Introductory Complex Analysis (Dover Books on Mathematics) by Richard A. Silverman (PDF)

Description

Introductory Complex Analysis is a scaled-down version of A. I. Markushevich’s masterly three-volume “Theory of Functions of a Complex Variable.” Dr. Richard Silverman, the editor and translator of the original, has prepared this shorter version expressly to meet the needs of a one-year graduate or undergraduate course in complex analysis. In his selection and adaptation of the more elementary topics from the original larger work, he was guided by a brief course prepared by Markushevich himself.The book begins with fundamentals, with a definition of complex numbers, their geometric representation, their algebra, powers and roots of complex numbers, set theory as applied to complex analysis, and complex functions and sequences. The notions of proper and improper complex numbers and of infinity are fully and clearly explained, as is stereographic projection. Individual chapters then cover limits and continuity, differentiation of analytic functions, polynomials and rational functions, Mobius transformations with their circle-preserving property, exponentials and logarithms, complex integrals and the Cauchy theorem , complex series and uniform convergence, power series, Laurent series and singular points, the residue theorem and its implications, harmonic functions (a subject too often slighted in first courses in complex analysis), partial fraction expansions, conformal mapping, and analytic continuation.Elementary functions are given a more detailed treatment than is usual for a book at this level. Also, there is an extended discussion of the Schwarz-Christolfel transformation, which is particularly important for applications.There is a great abundance of worked-out examples, and over three hundred problems (some with hints and answers), making this an excellent textbook for classroom use as well as for independent study. A noteworthy feature is the fact that the parentage of this volume makes it possible for the student to pursue various advanced topics in more detail in the three-volume original, without the problem of having to adjust to a new terminology and notation .In this way, IntroductoryComplex Analysis serves as an introduction not only to the whole field of complex analysis, but also to the magnum opus of an important contemporary Russian mathematician.

User’s Reviews

Editorial Reviews: About the Author Richard A. Silverman: Dover’s Trusted Advisor Richard Silverman was the primary reviewer of our mathematics books for well over 25 years starting in the 1970s. And, as one of the preeminent translators of scientific Russian, his work also appears in our catalog in the form of his translations of essential works by many of the greatest names in Russian mathematics and physics of the twentieth century. These titles include (but are by no means limited to): Special Functions and Their Applications (Lebedev); Methods of Quantum Field Theory in Statistical Physics (Abrikosov, et al); An Introduction to the Theory of Linear Spaces, Linear Algebra, and Elementary Real and Complex Analysis (all three by Shilov); and many more. During the Silverman years, the Dover math program attained and deepened its reach and depth to a level that would not have been possible without his valuable contributions.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐While somewhat obsolescent it is a good introduction to the topic.

⭐I originally bought this text because of the low price – $10 or so for a book on Complex Analysis is a steal, given what many textbooks are, new or used. Also, the book had positive to excellent reviews on this site, so I figured that I had little to lose.As it turns out, the book was a big disappointment for me. Essentially, it is an abridged edition of a much larger work written by a prominent Russian mathematician. Hence, the organization is clear and logical, and for those who have already taken a class and are reasonably considered experts, there are many clear and fascinating interconnections. There is nothing really wrong with the development of the book, and Dr. Silverman understands the topic well.Yet, what I was looking for was something to help me to understand the class and subject, and this was where the book proved unhelpful. It is too short for the average reader to be able to appreciate the subtleties of thought and organization of a master mathematician, and contains too few examples to help a student. The examples are basic and perfunctory and do not deepen understanding and are a kind of non-essential blip in the logical development. It would have been better to have no examples and to have a very technical monograph on part of the topic than to pretend to thoroughness re: complex analysis in its entirety.So, for a student it is not helpful, and specialists can do much better. On the other hand, the development is clear and insightful, and $10 is pretty cheap for a book of reasonable quality.

⭐Great complex analysis text — I will use this for teaching two semesters of complex analysis. Lots of examples and gives all the necessary theory. It explains even basic concepts in analysis and topology as needed, so the student doesn’t have to look for other references. Since it is a bit old, in a very few places the terminology/notation is a little outdated. The book contains lots of exploring of the individual complex functions and at the same time all the theory I would ask for. In some places I would do the proofs a little differently — the author is very hands-on.

⭐My aim is not to comment on the book.I just want to pay a salute to Dr. Silverman who have spenthis time in translating mnay of the books written not on English.Most of the books are of high quality.Without him, we have no chance in reading these books.Thnaks a lot to Dr. Sliverman again!!One pity is that in the translating books,no mention of Dr. Silverman’s life.For example, which university he is teaching?

⭐It’s O.K. in the first part (first six chapters). It has few problems and most of them are demonstrations after chapter six. I think it is pretty theoretical for engineering. It’s O.K. as a support book.

⭐Excellent value. Book is slightly worn, but since I am buying the contents, the superficial blemishes hardly matter.

⭐Equations and mathematical symbols are impossible to read. Do not purchase technical books until kindle readers support them.

⭐Comprehensive.

⭐Un libro bastante claro. Lo adquirí porque estoy cursando la materia de Variable Compleja y me ha sido de gran utilidad. Además de que puede ser empleado de forma autodidacta sin que sea difícil. Llegó en excelentes condiciones porque su empaquetado fue meticulosamente planeado.Es un buen libro para aprender analisis complejo, aunque, como insinua el titulo de mi reseña, no es del todo una introduccion, pues en ocasiones se puede llegar a necesitar ampliar por cuenta propia el materia presentado en el libro. Util para estudiantes que posean conocimientos de analisis real y algo de teoria en ecuaciones diferenciales, ademas de calculo vectorial.El libro es bueno sin embargo llegó maltratado porque lo empaquetaron mal, a libros de estilo los deberían proteger más. Fuera de eso es un buen libro.Livro muito bom, baseado na obra de um grande matemático russo!!!! Objetivo, claro, conciso, e uma ótima introdução a versão ampliada russa.this book is useful to all students and lecturers for quick reference and it is also use ful to scholars to their reserch

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