Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter. This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: Linear Algebra, Acheson: Elementary Fluid Dynamics, Jordan and Smith: Nonlinear Ordinary Differential Equations, Smith: Numerical Solution of Partial Differential Equations, Wilson: Graphs, Colourings and the Four-Colour Theorem, Bishop: Neural Networks for Pattern Recognition, Gelman and Nolan: Teaching Statistics.

Complex Analysis is an introductory textbook designed for absolute beginners, offering a clear and straightforward exploration of complex numbers and functions. The book presents fundamental concepts in a step-by-step manner, making complex analysis accessible to those with little or no prior mathematical knowledge. Through practical examples and intuitive explanations, readers will discover the beauty of complex functions, the significance of Cauchy's integral formula, and the application of power series. Ideal for students and curious learners alike, this book serves as a solid foundation for further studies in mathematics.

The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manor. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.

Designed for the undergraduate student with a calculus background but no prior experience with complex analysis, this text discusses the theory of the most relevant mathematical topics in a student-friendly manner. With a clear and straightforward writing style, concepts are introduced through numerous examples, illustrations, and applications. Each section of the text contains an extensive exercise set containing a range of computational, conceptual, and geometric problems. In the text and exercises, students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section devoted exclusively to the applications of complex analysis to science and engineering, providing students with the opportunity to develop a practical and clear understanding of complex analysis. The Mathematica syntax from the second edition has been updated to coincide with version 8 of the software. --

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 theory of complex analysis, and then examines its geometrical interpretation and application to Dirichlet and Neumann boundary value problems. A discussion of complex analysis now forms the first three chapters of the book, with a description of conformal mapping and its application to boundary value problems for the two-dimensional Laplace equation forming the final two chapters. This new structure enables students to study theory and applications separately, as needed. In order to maintain brevity and clarity, the text limits the application of complex analysis to two-dimensional boundary value problems related to temperature distribution, fluid flow, and electrostatics. In each case, in order to show the relevance of complex analysis, each application is preceded by mathematical background that demonstrates how a real valued potential function and its related complex potential can be derived from the mathematics that describes the physical situation.

The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns.

This book presents a way of learning complex analysis, using Mathematica. Includes CD with electronic version of the book.

Mit der Festschrift zum 65. Geburtstag wird mit Hartmut Kuhne ein Wissenschaftler geehrt, der durch seine langjahrige Lehr- und Ausgrabungstatigkeit zahlreiche Schuler im In- und Ausland hervorgebracht und sich grosse Verdienste um die Archaologie Syriens, aber auch Anatoliens erworben hat.Die von renommierten Archaologen und Philologen verfassten Beitrage zu den "Fundstellen" tragen dieser Lebensleistung Rechnung. Der chronologische Rahmen reicht vom Neolithikum Westsyriens (K. Bartl) und Sudwestanatoliens (E. Abay) bis zur Romanisierung Ostsyriens(A. Oettel) und der spatantiken Besiedlung des Tell Feheriye (N. Ritter). Einen Schwerpunkt bildet die mittel- und neuassyrische bzw. spathethitische Zeit. Dabei werden bau- und kunstgeschichtliche Fragen zur Architektur von Hama (P. Matthiae), Karkamis (M. Pucci), Tall Seh Hamad (A. Kose) und Kar Tukulti-Ninurta (A. Gilibert) ebenso thematisiert wie die Bestattungssitten in Tell Sabi Abyad (P. Akkermans/ E. Smits), Tall Knedig (S. Kulemann-Ossen/L. Martin) und Dur Katlimmu (J. Kreppner). W. Rollig, K. Radner und E. Cancik-Kirschbaum betrachten diesen Zeitraum aus historischem Blickwinkel. R. Bernbeck widmet sich in seinem Beitrag der historisch verzerrten Gestalt der Semiramis. D. Bonatz betrachtet "Bartlosigkeit in Assyrien" aus kulturanthropologischer Sicht. G. Bunnens beschaftigt sich mit der "damnatio memoriae" in den Wandmalereien von Til Barsib. V. Haas wirft am Beispiel des urartaischen Urzana-Siegels Licht auf die Forschungsgeschichte der altorientalischen Glyptik.

This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text slowly and carefully develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem, the Riemann mapping theorem, and the theorem of Mittag-Leffler can be treated without sidestepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a wide selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.

This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.