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 An excellent(and cheap!) text February 8, 2000
A MATH NERD (Cambridge, MA)
23 out of 23 found this review helpful
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
excellent, rigorous work February 12, 2000
Ted Shane (usa)
6 out of 6 found this review helpful
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.
Great Book on complex analysis May 12, 2002
6 out of 6 found this review helpful
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!
a classic August 5, 2006
Palle E T Jorgensen (Iowa City, Iowa United States)
5 out of 5 found this review helpful
Silverman's book starts at complex numbers functions and sequences, and it covers some central aspects of complex function theory, elementary geometry, Mobius transformations, harmonic and analytic functions.
The central topics are (in this order) geometry of the plane, fundamentals of complex numbers, limits and a brief calculus review, calculus and geometry of the plane, harmonic functions, complex numbers, integrals, power series and analytic functions, and the standard Cauchy-and residue theorems, ending with a brief chapter on conformal mappings.
The book was published first in 1967, but reprinted since by Dover. It is suitable as a text or as a supplement in a standard course in complex function theory, at the late undergraduate level. While it contains the standard elements in such a course, we note that a systematic treatment of power series comes relatively late, in Chapter 10, beginning on page 195 (halfway into the book.) Some readers might want to begin with that.
Of other Dover titles on the same subject we recommend the books by Volkovyskii et al, Schwerdtfeger, and Flanigan. Review by Palle Jorgensen, August 5, 2006.
Nice book on complex analysis December 1, 2008
Ricardo Avila
On 2001, I took a graduate course on complex analysis having very little previous knowledge about it, 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 once again 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! and is cheap!(by the way, I am the same person as the one on the review called "Great book on complex analysis", the only difference is that on that occasion I didn't leave my name so now I've done it finally)
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