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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis

Problems and Solutions for Complex Analysis (Paperback, 1999 ed.): Rami Shakarchi Problems and Solutions for Complex Analysis (Paperback, 1999 ed.)
Rami Shakarchi
R2,320 Discovery Miles 23 200 Ships in 10 - 15 working days

All the exercises plus their solutions for Serge Lang's fourth edition of "Complex Analysis," ISBN 0-387-98592-1. The problems in the first 8 chapters are suitable for an introductory course at undergraduate level and cover power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, and harmonic functions. The material in the remaining 8 chapters is more advanced, with problems on Schwartz reflection, analytic continuation, Jensen's formula, the Phragmen-Lindeloef theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and Zeta function. Also beneficial for anyone interested in learning complex analysis.

Complexity - Hierarchical Structures and Scaling in Physics (Paperback, Revised): Remo Badii, Antonio Politi Complexity - Hierarchical Structures and Scaling in Physics (Paperback, Revised)
Remo Badii, Antonio Politi
R1,950 Discovery Miles 19 500 Ships in 12 - 19 working days

This is a comprehensive discussion of complexity as it arises in physical, chemical and biological systems, as well as in mathematical models of nature. The aim of this book is to illustrate the ways in which complexity manifests itself and to introduce a sequence of increasingly sharp mathematical methods for the classification of complex behavior. This book will be of interest to graduate students and researchers in physics (nonlinear dynamics, fluid dynamics, solid-state, cellular automata, stochastic processes, statistical mechanics and thermodynamics), mathematics (dynamical systems, ergodic and probability theory), information and computer science (coding, information theory and algorithmic complexity), electrical engineering and theoretical biology.

Introduction to Complex Analysis (Paperback, Softcover reprint of the original 1st ed. 1997): E.M. Chirka Introduction to Complex Analysis (Paperback, Softcover reprint of the original 1st ed. 1997)
E.M. Chirka; Edited by A.G. Vitushkin; P. Dolbeault, G. M. Khenkin, A.G. Vitushkin
R1,673 Discovery Miles 16 730 Ships in 10 - 15 working days

From the reviews: "... In sum, the volume under review is the first quarter of an important work that surveys an active branch of modern mathematics. Some of the individual articles are reminiscent in style of the early volumes of the first Ergebnisse series and will probably prove to be equally useful as a reference; ...for the appropriate reader, they will be valuable sources of information about modern complex analysis." Bulletin of the Am.Math.Society, 1991"... This remarkable book has a helpfully informal style, abundant motivation, outlined proofs followed by precise references, and an extensive bibliography; it will be an invaluable reference and a companion to modern courses on several complex variables." ZAMP, Zeitschrift für Angewandte Mathematik und Physik, 1990

Fourier Restriction, Decoupling, and Applications (Hardcover): Ciprian Demeter Fourier Restriction, Decoupling, and Applications (Hardcover)
Ciprian Demeter
R1,799 Discovery Miles 17 990 Ships in 12 - 19 working days

The last fifteen years have seen a flurry of exciting developments in Fourier restriction theory, leading to significant new applications in diverse fields. This timely text brings the reader from the classical results to state-of-the-art advances in multilinear restriction theory, the Bourgain-Guth induction on scales and the polynomial method. Also discussed in the second part are decoupling for curved manifolds and a wide variety of applications in geometric analysis, PDEs (Strichartz estimates on tori, local smoothing for the wave equation) and number theory (exponential sum estimates and the proof of the Main Conjecture for Vinogradov's Mean Value Theorem). More than 100 exercises in the text help reinforce these important but often difficult ideas, making it suitable for graduate students as well as specialists. Written by an author at the forefront of the modern theory, this book will be of interest to everybody working in harmonic analysis.

