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Basic Complex Analysis Third Edition Edition

3.9 out of 5 stars 25 customer reviews
ISBN-13: 978-0716728771
ISBN-10: 071672877X
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Product Details

  • Hardcover: 600 pages
  • Publisher: W. H. Freeman; Third Edition edition (December 15, 1998)
  • Language: English
  • ISBN-10: 071672877X
  • ISBN-13: 978-0716728771
  • Product Dimensions: 7.5 x 1.2 x 9.6 inches
  • Shipping Weight: 2.2 pounds
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (25 customer reviews)
  • Amazon Best Sellers Rank: #411,301 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

By C. Dolan on May 12, 2006
Format: Hardcover
When I first started with this book, I was not a fan. However, the book grew on me over time. Marsden and Hoffman do a very good job of blending both theoretical and computational aspects of complex analysis. They do a very good job of motivating and explaining the proofs, and they do not leave out any details (this is both good and bad - it can distracting, but as long as you pay attention, you will never get lost). The illustrations in the text are for the most part illuminating and useful, and the worked examples at the end of each section are not bad as well.

I did have a few minor problems, though. While many of the exercises are good, some of them seemed rather trivial. The chapter on conformal mapping could use some work. The binding on mine started to come apart by the end of the semester, although that may have been my fault.
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Format: Hardcover Verified Purchase
I used an earlier edition of this text as an instructor 20 years ago. The students in my class at the time were equally divided among the fields of mathematics, physics, and engineering. The book proved to be quite useful for all of them. Marsden skillfully strikes a balance between the needs of math majors preparing for graduate study and the needs of physics and engineering students seeking applications of complex analysis.
The book is clearly written and well-organized, with plenty of examples and exercises. My only significant criticism of the first edition was the author's tendency to label many examples of contour integration as theorems. Technically, there is nothing wrong this, but I found that some of my students tended to memorize the statements of these "theorems" rather than focus on the methods of integration discussed (for example, "Pac-Man" integrals with branch cuts along rays other than the positive real axis). Nonetheless, this is a fine text that has--not surprisingly--continued to be widely used for over two decades.
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Format: Hardcover Verified Purchase
If you are using this book for a course, I recommend you get a supplement book with more problems and better examples. This book is difficult to work through because it doesn't use the classical "example follows theorem." Instead, it places all the examples at the end of the chapter.

What is worse is that the examples tend to require compound knowledge. That is, they tend to test your ability to grasp more than one concept at a time instead of sequentially building up that current subjects. Also, please note that many of the examples assume that you worked out a problem in the previous exercises.

As for the lack of rigor, it can make some areas of complex variables easy (specially the areas involving deformations), while making other things much harder. Geometric intuition will be highly emphasized but poorly depicted. Overall, I hated this book because I had to beat myself up to grasp examples.
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Format: Hardcover
This is an excellent work by any standard. Moreover, the fact that the book has seen only three editions in 30 years is a testament to its relevance and thoroughness and incisiveness.

About the authors: Dr. Marsden was a truly elite ISI cited researcher and applied mathematician with a very deep understanding of the topic (he passed away last year) and Dr. Hoffman is a quality mathematician, and a gifted writer with a keen historical sense of the development of ideas within math. They make a great team.

The strength of the book, as some other reviewers have noted, is its thoroughness - the book does not skimp on proofs or on the technical development of the subject. As a student, this is very intimidating. Yet, over time, with more mathematical maturity, the book grew on me. The technical arguments that I found unnecessary and difficult to follow became enlightening and enriching, and helped me to better understand the material And the fact that it was not organized in the manner of an abstract algebra book, but rather had slight variations, and extensions of the discussions became quite appealing to me after time.

I think that one helpful standard is that the reader needs to have a solid background both in Analysis and abstract algebra (or at least a difficult upper level math class like topology). I would say that this book is written at the senior undergrad or grad level. Without a solid background, the books will be and is extremely intimidating. Perhaps it is helpful to have a second, less challenging, more computational complex analysis book beside this to get a picture of the forest instead of the trees. But other than that the book is wonderful.
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Format: Hardcover
I learned Complex Analysis from the 2nd ed. of the book and am definitely going to teach my class next year from the 3rd ed. It is easy to read and has examples and illustrations not found in Alfors, Rudin, or Cartan. Despite the other reader's comments, I believe that it is a wonderful book for students who are bright and for those who need help in comprehending new subjects.
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Format: Hardcover
One problem some students had with the book was that it can get a bit too wordy with its explanations, making theorems/concepts more difficult to understand. Other than that, it is a great book for undergraduates as the exercises consist of not only proofs, but also numerous computational problems which students can work through to practice applying the theorems. Examples at the end of each section are great and helpful.
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