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The Calculus Of Complex Functions
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Book Synopsis The Calculus of Complex Functions by : William Johnston
Download or read book The Calculus of Complex Functions written by William Johnston and published by American Mathematical Society. This book was released on 2022-04-01 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces complex analysis as a natural extension of the calculus of real-valued functions. The mechanism for doing so is the extension theorem, which states that any real analytic function extends to an analytic function defined in a region of the complex plane. The connection to real functions and calculus is then natural. The introduction to analytic functions feels intuitive and their fundamental properties are covered quickly. As a result, the book allows a surprisingly large coverage of the classical analysis topics of analytic and meromorphic functions, harmonic functions, contour integrals and series representations, conformal maps, and the Dirichlet problem. It also introduces several more advanced notions, including the Riemann hypothesis and operator theory, in a manner accessible to undergraduates. The last chapter describes bounded linear operators on Hilbert and Banach spaces, including the spectral theory of compact operators, in a way that also provides an excellent review of important topics in linear algebra and provides a pathway to undergraduate research topics in analysis. The book allows flexible use in a single semester, full-year, or capstone course in complex analysis. Prerequisites can range from only multivariate calculus to a transition course or to linear algebra or real analysis. There are over one thousand exercises of a variety of types and levels. Every chapter contains an essay describing a part of the history of the subject and at least one connected collection of exercises that together comprise a project-level exploration.
Book Synopsis Theory of Complex Functions by : Reinhold Remmert
Download or read book Theory of Complex Functions written by Reinhold Remmert and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lively and vivid look at the material from function theory, including the residue calculus, supported by examples and practice exercises throughout. There is also ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations - in the original language with their English translation - from their classical works. Yet the book is far from being a mere history of function theory, and even experts will find a few new or long forgotten gems here. Destined to accompany students making their way into this classical area of mathematics, the book offers quick access to the essential results for exam preparation. Teachers and interested mathematicians in finance, industry and science will profit from reading this again and again, and will refer back to it with pleasure.
Book Synopsis Calculus with Complex Numbers by : John B. Reade
Download or read book Calculus with Complex Numbers written by John B. Reade and published by CRC Press. This book was released on 2003-03-13 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series, and the fundamental theorem of algebra. The Residue Theorem for evaluating complex integrals is presented in a straightforward way, laying the groundwork for further study. A working knowledge of real calculus and familiarity with complex numbers is assumed. This book is useful for graduate students in calculus and undergraduate students of applied mathematics, physical science, and engineering.
Book Synopsis Functions of One Complex Variable by : J.B. Conway
Download or read book Functions of One Complex Variable written by J.B. Conway and published by Springer. This book was released on 1973-10-16 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - I) arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.
Book Synopsis Complex Analysis by : Jerry R. Muir, Jr.
Download or read book Complex Analysis written by Jerry R. Muir, Jr. and published by John Wiley & Sons. This book was released on 2015-05-26 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects Numerous figures to illustrate geometric concepts and constructions used in proofs Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes Appendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis.
Book Synopsis Complex Analysis with Vector Calculus by : T. M. J. A. Cooray
Download or read book Complex Analysis with Vector Calculus written by T. M. J. A. Cooray and published by Alpha Science Int'l Ltd.. This book was released on 2006 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on many years of experience of the author Complex Analysis with Vector Calculus provides clear and condensed treatment of the subject. It is primarily intended to be used by undergraduate students of engineering and science as a part of a course in engineering mathematics, where they are introduced to complex variable theory, through conceptual development of analysis. The book also introduces vector algebra, step by step, with due emphasis on various operations on vector field and scalar fields. Especially, it introduces proof of vector identities by use of a new approach and includes many examples to clarify the ideas and familiarize students with various techniques of problem solving.
Book Synopsis A First Course in Complex Analysis with Applications by : Dennis Zill
Download or read book A First Course in Complex Analysis with Applications written by Dennis Zill and published by Jones & Bartlett Learning. This book was released on 2009 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manor. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.
Book Synopsis An Introduction to Complex Function Theory by : Bruce P. Palka
Download or read book An Introduction to Complex Function Theory written by Bruce P. Palka and published by Springer Science & Business Media. This book was released on 1991 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text slowly and carefully develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem, the Riemann mapping theorem, and the theorem of Mittag-Leffler can be treated without sidestepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a wide selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.
