Average customer rating:
- A wonderful book
- Very thorough, very challenging exercises.
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Classical Complex Analysis (Jones and Bartlett Books in Mathematics and Computer Science)
Liang-Shin Hahn , and
Bernard Epstein
Manufacturer: Jones & Bartlett Publishers
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Binding: Hardcover
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ASIN: 086720494X |
Customer Reviews:
A wonderful book.......2007-04-27
For me this text is a joy and a delight. In the preface the authors remark that to acquire a thorough grasp of the subject requires hard work They assert the virtues of this book to be clarity of presentation, selection of topics, and interesting exercises. They express their hope that the book will help the student to become as enthusiastic about the subject as the authors are. In my case they achieve their goals.
Very many years ago I took complex analysis in grad school using the then-recent text by Ahlfors, and with a 100% Teutonic professor; I then found the subject boring. This book, however makes me enthusiastic. It is one of the few math texts I own that I like for bedtime reading, opening it to something of interest, or just to a random section or some exercises, and relaxing while reading as if it were an adventure novel. When I put it down, consequences trickle through my mind as I go to sleep. No, it's not an easy subject, but the authors make it an enthralling one, at least for me.
Very thorough, very challenging exercises........2006-06-16
This is not the easiest book on complex analysis to read, but nevertheless I really like it. If I had to use one word to describe it, it would be thorough. I have not read much beyond the first half of it, so my comments do not apply to the more advanced chapters.
The prose is sometimes clear, but at times you have to think very hard to get through it. Although there are a number of diagrams, I do not find them particularly helpful. The book does not move too fast, it actually moves quite slowly, but it explores a lot--it is very thorough.
This book has a ton of exercises, and some of them are very hard and very deep. I think the exercises are the best part of this book. This book makes me realize that a lot of other complex analysis textbooks do not have enough exercises, especially challenging ones. My favourite part are the exercises that explore counterexamples to converses of theorems. There are also a lot of great exercises involving infinite series.
I think this book would be most appropriate to someone who had already taken an undergraduate course in complex analysis and was taking a more advanced graduate course, or wanted to enrich their understanding on their own. This is a study text, not a reference text; it is ideal for learning and challenging a student. It is not concise, and it is harder to follow than the books by Lang, Newman & Bak, or Gamelin. However, I am convinced that someone reading this book would reach a deeper understanding of the subject than someone reading any of those other books.
Book Description
From the reviews: "This huge book written in several years by one of the few mathematicians able to do it, appears as a precise and impressive study (not very easy to read) of this bothsided question that replaces, in a coherent way, without being encyclopaedic, a large library of books and papers scattered without a uniform language. Instead of summarizing the author gives his own way of exposition with original complements. This requires no preliminary knowledge. ...The purpose which the author explains in his introduction, i.e. a deep probabilistic interpretation of potential theory and a link between two great theories, appears fulfilled in a masterly manner".M. Brelot in Metrika (1986)
Book Description
This book is an ideal text for an advanced course in the theory of complex functions. The author leads the reader to experience function theory personally and to participate in the work of the creative mathematician. The book contains numerous glimpses of the function theory of several complex variables, which illustrate how autonomous this discipline has become. Topics covered include Weierstrass's product theorem, Mittag-Leffler's theorem, the Riemann mapping theorem, and Runge's theorems on approximation of analytic functions. In addition to these standard topics, the reader will find Eisenstein's proof of Euler's product formula for the sine function; Wielandt's uniqueness theorem for the gamma function; a detailed discussion of Stirling's formula; Iss'sa's theorem; Besse's proof that all domains in C are domains of holomorphy; Wedderburn's lemma and the ideal theory of rings of holomorphic functions; Estermann's proofs of the overconvergence theorem and Bloch's theorem; a holomorphic imbedding of the unit disc in C3; and Gauss's expert opinion of November 1851 on Riemann's dissertation. Remmert elegantly presents the material in short clear sections, with compact proofs and historical comments interwoven throughout the text. The abundance of examples, exercises, and historical remarks, as well as the extensive bibliography, will make this book an invaluable source for students and teachers.
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Classical Potential Theory (Springer Monographs in Mathematics)
David H. Armitage , and
Stephen J. Gardiner
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover
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ASIN: 1852336188 |
Book Description
From its origins in Newtonian physics, potential theory has developed into a major field of mathematical research. This book provides a comprehensive treatment of classical potential theory: it covers harmonic and subharmonic functions, maximum principles, polynomial expansions, Green functions, potentials and capacity, the Dirichlet problem and boundary integral representations. The first six chapters deal concretely with the basic theory, and include exercises. The final three chapters are more advanced and treat topological ideas specifically created for potential theory, such as the fine topology, the Martin boundary and minimal thinness.
The presentation is largely self-contained and is accessible to graduate students, the only prerequisites being a reasonable grounding in analysis and several variables calculus, and a first course in measure theory. The book will prove an essential reference to all those with an interest in potential theory and its applications.
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An Introduction to Complex Analysis: Classical and Modern Approaches (Modern Analysis Series)
Wolfgang Tutschke , and
Harkrishan L. Vasudeva
Manufacturer: Chapman & Hall/CRC
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Binding: Hardcover
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ASIN: 1584884789 |
Book Description
Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole. To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison. Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.
