Applied Complex Variables

Complex Variables and Applications, 9e will serve, just as the earlier editions did, as a textbook for an introductory course in the theory and application of functions of a complex variable. This new

Kapoor (U. of Hyderabad, India) finds the theory of functions of a complex variable to be one of those areas of mathematics that were created for reasons not even remotely connected to any practical,

From the algebraic properties of a complete number field, to the analytic properties imposed by the Cauchy integral formula, to the geometric qualities originating from conformality, Complex Variables

Intended for engineering and math majors, this undergraduate textbook introduces the theory of complex numbers, defines transcendental functions of a complex variable, shows how evaluation of line int

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.

The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus

There was a special year devoted to the topic of several complex variables at the Mittag-Leffler Institute in Stockholm, Sweden, and this volume contains the resulting survey papers and research paper

???This monograph provides a concise, accessible snapshot of key topics in several complex variables, including the Cauchy Integral Formula, sequences of holomorphic functions, plurisubharmonic functi

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

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

The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested research

This is a reference book for academics working in the fields of several complex variables, PDE theory and geometry. The book collects articles on most recent developments in these fields with special

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

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

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

What Makes Variables Random: Probability for the Applied Researcher provides an introduction to the foundations of probability that underlie the statistical analyses used in applied research. By expla

This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variabl

A presentation of real examples of industrial uses for formal methods such as SCADE, the B-Method, ControlBuild, Matelo, etc. in various fields, such as railways, aeronautics, and the automotive indus

A presentation of real examples of industrial uses for formal methods such as SCADE, the B-Method, ControlBuild, Matelo, etc.

This monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometr

This is the first text of its kind to deal exclusively with applied social work ethics. It focuses on an eclectic mix of difficult moral questions or issues encountered in much modern day practice. It

This book gives guidance to solve problems in electromagnetics, providing both examples of solving serious research problems as well as the original results to encourage further investigations. The bo

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 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

Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. This revised edition has been updated throughout to reflect recent developments in the field. It contains 25% new material, including two brand new chapters on orthogonal polynomials in two variables, which will be especially useful for applications, and orthogonal polynomials on the unit sphere. The most modern and complete treatment of the subject available, it will be useful to a wide audience of mathematicians and applied scientists, including physicists, chemists and engineers.

The book, belonging to the series “Studies in Theoretical and Applied Statistics – Selected Papers from the Statistical Societies”, presents a peer-reviewed selection of contributions on relevant topi

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/.

In response to the exponentially increasing need to analyze vast amounts of data, Neural Networks for Applied Sciences and Engineering: From Fundamentals to Complex Pattern Recognition provides scient

This textbook introduces students progressively to various aspects of qualitative models and assumes a knowledge of basic principles of statistics and econometrics. Inferring qualitative characteristics of data on socioeconomic class, education, employment status, and the like - given their discrete nature - requires an entirely different set of tools from those applied to purely quantitative data. Written in accessible language and offering cogent examples, students are given valuable means to gauge real-world economic phenomena. After the introduction, early chapters present models with endogenous qualitative variables, examining dichotomous models, model specification, estimation methods, descriptive usage, and qualitative panel data. Professor Gourieroux also looks at Tobit models, in which the exogenous variable is sometimes qualitative and sometimes quantitative, and changing-regime models, in which the dependent variable is qualitative but expressed in quantitative terms. The fi