Ebook Complex Variables (Dover Books on Mathematics), by Francis J. Flanigan
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Complex Variables (Dover Books on Mathematics), by Francis J. Flanigan
Ebook Complex Variables (Dover Books on Mathematics), by Francis J. Flanigan
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A caution to mathematics professors: Complex Variables does not follow conventional outlines of course material. One reviewer noting its originality wrote: "A standard text is often preferred [to a superior text like this] because the professor knows the order of topics and the problems, and doesn't really have to pay attention to the text. He can go to class without preparation." Not so here — Dr. Flanigan treats this most important field of contemporary mathematics in a most unusual way. While all the material for an advanced undergraduate or first-year graduate course is covered, discussion of complex algebra is delayed for 100 pages, until harmonic functions have been analyzed from a real variable viewpoint. Students who have forgotten or never dealt with this material will find it useful for the subsequent functions. In addition, analytic functions are defined in a way which simplifies the subsequent theory. Contents include: Calculus in the Plane, Harmonic Functions in the Plane, Complex Numbers and Complex Functions, Integrals of Analytic Functions, Analytic Functions and Power Series, Singular Points and Laurent Series, The Residue Theorem and the Argument Principle, and Analytic Functions as Conformal Mappings.
Those familiar with mathematics texts will note the fine illustrations throughout and large number of problems offered at the chapter ends. An answer section is provided. Students weary of plodding mathematical prose will find Professor Flanigan's style as refreshing and stimulating as his approach.
- Sales Rank: #205118 in Books
- Published on: 1983-09
- Released on: 2010-09-20
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x 5.50" w x 1.00" l, .87 pounds
- Binding: Paperback
- 384 pages
Most helpful customer reviews
84 of 84 people found the following review helpful.
An extraordinary book
By Thiago Hartz
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 funny, easy to read, but, at the same time, quite rigorous and complete. I never saw a book about complex variables like this. It's wonderful! 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. This book makes every topic fantastically clear.
It's important to notice that the approach to complex variables adopted by Flanigan is entirely 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
2. Harmonic Functions in the 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
0 of 0 people found the following review helpful.
Different but Better
By changyau
Complex analysis is the most beautiful subject in math, and also easy to forget. Students often find that he/she forgot "everything"(no kidding!) about complex analysis even after one or two semesters in school, including me. After reading this book I found out why: I didn't have a good understanding of plane calculus. The first 1/3 of this book is all about plane calculus, and it is the right way to do.
You don't even have to know so called "calculus on manifold", the only manifold you need to know is a curve. Every theorems of complex variables in this book follows naturally from the contents of plane calculus, that' why you won't forget.
0 of 0 people found the following review helpful.
Don't Get This
By Amazon Customer
Sure, if you get Complex Analysis this just might be a good book. It's certainly not if it's the first time you're taking the course. Find yourself another complex analysis book, because this one just isn't all that great.
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