For student in mathematics, engineering, and physics. Includes comprehensive coverage of complex numbers, set theory, mapping, functions, Cauchy-Riemann conditions, power series, Taylor series, Green's theorem, Laurent expansions, singularities, residues, transformations, and numerous scientific applications.

For student in mathematics, engineering, and physics. Includes comprehensive coverage of complex numbers, set theory, mapping, functions, Cauchy-Riemann conditions, power series, Taylor series, Green's theorem, Laurent expansions, singularities, residues, transformations, and numerous scientific applications.

The Problem Solvers are an exceptional series of books that are thorough, unusually well-organized, and structured in such a way that they can be used with any text. No other series of study and solution guides has come close to the Problem Solvers in usefulness, quality, and effectiveness. Educators consider the Problem Solvers the most effective series of study aids on the market. Students regard them as most helpful for their school work and studies. With these books, students do not merely memorize the subject matter, they really get to understand it. Each Problem Solver is over 1,000 pages, yet each saves hours of time in studying and finding solutions to problems. These solutions are worked out in step-by-step detail, thoroughly and clearly. Each book is fully indexed for locating specific problems rapidly. An essential subject for students in mathematics, computer science, engineering, and science. The 19 chapters cover basic, as well as advanced, methods of numerical analysis. A large number of related applications are included.

REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Complex Variables II includes elementary mappings and Mobius transformation, mappings by general functions, conformal mappings and harmonic functions, applying complex functions to applied mathematics, analytic continuation, and analytic function properties.

Today, the theory of complex-valued functions finds widespread applications in various areas of mathematical research, as well as in electrical and mechanical engineering, aeronautics, and other disciplines. Complex analysis has become a basic course in mathematics, physics, and select engineering departments. This concise textbook provides a thorough introduction to the function theory of one complex variable. It presents the fundamental concepts with clarity and rigor, offering concise proofs that avoid lengthy and tedious arguments commonly found in mathematics textbooks. It goes beyond traditional texts by exploring less common topics, including the different approaches to constructing analytic functions, the conformal mapping criterion, integration of analytic functions along arbitrary curves, global analytic functions and their Riemann surfaces, the general inverse function theorem, the Lagrange–Bürmann formula, and Puiseux series. Drawing from several decades of teaching experience, this book is ideally suited for one or two semester courses in complex analysis. It also serves as a valuable companion for courses in topology, approximation theory, asymptotic analysis, and functional analysis. Abundant examples and exercises make it suitable for self-study as well.

This book discusses all the major topics of complex analysis, beginning with the properties of complex numbers and ending with the proofs of the fundamental principles of conformal mappings. Topics covered in the book include the study of holomorphic and analytic functions, classification of singular points and the Laurent series expansion, theory of residues and their application to evaluation of integrals, systematic study of elementary functions, analysis of conformal mappings and their applications—making this book self-sufficient and the reader independent of any other texts on complex variables. The book is aimed at the advanced undergraduate students of mathematics and engineering, as well as those interested in studying complex analysis with a good working knowledge of advanced calculus. The mathematical level of the exposition corresponds to advanced undergraduate courses of mathematical analysis and first graduate introduction to the discipline. The book contains a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic skills and test the understanding of concepts. Other problems are more theoretically oriented and illustrate intricate points of the theory. Many additional problems are proposed as homework tasks whose level ranges from straightforward, but not overly simple, exercises to problems of considerable difficulty but of comparable interest.

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-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.