Complex Variables and Applications

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

"This outstanding undergraduate text for students of science and engineering requires only a standard course in elementary calculus. Designed to provide a thorough understanding of fundamental concept

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

This textbook introduces the theory of complex variables at undergraduate level. A good collection of problems is provided in the second part of the book. The book is written in a user-friendly style

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.

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.

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

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.

This supplemental text allows instructors and students to add a MatLab content to a complex variables course. This book seeks to create a bridge between functions of a complex variable and MATLAB. Eve

This introduction to complex variable methods begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. Throughout the text, many of the important theoretical results in complex function theory are followed by relevant and vivid examples in physical sciences. This second edition now contains 350 stimulating exercises of high quality, with solutions given to many of them. Material has been updated and additional proofs on some of the important theorems in complex function theory are now included, e.g. the Weierstrass–Casorati theorem. The book is highly suitable for students wishing to learn the elements of complex analysis in an applied con

This text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. It begins by establishing the quotient

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

A concise monograph by two Russian experts provides an account of the operational calculus in two variables based on the two-dimensional Laplace transform. Suitable for advanced undergraduates and gra

The book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: wi

This volume conveys some of the surprises, puzzles and success stories in high-dimensional and complex data analysis and related fields. Its peer-reviewed contributions showcase recent advances in var

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 book deals with the analysis of the structure of complex networks by combining results from graph theory, physics, and pattern recognition. The book is divided into two parts. 11 chapters are ded

The purpose of this book, first published in 1939, updated in 1953, is to give a treatment of the so-called operational method and to illustrate its application to problems in various branches of technology. It is written primarily for technologists who use mathematics in solving technical problems in industrial and applied research work, and the treatment is sufficiently rigorous for their needs. The theory of the complex variable and of transform calculus occupy the first half of the book. A further third of the book describes the application of this theory to problems arising in electrical circuits; vibrational systems; aeroplane dynamics; the deflexion of beams; radio and television receivers; the solution of partial differential equations; electrical transmission limes; electrical wave filters; solenoids with metal cores; condenser microphones; loud speaker horns and the absorption of moisture. The final part contains over 100 problems - many with hints for their solution - append

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 systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and di

This volume contains the basics of what every scientist and engineer should know about complex analysis. A lively style combined with a simple, direct approach helps readers grasp the fundamentals, fr