- Hardcover: 468 pages
- Publisher: McGraw-Hill; 8 edition (January 10, 2008)
- Language: English
- ISBN-10: 0073051942
- ISBN-13: 978-0073051949
- Product Dimensions: 6.5 x 0.8 x 9.3 inches
- Shipping Weight: 1.7 pounds
- Average Customer Review: 52 customer reviews
- Amazon Best Sellers Rank: #544,901 in Books (See Top 100 in Books)
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Complex Variables and Applications 8th Edition
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About the Author
Churchill, Professor Emeritus of Mathematics, University of Michigan.
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The book is very light on applications of complex analysis, but it's in-depth enough and without being overwhelming in its rigour or inscrutable notation that it's very useful for science and engineering majors to have.
There are many examples in the book to help point out non obvious uses of the results, and also to point out the many pitfalls the less careful student may encounter when studying complex variables for the first time. Also abundant, are the exercises at the end of each chapter. Many of which have answers or hints at the back of the book, and many of the problems are more interesting than the lessons themselves which is always a good sign.
I should mention that this book does involve proofs with their associated theorems, and may also serve as a nice introduction into the theoretical side of Calculus (which we call "Analysis"). The proofs are complete, and require little in the way of filling in the blanks yourself. However these proofs are entirely mechanical, which means that they boil down to algebraic manipulation over conceptual/geometric reasoning almost every time. You will be able to work with the theorems, and prove some of them, but most people will have no insight into why it actually works.
Perhaps the absolute worst part about this book, is the almost complete lack of pictures. Complex analysis is a very geometric subject. Almost every algebraic proof could be preceded/replaced with simple reasoning that unveils how the geometry of the subject necessitates the theorem. The beauty of the subject can not be seen without more figures, and more time spent on the intuition behind the ideas. To see how amazing this subject can truly be, I can't recommend strongly enough Tristan Needham's "Visual Complex Analysis". Visual Complex Analysis
Needham's book is a bit slower, and is less computationally focused, but its reasoning is so clear that it makes the multitude of theorems seem obvious and necessary. Every aspect of complex variables from Cauchy's equations, to the exponential function is made intuitive through carefully looking at why such things should be. The multitude of amazing figures are used to incredible effect. After you read Needham's book you'll really appreciate the greatness of the thinkers who preceded the subject, and get a little bit closer to thinking like a real mathematician.
The problem is, you'll never remember all the results and techniques unless you either use them frequently outside of the classroom, or actually took the time to see why the results are true at a level that can be conveyed with words. So unless you need this book for a class I can't recommend paying the steep price. If you can find it at a library it's worth checking out. But if you had to pick one I would go with Needham's book any day, you'll thank me for it later.
That is why I am giving this a 4 stars becuase some of the problems are not straight forward and require much thinking- sometimes in class students were lost in class trying understand some of the homework problem especially the proving ones
I have learned much of complex Analysis/variables from this book and I will keep it in my Math Library for Reference later.