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Analysis of Complex Nonlinear Mechanical Systems: A Computer Algebra Assisted Approach
Martin Lesser
Manufacturer: World Scientific Pub Co Inc
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Binding: Paperback
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ASIN: 9810234775 |
Book Description
The book covers the fundamentals of the mechanics of multibody systems, i.e., systems of interconnected rigid bodies. A geometric view is emphasized in which the techniques and algorithms are motivated by the picture of the rigid body system as a point in the multidimensional space of all possible configurations. The reader is introduced to computer algebra methods in the form of a system, called Sophia, which is implemented in the Maple symbolic manipulation system. The first chapter provides a motivational introduction to the basic principles and an introduction to Maple. Kinematics based on the idea of tangent vectors to the configuration manifold sets the stage for dynamical analysis. The latter ranges from the Lagrange and Gibbs-Appell to Kane's equations. Coverage includes nonholonomic systems and redundant variable methods. The computer algebra methods included enable the treatment of nontrivial mechanical systems and the development of efficient numerical codes for simulation.
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Classical Complex Analysis (Pure and Applied Mathematics)
Mario O. Gonzalez
Manufacturer: Marcel Dekker
ProductGroup: Book
Binding: Hardcover
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ASIN: 0824784154 |
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Complex Analysis: Fundamentals of the Classical Theory of Functions
John Stalker
Manufacturer: Birkhäuser Boston
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ASIN: 081764038X |
Book Description
Complex Dynamics discusses the properties of conformal mappings in the complex plane, a subject that is closely connected to the study of fractals and chaos. Indeed the culmination of the book is a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. The book focuses on the analytic side of this contemporary subject. The text was developed out of a course taught over several semesters; its focus is to help students and instructors to familiarize themselves with complex dynamics. Topics covered include: conformal and quasi-conformal mappings, fixed points and conjugations, basic rational iteration (the Julia set), classification of periodic components, critical points and expanding maps, some applications of conformal mappings (e.g. Hermann rings), the local geometry of the Fatou set, and quadratic polynomials and the Mandelbrot set.
Customer Reviews:
My letter to Dr. Pickover about this book:.......1999-12-09
I got the Complex Dynamics book that Dr. McMullen recommended and I linked last to Amazon.com : there is no mention of programming anywhere in the book! It is Ivory tower math that enshrines the " Julia set" as perfect mathematics, ha, ha... Since I have used IFS to simulate Julia sets experimentally, I can say that I have a hard time recognizing it in their language! Something is dreadfully wrong in this axiomatic approach that ignores the actual math that is calculated and it's methods! The thesis on Herman's rings by the Dane is as good a complex dynamics text as this one and he actually defines terms like quasicomformal in Riemannian terms so that it can be understood! There is a real need for better bridging books between graduate level axiomatic approaches and beginning complex variables and programming! It should probably not be written by a professor type who will be forced to bend to " peers" in his use of language. Definition of terms and glossaries are so sadly missing in so many of these books!
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Complex Motion: First International Workshop, IWCM 2004, Günzburg, Germany, October 12-14, 2004, Revised Papers (Lecture Notes in Computer Science)
Manufacturer: Springer
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Binding: Paperback
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ASIN: 3540698647 |
Book Description
This book constitutes the thoroughly refereed post-proceedings of the First International Workshop on Complex Motion, IWCM 2004, held in Schloss Reisensburg, Günzburg, Germany, in October 2004.
The 17 full papers presented are fully revised to incorporate reviewers' comments and discussions at the workshop. The topics of presentations were optical flow, local motion estimation for image signals affected by strong disturbances, structure from motion, multicamera flow analysis, dynamic stereo, fluid motion analysis, furthermore the estimation of multiple motions, motion tracking, and many other areas where complex visual motion patterns have to be evaluated.
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Written over the course of Leskov’s career, each story in
The Enchanted Wanderer elucidates the very essence of the human condition; themes of love, despair, loneliness, and revenge are explored against the backdrop of nineteenth-century working-class Russia. Leskov deftly layers social satire and subtle criticism atop myth and fable, resulting in a richly entertaining collection.
Books:
- Classical Many-Body Problems Amenable to Exact Treatments: (Solvable and/or Integrable and/or Linearizable...) in One-, Two- and Three-Dimensional Space (Lecture Notes in Physics)
- Computational and Ambient Intelligence: 9th International Work-Conference on Artificial Neural Networks, IWANN 2007, San Sebastián, Spain, June 20-22, ... Science) (Lecture Notes in Computer Science)
- Computational Methods in Process Simulation
- Computational Methods in Statistics and Econometrics (Statistics: a Series of Textbooks and Monogrphs)
- Convex Analysis (Princeton Landmarks in Mathematics and Physics)
- Design Theory (Encyclopedia of Mathematics and its Applications)
- Diffraction by an Immersed Elastic Wedge
- Discrete Event Systems: Modeling and Performance Analysis (The Aksen Associates Series in Electrical and Computer Engineering)
- Dynamic Economics: Quantitative Methods and Applications
- Dynamic Modelling of Gas Turbines: Identification, Simulation, Condition Monitoring and Optimal Control (Advances in Industrial Control)
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