Introductory Complex Analysis

Rating:
Summary: excellent, rigorous work
Review: I was amazed by this book. In a small amount of space, it manages to present most of the important theoretical aspects of complex analysis, and rigorously, so you get all the detailed proofs. However, the book isn't big on applications, so you might consider getting an applied text to supplement this one. Also, the book is quite advanced. Some background in advanced calculus (Widder's book works great) would help you make more sense of the text. I read this after I learned applied compl. analysis, so I can't really judge this book as an introduction to the field, but for someone who is familiar with the essentials of complex analysis, this is an excellent theoretical supplement.

Rating:
Summary: Great Book on complex analysis
Review: Last year i took a graduate course on complex analysis having very little previous knowledge about it, cause i study physics and this was the book i used to help my self. This book resulted being a delight, it's wonderfull the way it is written the clarity, all theorems with proofs and starts from the basics till more advanced topics. I recently read it completely and the same thing happened: is a wonderfull book, my plan now is to get the bigger work of Markushevich, to extend the knowledge. In one word buy it you won't regret it!

Rating:
Summary: Pay a salute to Dr. Richard Silverman
Review: My aim is not to comment on the book.
I just want to pay a salute to Dr. Silverman who have spent
his 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?

Rating:
Summary: Pay a salute to Dr. Richard Silverman
Review: My aim is not to comment on the book.
I just want to pay a salute to Dr. Silverman who have spent
his 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?

Rating:
Summary: An excellent(and cheap!) text
Review: 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

Rating:
Summary: Lacking in examples and reasonable exercises
Review: We used this text for a one semester undergraduate course in complex analysis at North Dakota State, and the entire class HATED the text. There are few exercises and they are of poor quality. The text also contains few examples, and they are often completely missing when they are most needed. I don't even consider this text as having reference value in the future. Yes, it is a condensation of Silverman's translation of Markushevich's three volume work. One might be better off with the whole book, because this edition seems to be missing a lot. Our professor finally gave up on the text and spent twice the usual time preparing his lecture notes so that we wouldn't have to open the text ever again, and I don't plan to.