This book has just arrived last week at my home and I'm almost finishing the last chapter. I couldn't stop reading it. It's well written, easy to read, but, at the same time, quite rigorous and complete. I never saw a book about complex variables like this. It's true--as some other reviews have said--that some theorems are just stated and not entirely proved (e.g. the Riemann mapping theorem). But, by the other side, there is a great discussion about harmonic functions, the Cauchy integral theorem, the argument principle, conformal mappings, and many other topics.
It's important to notice that the approach to complex variables adopted by Flanigan is different from the standard textbooks. The main difference is that he starts discussing calculus on the real plane and only later he develops the complex calculus. His intention is to present first real harmonic functions, which he uses later to define analytic complex functions. Harmonic functions on the real plane become analytic functions on the complex plane, the Green theorem becomes the Cauchy integral theorem, analytic functions are seen as conformal maps, and so on. If you already know real calculus on the plane, this is probably the best way to approach complex calculus. Flanigan is quite convincing in his defense of this approach.
It's also important to notice that this is an introductory book designed to beginner students (like a second year undergraduate student in sciences or math). But the book is not interesting only to beginners, since the excellent explanations provided by Flanigan not only clarify many usually obscure points in complex analysis, but also furnish the reader with intuition about how things work in the complex plane. This kind of intuition is useful to any kind of student, at any level.
(Comment added in 2013: A few years after I wrote this review, I took a course in complex analysis at the graduate level and this "elementary book" was an absolutely great companion to Ahlfors's "Complex Analysis"! Now, having finished my PhD, I still have the same opinion about Flanigan that I had many years ago. If I had to chose a textbook to teach introductory complex analysis to undergraduate students in math or physics, I would definitely chose Flanigan's. At the undergraduate level, this book is second to none.)
To sum up, this is an extraordinary book, extremely well written, which has an interesting (and quite unusual) approach to the complex variables.
T. Hartz
* * * * *
Since there is no "search inside" for this book (actually, there wasn't when I wrote the review), these are the chapters:
1. Calculus in the plane (in the real plane, i.e. R^2)
2. Harmonic Functions in the Plane (once again, real plane)
3. Complex Numbers and Complex Functions
4. Integrals and Analytic Functions
5. Analytic Functions and Power Series
6. Singular Points and Laurent Series
7. The Residue Theorem and the Argument Principle
8. Analytic Functions as Conformal Mappings
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Customers find this complex analysis book to be one of the best in the subject, with good exercises and clear explanations. They appreciate its self-study value, with one customer noting how it makes important connections between complex analysis and geometry. Customers find the book easy to read and understand.
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16 customers mention content, 13 positive, 3 negative
...To sum up, this is an extraordinary book, extremely well written, which has an interesting (and quite unusual) approach to the complex...Read more
The book is great. Nothing to complain about it I have. It's really well written. Great for self studying. I really recommend that.Read more
I've read a lot of this book, and it is one of the best I've found on complex analysis....Read more
...Definitely the best book on the subject.Read more
8 customers mention self-study, 8 positive, 0 negative
...It has a lot of exercises and solutions in the back as well as helpful examples. Its great for self-study.Read more
...final in Complex Analysis, I can say confidently that this book was perfect for that....Read more
...Nothing to complain about it I have. It's really well written. Great for self studying. I really recommend that.Read more
...I am extremely satisfied with it. very good for self-study.Read more
7 customers mention readability, 6 positive, 1 negative
...Not a difficult read, but a working knowledge of calculus for one variable is prerequisite....Read more
...I couldn't stop reading it. It's well written, easy to read, but, at the same time, quite rigorous and complete....Read more
The book came in as described, easy to understand and is a good read. It was good doing business with youRead more
...It is quite interesting and clear. There are many good exercises! It's okay.Read more
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- Hebert Perez-RosesReviewed in Spain on April 28, 2020
Muy bien escrito y muy didáctico
Format: PaperbackVerified Purchase - Kleber Saldanha de SiqueiraReviewed in Brazil on June 29, 2024
Impressão do livro
Format: PaperbackVerified Purchase - OlenguReviewed in Italy on December 7, 2020
Terrible quality of the figures!
Format: PaperbackVerified Purchase - A good book with extremely bad print and paper quality.Reviewed in India on May 23, 2023
Extremely bad paper and print quality.
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