Introductory Complex Analysis (Dover Books on Mathematics)

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

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 Since it is a bit old, in a very few places the terminology/notation is a little outdated.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.

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.

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?

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

Comprehensive.

This book might just be the best Dover text out there-which isn't really saying much, considering how many of their books are total stinkers. To me, this is nearly an ideal math book: clear logical development punctuated with very well-chosen exercises. I know of no better book on the basics of complex analysis. If you've seen basic material about complex numbers and functions, as well as a few basic facts about real analysis, you can start in chapter seven, where complex integration is introduced, and used to prove all sorts of wonderful things. But if you haven't seen these basics, they are well-presented in the opening chapters, making this book extremely accessible. But it is in chapter seven that the book really begins, which is where the fundamental theorems of complex analysis start being proved. All of these proofs and chapters are extremely well-written, making the logical structure of the whole theory entirely transparent. This book is just an introduction, as the title says, and there is lots of advanced material not touched here, but this book provides an excellent foundation for further study. Chapter Titles: 1. Complex Numbers, Functions, and Sequences 2. Limits and Continuity 3. Differentiation. Analytic Functions 4. Polynomials and Rational Functions 5. Mobius Transforms 6. Exponentials and Logarithms 7. Complex Integrals. Cauchy's Integral Theorem 8. Cauchy's Integral Formula and Its Implications 9. Complex Series. Uniform Convergence 10. Power Series 11. Laurent Series. Singular points 12. The Reside Theorem and Its Implications 13. Harmonic Functions 14. Infinite Product and Partial Fraction Expansions 15. Conformal Mapping 16. Analytic Continuation

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.

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.

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

Excellent ouvrage, didactique et clair. Nombreux exercices corrigés, de multiples applications traitées en mathématiques et en physique. Ouvrage à recommander.

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.