Book Synopsis Introduction to the Theory of Complex Functions by : Jian-Ke Lu
Download or read book Introduction to the Theory of Complex Functions written by Jian-Ke Lu and published by World Scientific Publishing Company. This book was released on 2002-11-26 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the teaching experience of the authors, and therefore some of the topics are presented in a new form. For instance, the multi-valued properties of the argument function are discussed in detail so that the beginner may readily grasp the elementary multi-valued analytic functions. The residue theorem is extended to the case where poles of analytic functions considered may occur on the boundary of a region — which is very useful in applications but not seen in textbooks written in English.
Book Synopsis Classical Complex Analysis by : Mario Gonzalez
Download or read book Classical Complex Analysis written by Mario Gonzalez and published by CRC Press. This book was released on 1991-09-24 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt: Text on the theory of functions of one complex variable contains, with many elaborations, the subject of the courses and seminars offered by the author over a period of 40 years, and should be considered a source from which a variety of courses can be drawn. In addition to the basic topics in the cl
Book Synopsis Complex Function Theory by : Donald Sarason
Download or read book Complex Function Theory written by Donald Sarason and published by American Mathematical Society. This book was released on 2021-02-16 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Complex Function Theory.
Book Synopsis Complex Variables by : M. Ya Antimirov
Download or read book Complex Variables written by M. Ya Antimirov and published by San Diego ; Toronto : Academic Press. This book was released on 1998 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Variables is an extended course in complex analysis and its applications for engineering students and for those who use complex analysis in their work. In addition to classical results, it includes results recently obtained by the authors. Antimirov, Kolyshkin, and Vaillancourt have combined a rigorous presentation with clarity and many solved examples. The text introduces the theory of functions of one complex variable, and presents an evaluation of many new integration formulae and the summation of new infinite series by the calculus of residue. The book also includes the Fatou-Julia theory for meromorphic functions for finding selective roots of some transcendental equations as found in the applications. The exercises provided in the text are elementary and aim at the understanding of the theory of analytic functions. Answers to odd-numbered exercises are in the back of the book; answers to even-numbered exercises are provided in an accompanying instructor's manual. Key Features: * Uses direct mathematical language, avoiding unnecessary abstract style * Contains planes of domain and image of mappings which are always clearly specified and well-illustrated with figures * Provides several new integration and summation formulas, which may eventually find their way into symbolic softwares * Includes a large collection of exercises * Expands entire functions in infinite products into simpler forms than those found in many textbooks * Presents fresh information on the dynamics of meromorphic functions to solve transcendental equation found in the applications
Book Synopsis Function Theory of One Complex Variable by : Robert Everist Greene
Download or read book Function Theory of One Complex Variable written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 2006 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples andexercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem,and the Bergman kernel. The authors also treat $Hp$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.
Download or read book Complex Analysis written by Lars Ahlfors and published by . This book was released on 1979 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals.
Book Synopsis Classical Topics in Complex Function Theory by : Reinhold Remmert
Download or read book Classical Topics in Complex Function Theory written by Reinhold Remmert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician. The author includes numerous glimpses of the function theory of several complex variables, which illustrate how autonomous this discipline has become. In addition to standard topics, readers will find Eisenstein's proof of Euler's product formula for the sine function; Wielandts uniqueness theorem for the gamma function; Stirlings formula; Isssas theorem; Besses proof that all domains in C are domains of holomorphy; Wedderburns lemma and the ideal theory of rings of holomorphic functions; Estermanns proofs of the overconvergence theorem and Blochs theorem; a holomorphic imbedding of the unit disc in C3; and Gausss expert opinion on Riemanns dissertation. Remmert elegantly presents the material in short clear sections, with compact proofs and historical comments interwoven throughout the text. The abundance of examples, exercises, and historical remarks, as well as the extensive bibliography, combine to make an invaluable source for students and teachers alike
Download or read book Complex Analysis written by Murali Rao and published by World Scientific. This book was released on 1991 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a rigorous introduction to the theory of complex functions of one complex variable. The authors have made an effort to present some of the deeper and more interesting results, for example, Picard's theorems, Riemann mapping theorem, Runge's theorem in the first few chapters. However, the very basic theory is nevertheless given a thorough treatment so that readers should never feel lost. After the first five chapters, the order may be adapted to suit the course. Each chapter finishes with exercises.
Book Synopsis Complex Analysis for Mathematics and Engineering by : John H. Mathews
Download or read book Complex Analysis for Mathematics and Engineering written by John H. Mathews and published by Jones & Bartlett Learning. This book was released on 2001 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Analysis for Mathematics and Engineering strikes a balance between the pure and applied aspects of complex analysis, and presents concepts using a clear writing style. Believing that mathemati
