Search results for: complex-analysis-in-one-variable

Complex Analysis in One Variable

Author : Raghavan Narasimhan
File Size : 56.43 MB
Format : PDF, Mobi
Download : 658
Read : 202
Download »
The original edition of this book has been out of print for some years. The appear ance of the present second edition owes much to the initiative of Yves Nievergelt at Eastern Washington University, and the support of Ann Kostant, Mathematics Editor at Birkhauser. Since the book was first published, several people have remarked on the absence of exercises and expressed the opinion that the book would have been more useful had exercises been included. In 1997, Yves Nievergelt informed me that, for a decade, he had regularly taught a course at Eastern Washington based on the book, and that he had systematically compiled exercises for his course. He kindly put his work at my disposal. Thus, the present edition appears in two parts. The first is essentially just a reprint of the original edition. I have corrected the misprints of which I have become aware (including those pointed out to me by others), and have made a small number of other minor changes.

A Course In Complex Analysis In One Variable

Author : Moskowitz Martin
File Size : 70.3 MB
Format : PDF, Kindle
Download : 662
Read : 466
Download »
Complex analysis is a beautiful subject — perhaps the single most beautiful; and striking; in mathematics. It presents completely unforeseen results that are of a dramatic; even magical; nature. This invaluable book will convey to the student its excitement and extraordinary character. The exposition is organized in an especially efficient manner; presenting basic complex analysis in around 130 pages; with about 50 exercises. The material constantly relates to and contrasts with that of its sister subject; real analysis. An unusual feature of this book is a short final chapter containing applications of complex analysis to Lie theory.Since much of the content originated in a one-semester course given at the CUNY Graduate Center; the text will be very suitable for first year graduate students in mathematics who want to learn the basics of this important subject. For advanced undergraduates; there is enough material for a year-long course or; by concentrating on the first three chapters; for one-semester course.

Complex Analysis 2

Author : Eberhard Freitag
File Size : 76.91 MB
Format : PDF, ePub
Download : 818
Read : 1202
Download »
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: with the exception of some basic facts which can be found in the ̄rst volume. There is no comparable treatment in the literature.

Functions of One Complex Variable I

Author : John B. Conway
File Size : 37.70 MB
Format : PDF, Kindle
Download : 896
Read : 404
Download »
This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - 8 arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.

Elementary Theory of Analytic Functions of One or Several Complex Variables

Author : Henri Cartan
File Size : 74.59 MB
Format : PDF, Mobi
Download : 146
Read : 1292
Download »
Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.

Concise Complex Analysis

Author : Sheng Gong
File Size : 58.88 MB
Format : PDF, ePub
Download : 280
Read : 906
Download »
"This is a concise textbook of complex analysis for undergraduate and graduate students. Written from the viewpoint of modern mathematics - the d-equation, differential geometry, Lie group, etc. it contains all the traditional material on complex analysis. However, many statement and proofs of classical theorems in complex analysis have been made simpler, shorter and more elegant due to modern mathematical ideas and methods. For example, the Mittag-Leffer theorem is proved by the d-equation, the Picard theorem is proved using the methods of differential geometry, and so on."--BOOK JACKET.

Introduction to Complex Analysis in Several Variables

Author : Volker Scheidemann
File Size : 44.76 MB
Format : PDF, Kindle
Download : 586
Read : 1281
Download »
This book provides a comprehensive introduction to complex analysis in several variables. One major focus of the book is extension phenomena alien to the one-dimensional theory (Hartog's Kugelsatz, theorem of Cartan-Thullen, Bochner's theorem). The book primarily aims at students starting to work in the field of complex analysis in several variables and teachers who want to prepare a university lecture. Therefore, the book contains more than 50 examples and more than 100 supporting exercises.

Analysis of Several Complex Variables

Author : Takeo Ohsawa
File Size : 41.47 MB
Format : PDF
Download : 671
Read : 249
Download »
The latest in a growing list of good student-oriented titles representing translations of top Japanese mathematics; packaged in convenient softcover and reasonably priced; this title makes a fine supplementary text for a course on analysis.

Applied Complex Variables

Author : John W. Dettman
File Size : 66.9 MB
Format : PDF, ePub, Docs
Download : 280
Read : 886
Download »
Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.

