Customer Reviews

Basic Complex Analysis

5 star:		(10)
4 star:		(3)
3 star:		(6)
2 star:		(0)
1 star:		(2)

 

 

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.

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.

The book reveals complex analysis as a very elegant and lovely branch of mathematics. The level of rigour is not that of Marsden's other book, Elementary Classical Analysis. Instead, Basic Complex Analysis can be usefully read by non-maths majors, especially those in physics and engineering.

Key ideas are well covered. Starting with the Laurant series, which generalises the Taylor series. Then, from this, the idea of contour integration is examined. Giving rise to the Residue Theorem and the winding number. All because the only term that does not integrate to 0 is 1/z, which gives the complex log and its imaginary argument is the only thing left. So simple and powerful. Amazing that an essentially arbitrarily intricate contour integral can be given by the residues at the enclosed poles! Yet the text's derivation should get straightforward to follow for most readers.

If you are going onto advanced physics, like quantum electrodynamics, then this theorem is used extensively.

The book also covers important subsequent ideas. Especially conformal mapping and the Schwartz-Christoffel transformation. The treatment of conformal mapping, though, is only a hint of the richness of analysis available here.

The numerous problems are also good for the student to tackle.

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.

Used this book as an undergraduate... hated it... I kept using a little thin old edition of "Complex Variables and Applications" by Churchhill to actually teach math using english.... Ironically the instructor who was teaching out of his notes followed churchhills presentation closer then this text.

The treatment of this subject in this text is just so horrid for a FIRST LOOK AT COMPLEX THEORY. No elegance to it what so ever...

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.

This book has excellent examples and most of the proofs are very easy to understand. It's a great book to use if you're learning complex analysis on your own.

It's not, however, the only book you should use. I prefer math books that are more condensed with short, easy-to-read theorems. I would not list this book under such a category. In fact, many of it's theorems are so long, they require you to turn back and read other theorems pages earlier just to figure out what the necessary conditions are to use the theorem. I found this to be confusing and it slowed me down quite a bit. Therefore, if you have the same preference, I would suggest using this book only for its examples and exercises.

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.

This is the second book that I have read beside the Vector Calculus by Marsden and Hoffman. This book rushes you through with an introductory chapter and go right into the heart of complex analysis. The author assumes you to have a great professors that can explain things in detail when you can't quite understand what is written in the text. Unfortunately I did not have a great instructor.

The examples of the book are quite simple, compare to some end of section problems.

Overall this book has no surprises as it is quite dry, got bored from reading it. If it was not a required text book for a 3rd year complex analysis course, i wouldn't recommend it to anyone. There are many other books out there that are better written.

It is totally beyond me why this textbook on this rather difficult subject is not prevalent everywhere. The best start to the enticing area of complex analysis in existence. Prepares you perfectly for more complex texts. Fantastic.