Potential Theory in the Complex Plane (Hardcover): Thomas Ransford Potential Theory in the Complex Plane (Hardcover)
Thomas Ransford
R3,698 Discovery Miles 36 980 Ships in 12 - 19 working days

Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, harmonic measure, Green's functions, potentials and capacity. This is an introduction to the subject suitable for beginning graduate students, concentrating on the important case of two dimensions. This permits a simpler treatment than other books, yet is still sufficient for a wide range of applications to complex analysis; these include Picard's theorem, the Phragmen-Lindeloef principle, the Koebe one-quarter mapping theorem and a sharp quantitative form of Runge's theorem. In addition there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics, and gives a flavour of some recent research. Exercises are provided throughout, enabling the book to be used with advanced courses on complex analysis or potential theory.

Potential Theory in the Complex Plane (Paperback, New): Thomas Ransford Potential Theory in the Complex Plane (Paperback, New)
Thomas Ransford
R1,655 Discovery Miles 16 550 Ships in 12 - 19 working days

Ransford provides an introduction to the subject, concentrating on the important case of two dimensions, and emphasizing its links with complex analysis. This is reflected in the large number of applications, which include Picard's theorem, the Phragmén-Lindelöf principle, the Radó-Stout theorem, Lindelöf's theory of asymptotic values, the Riemann mapping theorem (including continuity at the boundary), the Koebe one-quarter theorem, Hilbert's lemniscate theorem, and the sharp quantitative form of Runge's theorem. In addition, there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics and gives a flavor of some recent research in the area.

An Introduction to the Theory of the Riemann Zeta-Function (Paperback, New Ed): S. J. Patterson An Introduction to the Theory of the Riemann Zeta-Function (Paperback, New Ed)
S. J. Patterson
R1,620 Discovery Miles 16 200 Ships in 12 - 19 working days

This is a modern introduction to the analytic techniques used in the investigation of zeta-function. Riemann introduced this function in connection with his study of prime numbers, and from this has developed the subject of analytic number theory. Since then, many other classes of "zeta-function" have been introduced and they are now some of the most intensively studied objects in number theory. Professor Patterson has emphasized central ideas of broad application, avoiding technical results and the customary function-theoretic approach.

Invariant Potential Theory in the Unit Ball of Cn (Paperback): Manfred Stoll Invariant Potential Theory in the Unit Ball of Cn (Paperback)
Manfred Stoll
R1,358 Discovery Miles 13 580 Ships in 10 - 15 working days

This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegoe integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables.

Visual Complex Analysis - 25th Anniversary Edition (Hardcover): Tristan Needham Visual Complex Analysis - 25th Anniversary Edition (Hardcover)
Tristan Needham; Foreword by Roger Penrose
R4,258 Discovery Miles 42 580 Ships in 12 - 19 working days

Complex Analysis is the powerful fusion of the complex numbers (involving the 'imaginary' square root of -1) with ordinary calculus, resulting in a tool that has been of central importance to science for more than 200 years. This book brings this majestic and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. The 501 diagrams of the original edition embodied geometrical arguments that (for the first time) replaced the long and often opaque computations of the standard approach, in force for the previous 200 years, providing direct, intuitive, visual access to the underlying mathematical reality. This new 25th Anniversary Edition introduces brand-new captions that fully explain the geometrical reasoning, making it possible to read the work in an entirely new way—as a highbrow comic book!

The Ergodic Theory of Discrete Groups (Paperback): Peter J. Nicholls The Ergodic Theory of Discrete Groups (Paperback)
Peter J. Nicholls
R2,133 Discovery Miles 21 330 Ships in 10 - 15 working days

The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. There has been a great resurgence of interest in the field, due in large measure to the pioneering work of Dennis Sullivan. Tools have been developed and applied with outstanding success to many deep problems. The ergodic theory of discrete groups has become a substantial field of mathematical research in its own right, and it is the aim of this book to provide a rigorous introduction from first principles to some of the major aspects of the theory. The particular focus of the book is on the remarkable measure supported on the limit set of a discrete group that was first developed by S. J. Patterson for Fuchsian groups, and later extended and refined by Sullivan.

