Complex Variables

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.

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Several Complex Variables is a central area of mathematics with strong interactions with partial differential equations, algebraic geometry, number theory, and differential geometry. The 1995–1996 MSRI program on Several Complex Variables emphasized these interactions and concentrated on developments and problems of interest that capitalize on this interplay of ideas and techniques. This collection, first published in 2000, provides a remarkably clear and complete picture of the status of research in these overlapping areas and will provide a basis for significant continued contributions from researchers. Several of the articles are expository or have extensive expository sections, making this an excellent introduction for students to the use of techniques from these other areas in several complex variables. Thanks to its distinguished list of contributors this volume provides a representative sample of the work done in Several Complex Variables.

This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997. Sinc

Fisher (Northwestern U.) introduces students with a calculus background to the theory and applications of complex variables. Appends exercise solutions and mapping and transform tables. This is a slig

A development of some of the principal applications of function theory in several complex variables to Banach algebras. The authors do not presuppose any knowledge of several complex variables on the

Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Topics inc

Basic treatment of the theory of analytic functions of a complex variable, touching on analytic functions of several real or complex variables as well as the existence theorem for solutions of differe

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such

This is an introductory text in several complex variables, using methods of integral representations. It begins with elementary local results, discusses basic new concepts of the multi-dimensional the

First half of this highly-regarded book covers complex number plane; functions and limits; Riemann surfaces, the definite integral; power series; meromorphic functions, and much more. The second half

The text covers enough material for an advanced undergraduate or first-year graduate course. Contents include calculus in the plane; harmonic functions in the plane; analytic functions and power serie

This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds was first published in 1982. It was intended be a synthesis of those topics and a broad introduction to the field. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a further knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts were designed to provide an introduction to the more advanced works in the subject.

This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those topics and a broad introduction to the field. Part I is suitable for advanced undergraduates and beginning postgraduates whilst Part II is written more for the graduate student. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a working knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts provide an introduction to the more advanced works in the subject.

Acclaimed text on essential engineering mathematics covers theory of complex variables, Cauchy-Riemann equations, conformal mapping, and multivalued functions, plus Fourier and Laplace transform theor

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 inc

This book provides engineers with focused treatment of the mathematics needed to understand probability, random variables, and stochastic processes, which are essential mathematical disciplines used i

Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex a

This classic book offers a comprehensive logical treatment of the theory of calculus and related topics. By concentrating on theory rather than on techniques and applications, the text provides studen

This book gives a comprehensive introduction to complex analysis in several variables. It clearly focusses on special topics in complex analysis rather than trying to encompass as much material as pos

A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based

Designed for a first course in real variables, this text encourages intuitive thinking and offers background for more advanced mathematical work. Topics include complex variables, measure theory, diff

This book presents holomorphic operator functions of a single variable and applications, which are focused on the relations between local and global theories. It is based on methods and technics of co

This book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective. Analytic combinatorics is a branch of enumeration that uses analytic techniques to estimate combinatorial quantities: generating functions are defined and their coefficients are then estimated via complex contour integrals. The multivariate case involves techniques well known in other areas of mathematics but not in combinatorics. Aimed at graduate students and researchers in enumerative combinatorics, the book contains all the necessary background, including a review of the uses of generating functions in combinatorial enumeration as well as chapters devoted to saddle point analysis, Groebner bases, Laurent series and amoebas, and a smattering of differential and algebraic topology. All software along with other ancillary material can be located via the book's website, http://www.cs.auckland.ac.nz/～mcw/Research/mvGF/asymultseq/ACSVbook/.

Multivariate procedures allow social workers and other human services researchers to analyze complex, multidimensional social problems and interventions in ways that minimize oversimplification. This

This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variabl