Complex Analysis

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A Complex Analysis Problem Book

Daniel Alpay
A Complex Analysis Problem Book Book PDF

Author : Daniel Alpay
Publisher : Birkhäuser
Page : 592 pages
File Size : 45,8 Mb
Release : 2016-10-26
Category : Mathematics
ISBN : 9783319421810

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A Complex Analysis Problem Book by Daniel Alpay Pdf

This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.

Visual Complex Analysis

Tristan Needham
Visual Complex Analysis Book PDF

Author : Tristan Needham
Publisher : Oxford University Press
Page : 620 pages
File Size : 52,9 Mb
Release : 1997
Category : Mathematics
ISBN : 0198534469

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Visual Complex Analysis by Tristan Needham Pdf

This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

A First Course in Complex Analysis with Applications

Dennis Zill,Patrick Shanahan
A First Course in Complex Analysis with Applications Book PDF

Author : Dennis Zill,Patrick Shanahan
Publisher : Jones & Bartlett Learning
Page : 471 pages
File Size : 43,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780763757724

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A First Course in Complex Analysis with Applications by Dennis Zill,Patrick Shanahan Pdf

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.

Complex Analysis

Elias M. Stein,Rami Shakarchi
Complex Analysis Book PDF

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 398 pages
File Size : 50,6 Mb
Release : 2010-04-22
Category : Mathematics
ISBN : 9781400831159

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Complex Analysis by Elias M. Stein,Rami Shakarchi Pdf

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Complex Analysis

Theodore W. Gamelin
Complex Analysis Book PDF

Author : Theodore W. Gamelin
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 44,7 Mb
Release : 2013-11-01
Category : Mathematics
ISBN : 9780387216072

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Complex Analysis by Theodore W. Gamelin Pdf

An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.

Complex Variables

Mark J. Ablowitz,Athanassios S. Fokas
Complex Variables Book PDF

Author : Mark J. Ablowitz,Athanassios S. Fokas
Publisher : Cambridge University Press
Page : 656 pages
File Size : 53,8 Mb
Release : 2003-04-28
Category : Mathematics
ISBN : 9781139439138

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Complex Variables by Mark J. Ablowitz,Athanassios S. Fokas Pdf

Complex variables provide powerful methods for attacking problems that can be very difficult to solve in any other way, and it is the aim of this book to provide a thorough grounding in these methods and their application. Part I of this text provides an introduction to the subject, including analytic functions, integration, series, and residue calculus and also includes transform methods, ODEs in the complex plane, and numerical methods. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann–Hilbert problems. The authors provide an extensive array of applications, illustrative examples and homework exercises. This 2003 edition was improved throughout and is ideal for use in undergraduate and introductory graduate level courses in complex variables.

Introduction to Complex Analysis

H. A. Priestley
Introduction to Complex Analysis Book PDF

Author : H. A. Priestley
Publisher : OUP Oxford
Page : 344 pages
File Size : 47,8 Mb
Release : 2003-08-28
Category : Mathematics
ISBN : 9780191037207

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Introduction to Complex Analysis by H. A. Priestley Pdf

Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter. This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: Linear Algebra, Acheson: Elementary Fluid Dynamics, Jordan and Smith: Nonlinear Ordinary Differential Equations, Smith: Numerical Solution of Partial Differential Equations, Wilson: Graphs, Colourings and the Four-Colour Theorem, Bishop: Neural Networks for Pattern Recognition, Gelman and Nolan: Teaching Statistics.

Complex Analysis

Serge Lang
Complex Analysis Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 45,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475718713

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Complex Analysis by Serge Lang Pdf

The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recom mend to anyone to look through them. More recent texts have empha sized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex anal ysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The systematic elementary development of formal and convergent power series was standard fare in the German texts, but only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book essentially decomposes into two parts.

Complex Analysis in one Variable

NARASIMHAN
Complex Analysis in one Variable Book PDF

Author : NARASIMHAN
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781475711066

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Complex Analysis in one Variable by NARASIMHAN Pdf

This book is based on a first-year graduate course I gave three times at the University of Chicago. As it was addressed to graduate students who intended to specialize in mathematics, I tried to put the classical theory of functions of a complex variable in context, presenting proofs and points of view which relate the subject to other branches of mathematics. Complex analysis in one variable is ideally suited to this attempt. Of course, the branches of mathema tics one chooses, and the connections one makes, must depend on personal taste and knowledge. My own leaning towards several complex variables will be apparent, especially in the notes at the end of the different chapters. The first three chapters deal largely with classical material which is avai lable in the many books on the subject. I have tried to present this material as efficiently as I could, and, even here, to show the relationship with other branches of mathematics. Chapter 4 contains a proof of Picard's theorem; the method of proof I have chosen has far-reaching generalizations in several complex variables and in differential geometry. The next two chapters deal with the Runge approximation theorem and its many applications. The presentation here has been strongly influenced by work on several complex variables.

Introductory Complex Analysis

Richard A. Silverman
Introductory Complex Analysis Book PDF

Author : Richard A. Silverman
Publisher : Courier Corporation
Page : 402 pages
File Size : 55,9 Mb
Release : 2013-04-15
Category : Mathematics
ISBN : 9780486318523

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Introductory Complex Analysis by Richard A. Silverman Pdf

Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.

Complex Analysis

Eberhard Freitag,Rolf Busam
Complex Analysis Book PDF

Author : Eberhard Freitag,Rolf Busam
Publisher : Springer Science & Business Media
Page : 552 pages
File Size : 43,5 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783540308232

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Complex Analysis by Eberhard Freitag,Rolf Busam Pdf

All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included

Principles of Complex Analysis

Serge Lvovski
Principles of Complex Analysis Book PDF

Author : Serge Lvovski
Publisher : Springer Nature
Page : 257 pages
File Size : 52,5 Mb
Release : 2020-09-26
Category : Mathematics
ISBN : 9783030593650

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Principles of Complex Analysis by Serge Lvovski Pdf

This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they are really indispensable. This approach provides a motivation for the reader to digest more abstract definitions (e.g., those of sheaves or line bundles, which are not mentioned in the book) when he/she is ready for that level of abstraction indeed. In the chapter on Riemann surfaces, several key results on compact Riemann surfaces are stated and proved in the first nontrivial case, i.e. that of elliptic curves.

Complex Analysis

John M. Howie
Complex Analysis Book PDF

Author : John M. Howie
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447100270

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Complex Analysis by John M. Howie Pdf

Complex analysis can be a difficult subject and many introductory texts are just too ambitious for today’s students. This book takes a lower starting point than is traditional and concentrates on explaining the key ideas through worked examples and informal explanations, rather than through "dry" theory.

An Introduction to Complex Analysis

Ravi P. Agarwal,Kanishka Perera,Sandra Pinelas
An Introduction to Complex Analysis Book PDF

Author : Ravi P. Agarwal,Kanishka Perera,Sandra Pinelas
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 44,5 Mb
Release : 2011-07-01
Category : Mathematics
ISBN : 9781461401957

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An Introduction to Complex Analysis by Ravi P. Agarwal,Kanishka Perera,Sandra Pinelas Pdf

This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.

Elementary Theory of Analytic Functions of One or Several Complex Variables

Henri Cartan
Elementary Theory of Analytic Functions of One or Several Complex Variables Book PDF

Author : Henri Cartan
Publisher : Courier Corporation
Page : 242 pages
File Size : 45,7 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780486318677

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Elementary Theory of Analytic Functions of One or Several Complex Variables by Henri Cartan Pdf

Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.