Introduction to Complex Analysis (Hardcover, 2nd Revised edition): Rolf Nevalinna, Veikko Paatero Introduction to Complex Analysis (Hardcover, 2nd Revised edition)
Rolf Nevalinna, Veikko Paatero
R1,906 Discovery Miles 19 060 Ships in 12 - 19 working days

It really is a gem, both in terms of its table of contents and the level of discussion. The exercises also look very good. --Clifford Earle, Cornell University This book has a soul and has passion. --William Abikoff, University of Connecticut This classic book gives an excellent presentation of topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem. The two quotes above confirm that the book can be successfully used as a text for a class or for self-study.

Operator Theory by Example (Hardcover): Stephan Ramon Garcia, Javad Mashreghi, William T Ross Operator Theory by Example (Hardcover)
Stephan Ramon Garcia, Javad Mashreghi, William T Ross
R3,235 Discovery Miles 32 350 Ships in 12 - 19 working days

Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator. The text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well-researched historical facts which place each chapter within the broader context of the development of the field as a whole.

Functions of Several Complex Variables and Their Singularities (Hardcover, Illustrated Ed): Functions of Several Complex Variables and Their Singularities (Hardcover, Illustrated Ed)
R2,642 Discovery Miles 26 420 Ships in 12 - 19 working days

The book provides an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. The topics include Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, fundamentals of differential topology, and the topology of singularities. The aim of the book is to guide the reader from the fundamentals to more advanced topics of recent research. All the necessary prerequisites are specified and carefully explained. The general theory is illustrated by various examples and applications.

Complex Functions - An Algebraic and Geometric Viewpoint (Paperback): Gareth A. Jones, David Singerman Complex Functions - An Algebraic and Geometric Viewpoint (Paperback)
Gareth A. Jones, David Singerman
R1,901 Discovery Miles 19 010 Ships in 12 - 19 working days

An elementary account of many aspects of classical complex function theory, including Mobius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. The book is based on lectures given to advanced undergraduate students and is well suited as a textbook for a second course in complex function theory.

Several Complex Variables and Complex Manifolds II (Paperback): Mike Field Several Complex Variables and Complex Manifolds II (Paperback)
Mike Field
R1,499 Discovery Miles 14 990 Ships in 10 - 15 working days

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.

Computer-Aided Verification of Coordinating Processes - The Automata-Theoretic Approach (Paperback): Robert P. Kurshan Computer-Aided Verification of Coordinating Processes - The Automata-Theoretic Approach (Paperback)
Robert P. Kurshan
R1,856 Discovery Miles 18 560 Ships in 10 - 15 working days

Formal verification increasingly has become recognized as an answer to the problem of how to create ever more complex control systems, which nonetheless are required to behave reliably. To be acceptable in an industrial setting, formal verification must be highly algorithmic; to cope with design complexity, it must support a top-down design methodology that leads from an abstract design to its detailed implementation. That combination of requirements points directly to the widely recognized solution of automata-theoretic verification, on account of its expressiveness, computational complexity, and perhaps general utility as well.

This book develops the theory of automata-theoretic verification from its foundations, with a focus on algorithms and heuristics to reduce the computational complexity of analysis. It is suitable as a text for a one-or two-semester graduate course, and is recommended reading for anyone planning to use a verification tool, such as COSPAN or SMV. An extensive bibliography that points to the most recent sources, and extensive discussions of methodology and comparisons with other techniques, make this a useful resource for research or verification tool development, as well.

Originally published in 1995.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Orthogonal Polynomials and Random Matrices - A Riemann-Hilbert Approach (Paperback, UK ed.): Orthogonal Polynomials and Random Matrices - A Riemann-Hilbert Approach (Paperback, UK ed.)
R1,172 Discovery Miles 11 720 Ships in 12 - 19 working days

This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random $n {\times} n$ matrices exhibit universal behavior as $n {\rightarrow} {\infty}$? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.

