, both in the text and in the solutions of the Exercises. The book begins with a review of arithmetical operations with complex numbers. Separate chapters discuss the fundamentals of complex analysis; the concept of conformal transformations; the most important of the elementary functions; and the complex potential for a plane vector field and the application of the simplest methods of function theory to the analysis of such a field. Subsequent chapters cover the fundamental apparatus of the theory of regular functions, i.e. basic integral theorems and expansions in series; the general concept of an analytic function; applications of the theory of residues; and polygonal domain mapping. This book is intended for undergraduate and postgraduate students of higher technical institutes and for engineers wishing to increase their knowledge of theory.
Download or read book Complex Analysis with Applications to Number Theory written by Tarlok Nath Shorey and published by Springer Nature. This book was released on 2020-11-13 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses major topics in complex analysis with applications to number theory. This book is intended as a text for graduate students of mathematics and undergraduate students of engineering, as well as to researchers in complex analysis and number theory. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two and three manifolds and number theory. In additional to solved examples and problems, the book covers most of the topics of current interest, such as Cauchy theorems, Picard’s theorems, Riemann–Zeta function, Dirichlet theorem, gamma function and harmonic functions.
