Product Description
This book is intended to serve as a text for both beginning andsecond courses in complex analysis of functions of one complexvariable. The material that is appropriate for more advanced study isdeveloped from elementary material. The concepts are illustrated withlarge numbers of examples, many of which involve problems studentsencounter in other courses. For example, students who have taken anintroductory physics course will have encountered analysis of simpleAC circuits. This text revisits such analysis using complex numbers.Cauchy's residue theorem is used to evaluate many types of definiteintegrals that students are introduced to in the beginning calculussequence. Methods of conformal mapping are used to solve problems inelectrostatics. The book contains material that is not considered inother popular complex analysis texts. For example, one chapter isdevoted to an analysis of multivalued functions, with applications tothe evaluation of certain types of integrals. Another chapter dealswith the singularity structure of functions that are defined byintegrals which cannot be evaluated in terms of elementary functions.A third chapter develops dispersion relations, which are mathematicaltools for determining a complete function from a knowledge of just thereal part, or just the imaginary part of the function. ... Read more

Customer Reviews (1)

elegant and useful theorems
The text takes you from simple complex number manipulation all the way to contour integration. Cohen draws in examples from various sciences and engineering, to illustrate the myriad usages of complex analysis.

If you are a student majoring in the physical sciences, engineering or, of course, maths, this text can be valuable in teaching the key ideas. Like residues, Laurant series, index numbers and the Residue Theorem. While some of you might at first wonder at the relevance of this to anything useful, the book's examples should disabuse you. Culminating in being able to evaluate a contour integral by finding the enclosed singularities. Elegant and beautiful. Hopefully, you will agree by the time you've gone through the book. ... Read more

Product Description
Norton's Complex Variables for Scientists and Engineers is a new textbook, originally written for the Complex Analysis term of an undergraduate Mathematical Methods of Physics sequence at UCLA. It does not assume any prior knowledge of complex numbers or functions and is therefore suitable for a first course in the subject for undergraduate students who have had an introductory course in the standard calculus of real variables.

The book provides a thorough grounding in the theory of complex functions. The mathematics is careful, yet accessible to any student who knows basic calculus. It covers the subjects essential in any scientific or engineering discipline that uses mathematics beyond the elementary level. The reader will find a clear presentation of complex differentiation and integration, Cauchy's theorem and integral formula, and infinite series and products. There is a long and thorough section on applying the residue theorem to the evaluation of real integrals, and a section on special functions and their integral representations. The book includes the conformal property of analytic functions and its applications to boundary value problems in electrostatics; a topological analysis that leads to the extension of the residue theorem to multiply-connected regions and contours; a section on the method of steepest descent; a section on the Riemann zeta function; and a discussion of the convergence of integral representations, which is rarely presented in detail in introductory texts. Those who want to see the mathematics done carefully, and who are looking for more than a 'cook-book' treatment that presents the basic techniques without exploring all the nooks and crannies of the subject, will find these sections especially satisfying. The preface suggests how to extract a bare-bones course for those in a hurry, without losing sight of the beauty and depth of the subjects. ... Read more

Product Description
The Student Study Guide consists of seven chapters which correspond to the seven chapters of A First Course in Complex Analysis with Applications, Second Edition. Each chapter includes: Review Topics, Summaries, Exercises, and Focus on Concepts Problems. Solutions to odd exercises are included. ... Read more

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The book is written for graduate students who have read the first book and like to see the proofs which were not given there and/or want to see the full extent of the theory. On the other hand it can be read independently from the first one, only a modest knowledge on Fourier series/tranform is required to understand the examples.

This book fills a major gap in the textbook literature, as a full proof of Pontryagin Duality and Plancherel Theorem is hard to come by. It is usually given in books that focus on C*-algebras and thus carry too much technical overload for the reader who only wants these basic results of Harmonic Analysis. Other proofs use the structure theory which carries the reader away in a different direction. Here the authors consider the Banach-algebra approach more elegant and enlighting. They provide a streamlined approach that reaches the main results directly, and they also give the generalizations to the non-Abelian case.

Another main pillar of Harmonic analysis is the Poisson Summation Formula. We give its generalization to LCA-groups. The Selberg Trace Formula is considered the generalization of the Poisson Formula to non-abelian groups. The authors give the first textbook approach to this deep and useful formula in full generality. The last two chapters are devoted to examples of applications of the Selberg Trace Formula.

Product Description
There is a need for more inclusive holistic approaches to identify and analyze safety-related system risks. Systems are becoming increasingly more complex, diverse, and vastly distributed. Conventional approaches of conducting hazard analyses and risk assessment do have limitations. This book addresses some of these limitations and a number of inclusive approaches are discussed, which can be applied against the limitations. The book emphasizes scenario-driven hazard analysis as a means to conduct more holistic analysis.

It discusses safety analyses of large complex systems; which are comprised of software, firmware, hardware, the human and the environment.  “System thinking” in problem solving is emphasized throughout the book. The book is comprised of three parts. The first part Risk identification covers topics including understanding risk, evaluating safety, and scenario-driven hazard analysis. The second part Risk elimination and control addresses eliminating risk and provides hazard control methods, techniques, and applications. Finally managing safety-related risks covers key concepts and observations associated with a safety management and other topics including making safety-related decisions.

At the end of each chapter there are “Questions and Topics for Further Discussion”, which enables the book to be used for graduate and undergraduate education, and specialized courses or instructional development.    ... Read more

Product Description
This textbook is an introduction to the classical theory of functions of a complex variable. The author's aim is to explain the basic theory in an easy to understand and careful way. He emphasizes geometrical considerations, and, to avoid topological difficulties associated with complex analysis, begins by deriving Cauchy's integral formula in a topologically simple case and then deduces the basic properties of continuous and differentiable functions. The remainder of the book deals with conformal mappings, analytic continuation, Riemann's mapping theorem, Riemann surfaces and analytic functions on a Riemann surface. The book is profusely illustrated and includes many examples. Problems are collected together at the end of the book. It should be an ideal text for either a first course in complex analysis or more advanced study. ... Read more

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The seventh edition of this classic text has retained the features that make it popular, while updating its treatment and inclusion of Computer Algebra Systems and Programming Languages. Interesting and timely applications motivate and enhance readers' understanding of methods and analysis of results. This text incorporates a balance of theory with techniques and applications, including optional theory-based sections in each chapter. The exercise sets include additional challenging problems and projects which show practical applications of the material. Also, sections which discuss the use of computer algebra systems such as Maple®, Mathematica®, and MATLAB®, facilitate the integration of technology in the course. Furthermore, the text incorporates programming material in both FORTRAN and C. The breadth of topics, such as partial differential equations, systems of nonlinear equations, and matrix algebra, provide comprehensive and flexible coverage of all aspects of numerical analysis.

Preliminaries; Solving Nonlinear Equations; Solving Sets of Equations; Interpolation and Curve Fitting; Approximation of Functions; Numerical Differentiation and Integration; Numerical Solution of Ordinary Differential Equations; Optimization; Partial Differential Equations; Finite Element Analysis

For all readers interested in applied numerical analysis.

Customer Reviews (12)

One of the very best numerical analysis books
I've owned a copy of this since I was an undergrad back in the late 1970's when it was just in its second edition. I haven't seen a book dedicated to the teaching of numerical analysis that explains algorithms more clearly. The authors go into great detail not just on the how's but the why's - the motivation of doing things a certain way. Strangely enough, though, the numerous mistakes just get worse with age, not better. My old original second edition printed in 1980 has relatively few errors. This seventh edition has errors to the point of distraction. If you must have this for a text you might want to also pick up a copy of the very economical Introduction to Numerical Analysis: Second Edition (Dover Books on Advanced Mathematics) by Hillebrand. It's an oldie but a goodie. If you think Gerald's text is in error look up the topic in Hillebrand and insure you understand the topic. Chances are you do and there is a numerical error in Gerald's text that contradicts your own correct understanding. Finally, any student of numerical analysis simply must have a copy of Numerical Recipes 3rd Edition: The Art of Scientific Computing. That one is more of the "give a man a fish" variety and has the source code and some explanation, but is by no means a textbook.

