Complex Analysis

This user-friendly textbook introduces complex analysis at the beginning graduate or advanced undergraduate level. Unlike other textbooks, it follows Weierstrass' approach, stressing the importance of power series expansions instead of starting with the Cauchy integral formula, an approach that illuminates many important concepts. This view allows readers to quickly obtain and understand many fundamental results of complex analysis, such as the maximum principle, Liouville's theorem, and Schwarz's lemma. The book covers all the essential material on complex analysis, and includes several elegant proofs that were recently discovered. It includes the zipper algorithm for computing conformal maps, as well as a constructive proof of the Riemann mapping theorem, and culminates in a complete proof of the uniformization theorem. Aimed at students with some undergraduate background in real analysis, though not Lebesgue integration, this classroom-tested textbook will teach the skills and intui

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

This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and pa

Now in its fourth edition, the first part of this book is devoted to the basic material of complex analysis, while the second covers many special topics, such as the Riemann Mapping Theorem, the gamma

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

The development of complex analysis is based on issues related to holomorphic continuation and holomorphic approximation. This volume presents a unified view of these topics in finite and infinite dim

Presents Real & Complex Analysis Together Using a Unified ApproachA two-semester course in analysis at the advanced undergraduate or first-year graduate levelUnlike other undergraduate-level texts

All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumedProvides a more in-depth introduction to

A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. Chiefly classical in content, it emphasizes the g

A concise textbook on complex analysis for undergraduate and graduate students, this book is written from the viewpoint of modern mathematics: the Bar {Partial}-equation, differential geometry, Lie gr

Complex Analysis and Applications, Second Edition explains complex analysis for students of applied mathematics and engineering. Restructured and completely revised, this textbook first develops the t

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 exten

The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. The first part comprises the basic core of a course in complex analysis

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 stude

Now in its fourth edition, the first part of this book is devoted to the basic material of complex analysis, while the second covers many special topics, such as the Riemann Mapping Theorem, the gamma

Classic Complex Analysis is a text that has been developed over decades of teaching with an enthusiastic student reception. The first half of the book focuses on the core material. An early chapter

The volume is an enlarged edition of a classic textbook on complex analysis. It bridges the gap between the classical material of the first edition and recent advances in half-plane Loewner theory, th

The volume is an enlarged edition of a classic textbook on complex analysis. It bridges the gap between the classical material of the first edition and recent advances in half-plane Loewner theory, th

Students often find the subject of complex analysis very difficult. An opening chapter provides a brief history of complex analysis which sets it in context and provides motivation.

This textbook is intended for a one semester course in complex analysis for upper level undergraduates in mathematics. Applications, primary motivations for this text, are presented hand-in-hand with

Intended for use in a first course on complex analysis, this expanded second edition is arranged in short chapters and in such a way that much of the technical materials can be treated as optional (se

Inequalities from Complex Analysis is a careful, friendly exposition of some rather interesting mathematics. The author gives a novel presentation of some standard mathematics as well as some results

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

Complex Analysis with Mathematica offers a way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos and advanced conformal mapping. A CD is included which contains a live version of the book: in particular all the Mathematica code enables the user to run computer experiments.

This book presents complex analysis in one variable in the context of modern mathematics, with clear connections to several complex variables, de Rham theory, real analysis, and other branches of math

Maximizing reader insights into the fundamentals of complex analysis, and providing complete instructions on how to construct and use mathematical tools to solve engineering problems in potential theo

The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interpla

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

After the pioneering work on complex dynamics by Fatou and Julia in the early 20th century, Noel Baker went on to lay the foundations of transcendental complex dynamics. As one of the leading exponents of transcendental dynamics, he showed how developments in complex analysis such as Nevanlinna theory could be applied. His work has inspired many others to take up this increasingly active subject, and will continue to do so. Presenting papers by researchers in transcendental dynamics and complex analysis, this book is written in honour of Noel Baker. The papers describe the state of the art in this subject, with new results on completely invariant domains, wandering domains, the exponential parameter space, and normal families. The inclusion of comprehensive survey articles on dimensions of Julia sets, buried components of Julia sets, Baker domains, Fatou components of functions of small growth, and ergodic theory of transcendental meromorphic functions means this is essential reading f

Moskowitz (mathematics, City University of New York Graduate Center) explains fundamentals of basic complex analysis and relates them to real analysis. Coverage progresses from integration along a con