Complex Variables: Harmonic and Analytic Functions

Rating:
Summary: Perfect...
Review: ...for engineers and scientists. As some of the reviewers have mentioned, the graduate student in mathematics or theoretical physics may want something a bit more formal, and a bit more comprehensive. However for a researcher such as myself (working in physical chemistry), the treatment of the topics presented is spot on. Having said that, the aforementioned graduate students may benefit fom the crystal clear exposition and emphasis on an intuitive understanding of complex analysis too. For the price Dover are asking, this book is a must have.

Rating:
Summary: Perfect...
Review: ...for engineers and scientists. As some of the reviewers have mentioned, the graduate student in mathematics or theoretical physics may want something a bit more formal, and a bit more comprehensive. However for a researcher such as myself (working in physical chemistry), the treatment of the topics presented is spot on. Having said that, the aforementioned graduate students may benefit fom the crystal clear exposition and emphasis on an intuitive understanding of complex analysis too. For the price Dover are asking, this book is a must have.

Rating:
Summary: Excellent undergrad text
Review: Comparing this to other books, I think this is the best complex variable book I have seen at the undergrad level. I say that because the overall style is very informal and very easy to read, almost "babyish" in a small sense. Also the text generally developes the basics of advanced calculus needed for the book (stuff like uniform convergence, the M-test, proof of the increment theorem of two variables, etc etc.) in the same informal style which makes this book almost worthwhile alone as a supplement to an advanced calculus course. It does cover all the material that is needed for a complex variable course, but I would be weary to use it for a beginning graduate course since it is a little on the easy side, and I think one would expect a graduate student to be at a higher "maturity" level then that of this book. But for an undergradute course, all of the above (espically a book that has can provide an easy review of advanced calculus) is just what is needed in my opinion. And besides, the price is quite nice too :)

Rating:
Summary: Excellent undergrad text
Review: Comparing this to other books, I think this is the best complex variable book I have seen at the undergrad level. I say that because the overall style is very informal and very easy to read, almost "babyish" in a small sense. Also the text generally developes the basics of advanced calculus needed for the book (stuff like uniform convergence, the M-test, proof of the increment theorem of two variables, etc etc.) in the same informal style which makes this book almost worthwhile alone as a supplement to an advanced calculus course. It does cover all the material that is needed for a complex variable course, but I would be weary to use it for a beginning graduate course since it is a little on the easy side, and I think one would expect a graduate student to be at a higher "maturity" level then that of this book. But for an undergradute course, all of the above (espically a book that has can provide an easy review of advanced calculus) is just what is needed in my opinion. And besides, the price is quite nice too :)

Rating:
Summary: Excellent Textbook for Upper Division
Review: I looked at a number of books on complex variables. The one by Ahlfors is the classic text for graduate school. But that one costs (...)a lot of money. Flanigan's book covers all the basic material, and it includes theorems and topics that are often missing from many textbooks, such as the Poisson Kernel. Overall, it is an extremely well-written textbook with lots of good illustrations and examples. And, no offense to anyone, it appears to cover all the basic material that I need for my Ph.D. qualifying exams. Anyway, for about ten bucks you can't lose with this one. Great book!

Rating:
Summary: Excellent Textbook for Upper Division
Review: This book is unusual in that it starts out with harmonic functions and only later develops the complex analysis. I think this approach develops intuition about complex analysis. The book contains numerous examples and very illustrative diagrams. There are also interesting historical references, which make the book easier to read. This is a good book for you if the popular book by in Ruel & Churchill does not suit you.