Oddly enough the table of contents is not included in the product description for this book, so I show that next just so you'll know what you're getting

0. Preliminaries.
Analysis versus Numerical Analysis.
Computers and Numerical Analysis.
An Illustrative Example.
Kinds of Errors in Numerical Procedures.
Interval Arithmetic.
Parallel and Distributed Computing.
Measuring the Efficiency of Procedures.
1. Solving Nonlinear Equations.
Interval Halving (Bisection).
Linear Interpolation Methods.
Newton's Method.
Muller's Method.
Fixed-Point Iteration.
Other Methods.
Nonlinear Systems.
2. Solving Sets of Equations.
Matrices and Vectors.
Elimination Methods.
The Inverse of a Matrix and Matrix Pathology.
Almost Singular Matrices - Condition Numbers.
Interactive Methods.
Parallel Processing.
3. Interpolation and Curve Fitting.
Interpolating Polynomials.
Divided Differences.
Spline Curves.
Bezier Curves and B-Splines.
Interpolating on a Surface.
Least Squares Approximations.
4. Approximation of Functions.
Chebyshev Polynomials and Chebyshev Series.
Rational Function Approximations.
Fourier Series.
5. Numerical Differentiation and Integration.
Differentiation with a Computer.
Numerical Integration - The Trapezoidal Rule.
Simpson's Rules.
An Application of Numerical Integration - Fourier Series and Fourier Transforms Adaptive Integration.
Gaussian Quadrature.
Multiple Integrals.
Applications of Cubic Splines.
6. Numerical Solution of Ordinary Differential Equations.
The Taylor Series Method.
The Euler Method and Its Modification.
Runge-Kutta Methods.
Multistep Methods.
Higher-Order Equations and Systems.
Stiff Equations.
Boundary-Value Problems.
Characteristic-Value Problems.
7. Optimization.
Finding the Minimum of y = f(x).
Minimizing a Function of Several Variables.
Linear Programming.
Nonlinear Programming.
Other Optimizations.
8. Partial Differential Equations.
Elliptic Equations.
Parabolic Equations.
Hyperbolic Equations.
9. Finite Element Analysis.
Mathematical Background.
Finite Elements for Ordinary Differential Equation.
Finite Elements for Partial Differential Equation.
Appendices.
A. Some Basic Information from Calculus.
B. Software Resources.
Answers to Selected Exercises.

poor print quality (7th ed.)
My copy (7th ed, paperback, ISBN 0321133048, bought from amazon.com) is of poor newspaper-like print quality.

The book typography uses black color and three halftones (titles, ref. numbers, chart curves, captions, example boxes), but the halftones are printed only at 85 LPI. Some figure captions are barely readable - you see only coarse black/white screen.

It really upsets me that such flagrant manufactuing defects spoils the impression of otherwise good book.

The content of the book is exactly what I looked for. You can quickly grasp the essentials about solving the nonlinear and linear sets of equations. The book style is motivating and I was quickly able to reveal some false statements about numerical effectivity of algorithms. Navigation in the book is simple, but I would prefer more detailed contents in the beginning of the each chapter - some sections (e.g. LU decomposition) are neither in general contents nor in chapter's contents.

The part on optimization is too brief. There are better introductory level books on this subject.

Pretty Darn Good
Nowadays with all the circuit and matrix computer aided systems out there, the basics of numerical methods gets overlooked.This book keeps to these fundamentals methods and is an excellent bridge between purely closed-form knowledge taught in schools and the open-form procedures quietly employed in most computer aided engineering systems.

Particularly fond of this text's discussion on boundary-value problems.

It now heads my list for potential texts in my numerical methods course
Last academic year, I taught a course in numerical analysis. It was the first time that I had the opportunity to do so and I enjoyed it very much. I do double duty as a mathematician and a computer science instructor, and this was an opportunity to simultaneously exercise both skills. Since I will probably be teaching it again next academic year, I examined this book as a possible text for the course.
I was impressed with the approach and the level of exposition. In general, two assumptions can be made concerning the background of the students. The first is that they know differential and integral calculus and the second that they have some programming experience. While the authors assume the first, they reduce the level of the second assumption. The programming exercises are in Matlab and require very little programming knowledge. There are also few actual programming examples; most of the complex algorithms are expressed in an advanced pseudocode. I am strongly in favor of this approach; most people will be using a system other than Matlab.
There are many exercises at the end of the chapters and the solutions to many of them are included in an appendix. A set of problems called "Applied problems and projects" is also included at the end of each chapter. These are more complex problems that are on the level of significant programming projects. They also are truly real world problems, dealing with topics such as interest computations, solving solution problems, solving differential equations numerically and the history of mathematics. If you regularly give such problems in your numerical methods class, then you will love these sections.
The breadth of coverage is sufficient so that a two-semester sequence could be taught using this book. The chapter headings are:

*) Preliminaries
*) Solving nonlinear equations
*) Solving sets of equations
*) Interpolation and curve fitting
*) Approximation of functions
*) Numerical differentiation and integration
*) Numerical solution of ordinary differential equations
*) Optimization
*) Partial-differential equations
*) Finite-element analysis

At this time, this book is at the top of my list of possible texts for the next time I teach numerical analysis. Since that is still at least a year away, I cannot say that I will definitely adopt it. However, barring no new and better book appearing, it will be the chosen one.

Numerous errors in text
Have to agree with earlier post, book looks nice and clear but numerous errors make actually using (vs. just browsing) the material very difficult.7th edition ADI section has numerous mislabed equations, incorrect data values, unfortunate.Suggest look elsewhere for a numerical analysis book. ... Read more

Product 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. ... Read more

Product Description
A lively and vivid look at the material from function theory, including the residue calculus, supported by examples and practice exercises throughout. There is also ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations - in the original language with their English translation - from their classical works. Yet the book is far from being a mere history of function theory, and even experts will find a few new or long forgotten gems here. Destined to accompany students making their way into this classical area of mathematics, the book offers quick access to the essential results for exam preparation. Teachers and interested mathematicians in finance, industry and science will profit from reading this again and again, and will refer back to it with pleasure. ... Read more

Customer Reviews (3)

Depends on what you use it for
In a nutshell, it is good indeed as a leisurely reading, at bedtime, as the series description suggests. It should NOT be used as a text, in my opinion.

The most important quality of a good graduate level text is usability for a qualifying exam preparation. Thus, everything should be covered in a concise manner, appropriate for late night crumming. This book is not designed for that. And, with all due respect to Goethe, Schiller, and Heine, I could not appreciate an accidental quotation from a classic when my stay in grad school was at stake.

(for the record, I passed with flying colors, only thanks to good old references by Conway and Ahlfors, however dry but perfectly readable, especially if you have a prior experience or a helpful professor)

Another point to consider: a price can be a factor for a broke grad student, so, Ahlfors will give you more stuff for your buck, especially if you are planning on taking a second semester of this amazing topic.

A good, original and solid introduction to complex functions
This is the english translation of a german textbook. Among its qualities are: very good order of subjects, a good synthesis of classical results and theorems, an open view on current research in the field, glimpses of functions of several complex variables and historical notes.

This covers all the basic material needed for a graduate in mathematics preparing him/her to read the sequel: "Classical Topics in Complex Function Theory". Same author (with Grauert), same editor.

My only regret is the relatively few exercices compared to other books, but this quite easy to find anyway in the litterature.

Most quotations are both in the original language and translated.

A goldmine!
This book is a beautiful look at classical complex analysis. At first glance it may look like it doesn't cover that much, but look carefully at the text. There are many great books on the subject, but this is one of thebest. For example, I love Alhfors, but it is a bit dry. This book however,is not dry at all. ... Read more

Product Description
This book builds upon the earlier volume Problems in Analysis, more than doubling it with a new section of problems on complex analysis. The problems on real analysis from the earlier book have all been checked, and stylistic, typographical, and mathematical errors have been corrected. The problems in complex analysis cover most of the principal topics in the theory of functions of a complex variable. The problems in the book cover, in real analysis: set algebra, measure and topology, real- and complex-valued functions, and topological vector spaces; in complex analysis: polynomials and power series, functions holomorphic in a region, entire functions, analytic continuation, singularities, harmonic functions, families of functions, and convexity theorems. ... Read more

Product Description

Presents Real & Complex Analysis Together Using a Unified Approach
A two-semester course in analysis at the advanced undergraduate or first-year graduate level

Unlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together. It takes a unified, elegant approach to the theory that is consistent with the recommendations of the MAA’s 2004 Curriculum Guide.

By presenting real and complex analysis together, the authors illustrate the connections and differences between these two branches of analysis right from the beginning. This combined development also allows for a more streamlined approach to real and complex function theory. Enhanced by more than 1,000 exercises, the text covers all the essential topics usually found in separate treatments of real analysis and complex analysis. Ancillary materials are available on the book’s website.

This book offers a unique, comprehensive presentation of both real and complex analysis. Consequently, students will no longer have to use two separate textbooks—one for real function theory and one for complex function theory.

Customer Reviews (1)

a unique collection
This nice little book by Volkovyskii et al (translated from Russian) is a collection of exercises, and it covers the central aspects of and themes in complex function theory, elementary geometry, harmonic and analytic functions. It contains graphics and illustrations, and the last third of the book consists of answers and solutions.

The central topics are (in this order) complex numbers, calculus and geometry of the plane, conformal mappings, harmonic functions, power series and analytic functions, and the standard Cauchy-and residue theorems, symmetry, Laurent series, infinite products, ending with a brief chapter on Riemann surfaces, and applications to hydrodynamics and electrostatics. All the material is presented in the form of exercises.

The book was published first in 1965, but reprinted since by Dover. It is suitable and recommended as a supplement in a standard course in complex function theory, late undergraduate level, or beginning graduate.

Of other Dover titles on the same subject we recommend the books by Flanigan, Schwerdtfeger, and Silverman. Review by Palle Jorgensen, August 5, 2006.



... Read more

Product Description
Effective for undergraduate and postgraduate students, the single-volume Complex Analysis functions as both a textbook and a reference, depending on the conducted course's structure. The only prerequisites are rudiments of real analysis and linear algebra. Special features include an integrated approach to the concept of differentiation for complex valued functions of a complex variable, unified Cauchy Riemann equations, complex versions of real intermediate value theorem, and exhaustive treatment of contour integration. The book also offers an introduction to the theory of univalent functions on the unit disc, including a brief history of the Bieberbach's conjecture and its solutions. ... Read more

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Foundations of Complex Analysis is aimed at giving students a good foundation of complex analysis and provides a basis for solving problems in mathematics, physics, engineering and many other sciences. Each chapter is supplemented with well-structured examples, and exercises with hints and outlines for solutions. This book can be used as a textbook for a two semester course in complex analysis, or as a supplementary text for an advanced course in function theory. This second edition has gone through a major revision of the 1995 edition. As far as possible many sections are made less dependent on other sections in order to ensure flexibility in designing a course content. ... Read more

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This introduction to complex variable methods begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. Throughout the text, many of the important theoretical results in complex function theory are followed by relevant and vivid examples in physical sciences. This second edition now contains 350 stimulating exercises of high quality, with solutions given to many of them. Material has been updated and additional proofs on some of the important theorems in complex function theory are now included, e.g. the Weierstrass-Casorati theorem. The book is highly suitable for students wishing to learn the elements of complex analysis in an applied context. ... Read more

Customer Reviews (1)

A complex book about complex math
I'm reading this book as part of a class in complex function theory, having had a fair amount of background in calculus and some theory in complex numbers, but never a careful analysis of complex numbers. This book provides that analysis, explaining everything you need to know about complex functions and variables for proper application.

While there are some graphs and drawings here and there, it is of course a book on math. It contains a huge amount of helpful exercises, with answers to about half of them, many of them bringing your insight beyond the text itself. That is to say, make the darn exercises, because they are what will truly get you a feeling for complex numbers (and some of them are truly great fun).

Kwok shows us the beauty of all calculus coming together in one place, and does so by applying the newly learned techniques to real physics every once in a while, where difficult problems vanish in the light of complex math.

... though I do admit this is not specific for Applied Complex Variables...

Ah yes, the book! Well, it's a work from Cambridge, which has been known for Math-based analysis of physics for centuries, and I think that says enough. I really can't think of any downsides, so if you're looking for a good introduction to Cauchy-Riemann, Taylor and Laurent series, Riemann spheres and surfaces, Bromwich integrals, conformal mappings, etcetera, why not pick up this book? ... Read more

Product 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. ... Read more

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Since their inception, Clifford algebras have been used as a mathematical tool for the description of physical phenomena. However, Clifford algebras have become an increasingly rich area of research with a significant number of important applications not only to mathematical physics, but to numerical analysis, harmonic analysis, and computer science as well. This book details: Systems of first-order linear differential equations that arise naturally in the setting of Clifford algebras; some well-known systems that play a role in electromagnetism and quantum mechanics, and others that figure prominently in harmonic analysis.