Complex Geometry - Collection of Papers Dedicated to Hans Grauert (Paperback, Softcover reprint of the original 1st ed. 2002):... Complex Geometry - Collection of Papers Dedicated to Hans Grauert (Paperback, Softcover reprint of the original 1st ed. 2002)
Ingrid Bauer, F. Catanese, Y. Kawamata, Thomas Peternell, Y.-T. Siu
R3,043 Discovery Miles 30 430 Ships in 10 - 15 working days

This volume contains a collection of research papers dedicated to Hans Grauert on the occasion of his seventieth birthday. Hans Grauert is a pioneer in modern complex analysis, continuing the il lustrious German tradition in function theory of several complex variables of Weierstrass, Behnke, Thullen, Stein, Siegel, and many others. When Grauert came on the scene in the early 1950's, function theory was going through a revolutionary period with the geometric theory of complex spaces still in its embryonic stage. A rich theory evolved with the joint efforts of many great mathematicians including Oka, Kodaira, Cartan, and Serre. The Car tan Seminar in Paris and the Kodaira Seminar provided important venues an for its development. Grauert, together with Andreotti and Remmert, took active part in the latter. In his career he has nurtured a great number of his own doctoral students as well as other young mathematicians in his field from allover the world. For a couple of decades his work blazed the trail and set the research agenda in several complex variables worldwide. Among his many fundamentally important contributions, which are too numerous to completely enumerate here, are: 1. The complete clarification of various notions of complex spaces. 2. The solution of the general Levi problem and his work on pseudo convexity for general manifolds. 3. The theory of exceptional analytic sets. 4. The Oka principle for holomorphic bundles. 5. The proof of the Mordell conjecture for function fields. 6. The direct image theorem for coherent sheaves."

Air Force Capability Development Planning - Analytical Methods to Support Investment Decisions (Paperback): James A. Leftwich,... Air Force Capability Development Planning - Analytical Methods to Support Investment Decisions (Paperback)
James A. Leftwich, Debra Knopman, Jordan R Fischbach
R670 R476 Discovery Miles 4 760 Save R194 (29%) Ships in 9 - 17 working days
Elements of the Theory of Elliptic Functions (Paperback, New edition): N. I. Akhiezer Elements of the Theory of Elliptic Functions (Paperback, New edition)
N. I. Akhiezer
R4,437 Discovery Miles 44 370 Ships in 12 - 19 working days

This book contains a systematic presentation of the theory of elliptic functions and some of its applications. A translation from the Russian, this book is intended primarily for engineers who work with elliptic functions. It should be accessible to those with background in the elements of mathematical analysis and the theory of functions contained in approximately the first two years of mathematics and physics courses at the college level.

Dynamics in One Complex Variable. (AM-160) - (AM-160) - Third Edition (Paperback, 3rd Revised edition): John Milnor Dynamics in One Complex Variable. (AM-160) - (AM-160) - Third Edition (Paperback, 3rd Revised edition)
John Milnor
R2,025 Discovery Miles 20 250 Ships in 12 - 19 working days

This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattes map has been made more inclusive, and the ecalle-Voronin theory of parabolic points is described. The residu iteratif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated.

Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field."

Hardy Spaces (Hardcover): Nikolai Nikolski Hardy Spaces (Hardcover)
Nikolai Nikolski; Translated by Daniele Gibbons, Greg Gibbons
R1,882 Discovery Miles 18 820 Ships in 12 - 19 working days

The theory of Hardy spaces is a cornerstone of modern analysis. It combines techniques from functional analysis, the theory of analytic functions and Lesbesgue integration to create a powerful tool for many applications, pure and applied, from signal processing and Fourier analysis to maximum modulus principles and the Riemann zeta function. This book, aimed at beginning graduate students, introduces and develops the classical results on Hardy spaces and applies them to fundamental concrete problems in analysis. The results are illustrated with numerous solved exercises that also introduce subsidiary topics and recent developments. The reader's understanding of the current state of the field, as well as its history, are further aided by engaging accounts of important contributors and by the surveys of recent advances (with commented reference lists) that end each chapter. Such broad coverage makes this book the ideal source on Hardy spaces.

Real Submanifolds in Complex Space and Their Mappings (PMS-47) (Hardcover): M.Salah Baouendi, Peter Ebenfelt, Linda Preiss... Real Submanifolds in Complex Space and Their Mappings (PMS-47) (Hardcover)
M.Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild
R4,652 Discovery Miles 46 520 Ships in 10 - 15 working days

This book presents many of the main developments of the past two decades in the study of real submanifolds in complex space, providing crucial background material for researchers and advanced graduate students. The techniques in this area borrow from real and complex analysis and partial differential equations, as well as from differential, algebraic, and analytical geometry. In turn, these latter areas have been enriched over the years by the study of problems in several complex variables addressed here. The authors, M. Salah Baouendi, Peter Ebenfelt, and Linda Preiss Rothschild, include extensive preliminary material to make the book accessible to nonspecialists.

One of the most important topics that the authors address here is the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on real submanifolds. They present the main results in this area with a novel and self-contained approach. The book also devotes considerable attention to the study of holomorphic mappings between real submanifolds, and proves finite determination of such mappings by their jets under some optimal assumptions. The authors also give a thorough comparison of the various nondegeneracy conditions for manifolds and mappings and present new geometric interpretations of these conditions. Throughout the book, Cauchy-Riemann vector fields and their orbits play a central role and are presented in a setting that is both general and elementary.

Arbeitsbuch Mathematik - Aufgaben, Hinweise, Loesungen und Loesungswege (German, Paperback, 5. Aufl. 2022): Tilo Arens, Frank... Arbeitsbuch Mathematik - Aufgaben, Hinweise, Loesungen und Loesungswege (German, Paperback, 5. Aufl. 2022)
Tilo Arens, Frank Hettlich, Christian Karpfinger, Ulrich Kockelkorn, Klaus Lichtenegger, …
R1,477 Discovery Miles 14 770 Ships in 10 - 15 working days

Dieses Arbeitsbuch enthalt die Aufgaben, Hinweise, Loesungen und Loesungswege zu allen sechs Teilen des Lehrbuchs Arens et al., Mathematik. Die Inhalte des Buchs stehen als PDF-Dateien auf der Website des Verlags zur Verfugung. Durch die stufenweise Offenlegung der Loesungen ist das Werk bestens geeignet zum Selbststudium, zur Vorlesungsbegleitung und als Prufungsvorbereitung. Inhaltlich spannt sich der Bogen von elementaren Grundlagen uber die Analysis einer Veranderlichen, der linearen Algebra, der Analysis mehrerer Veranderlicher bis hin zu fortgeschrittenen Themen der Analysis, die fur die Anwendung besonders wichtig sind, wie partielle Differenzialgleichungen, Fourierreihen und Laplacetransformationen. Auch eine Vielzahl von Aufgaben zur Wahrscheinlichkeitsrechnung und Statistik ist enthalten.

Hidden Harmony-Geometric Fantasies - The Rise of Complex Function Theory (Hardcover, 2013 ed.): Umberto Bottazzini, Jeremy Gray Hidden Harmony-Geometric Fantasies - The Rise of Complex Function Theory (Hardcover, 2013 ed.)
Umberto Bottazzini, Jeremy Gray
R5,879 Discovery Miles 58 790 Ships in 12 - 19 working days

This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject Cauchy, Riemann, and Weierstrass it looks at the contributions of authors from d Alembert to Hilbert, and Laplace to Weyl.

Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions.

The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory. "

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