Complex Variables

Author : Carlos A. Berenstein
File Size : 86.65 MB
Format : PDF, Docs
Download : 378
Read : 1228
Download »
This text gives an overview of the basic properties of holomorphic functions of one complex variable. Topics studied in this overview include a detailed description of differential forms, homotopy theory, and homology theory, as the analytic properties of holomorphic functions, the solvability of the inhomogeneous Cauchy-Riemann equation with emphasis on the notation of compact families, the theory of growth of subharmonic functions, and an introduction to the theory of sheaves, covering spaces and Riemann surfaces. To further illuminate the material, a large number of exercises of differing levels of difficulty have been added.

Complex Analysis

Author : Man Wah Wong
File Size : 51.70 MB
Format : PDF, Mobi
Download : 910
Read : 555
Download »
This book is ideal for a one-semester course for advanced undergraduate students and first-year graduate students in mathematics. It is a straightforward and coherent account of a body of knowledge in complex analysis, from complex numbers to Cauchy's integral theorems and formulas to more advanced topics such as automorphism groups, the Schwarz problem in partial differential equations, and boundary behavior of harmonic functions.The book covers a wide range of topics, from the most basic complex numbers to those that underpin current research on some aspects of analysis and partial differential equations. The novelty of this book lies in its choice of topics, genesis of presentation, and lucidity of exposition.

Holomorphic Operator Functions of One Variable and Applications

Author : Israel Gohberg
File Size : 31.50 MB
Format : PDF, ePub
Download : 986
Read : 632
Download »
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 complex analysis of several variables.

Complex Analysis with MATHEMATICA

Author : William T. Shaw
File Size : 76.54 MB
Format : PDF
Download : 525
Read : 499
Download »
This book presents a way of learning complex analysis, using Mathematica. Includes CD with electronic version of the book.

A Course in Complex Analysis

Author : Wolfgang Fischer
File Size : 57.31 MB
Format : PDF, ePub, Docs
Download : 228
Read : 1208
Download »
This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions (elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem ...) and – a new feature in this context! – to exhibiting basic facts in the theory of several complex variables. Part of the book is a translation of the authors’ German text “Einführung in die komplexe Analysis”; some material was added from the by now almost “classical” text “Funktionentheorie” written by the authors, and a few paragraphs were newly written for special use in a master’s programme.

Complex Analysis

Author : Serge Lang
File Size : 53.15 MB
Format : PDF, Kindle
Download : 865
Read : 349
Download »
The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. The first half, more or less, can be used for a one-semester course addressed to undergraduates. The second half can be used for a second semester, at either level. Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra read ing material for students on their own. A large number of routine exer cises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recommend to anyone to look through them. More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues.

Function Theory of One Complex Variable

Author : Robert Everist Greene
File Size : 64.45 MB
Format : PDF
Download : 415
Read : 1009
Download »
Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples and exercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel. The authors also treat $H^p$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.

Pseudo Differential Operators Complex Analysis and Partial Differential Equations

Author : Bert-Wolfgang Schulze
File Size : 84.61 MB
Format : PDF, Kindle
Download : 752
Read : 239
Download »
Consists of the expository paper based on the 6-hour minicourse given by Professor Bert-Wolfgang Schulze, and sixteen papers based on lectures given at the workshop and on invitations.

Harmonic and Complex Analysis in Several Variables

Author : Steven G. Krantz
File Size : 68.83 MB
Format : PDF, ePub, Docs
Download : 893
Read : 728
Download »
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 analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.

Carleman s Formulas in Complex Analysis

Author : L.A. Aizenberg
File Size : 21.70 MB
Format : PDF, ePub, Docs
Download : 315
Read : 1263
Download »
Integral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)). They solve the classical problem of recovering at the points of a do main D a holomorphic function that is sufficiently well-behaved when approaching the boundary aD, from its values on aD or on S. Alongside with this classical problem, it is possible and natural to consider the following one: to recover the holomorphic function in D from its values on some set MeaD not containing S. Of course, M is to be a set of uniqueness for the class of holomorphic functions under consideration (for example, for the functions continuous in D or belonging to the Hardy class HP(D), p ~ 1).

Complex Analysis

Author : Jane P. Gilman
File Size : 87.30 MB
Format : PDF, Mobi
Download : 375
Read : 774
Download »
Organizing the basic material of complex analysis in a unique manner, the authors of this versatile book aim is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician.