Problems and Solutions for Complex Analysis [Paperback]

Rami Shakarchi (Author), Serge Lang (Author)

Book Description

Publication Date: October 14, 1999 | ISBN-10: 0387988319 | ISBN-13: 978-0387988313 | Edition: 1

All the exercises plus their solutions for Serge Lang's fourth edition of "Complex Analysis," ISBN 0-387-98592-1. The problems in the first 8 chapters are suitable for an introductory course at undergraduate level and cover power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, and harmonic functions. The material in the remaining 8 chapters is more advanced, with problems on Schwartz reflection, analytic continuation, Jensen's formula, the Phragmen-Lindeloef theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and Zeta function. Also beneficial for anyone interested in learning complex analysis.

Product Details

• Paperback: 257 pages
• Publisher: Springer; 1 edition (October 14, 1999)
• Language: English
• ISBN-10: 0387988319
• ISBN-13: 978-0387988313
• Product Dimensions: 9.1 x 6.1 x 0.6 inches
• Shipping Weight: 13.6 ounces (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #235,573 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

27 of 32 people found the following review helpful:

5.0 out of 5 stars The Right Stuff !!!!!!!!!!!!!!, March 12, 2002

By A Customer

This review is from: Problems and Solutions for Complex Analysis (Paperback)

I bought this book with the goal to enhance my problem solving skills on complex analysis. I am a theoritical physics student and needed to gain a very comprehensive and operational understanding of the topic. This book had it all: it's very well written, very rigourous and gives an extra dimension to just reading a pure text explaining the theory of the subject. I wish we had this type of books in physics ! Lang's book and Shakarchi's solutions are the winning combination to learn complex analysis!!!!! 2 thumbs up

1 of 1 people found the following review helpful:

5.0 out of 5 stars Text, April 18, 2011

By 

Brian - See all my reviews
(REAL NAME)   

This review is from: Problems and Solutions for Complex Analysis (Paperback)

I feel some sort of counter balance is in order for the seemingly unbalanced reviews.

I have used Lang's UA text and have Shakarchi associated solutions manual. I have found them to be of high quality and are great for self-study or supplemental work. Although I have not yet purchased the Lang / Shakarchi texts on CA, upon online review they appear to be of high quality also.

I think it is unfortunate that people feel the need leave such negative reviews for reasons that have little or nothing to do with the text.

6 of 19 people found the following review helpful:

1.0 out of 5 stars I have little taste for answer books, especially when they are wrong, December 3, 2009

By 

mathwonk - See all my reviews

This review is from: Problems and Solutions for Complex Analysis (Paperback)

I gave a take home test of problems from Lang, because the answers are not in the back of the book. A student challenged my answer to one question, because Shakarchi says the answer is something different. I did not realize anyone had gone to the absurd trouble of publishing answers to the excellent exercises in Lang's book until then. But Shakarchi is wrong, having made a careless error. Reading books of answers to problems is like reading a book about physical exercise only worse, since not only do you not benefit from the exercise of doing it yourself, but you lose most of the potential benefit of the exercise after seeing the answer. At least with physical exercise you do not lose anything from watching it done if afterwards you do it yourself. Look on page 85 of this book where Shakarchi asserts that problems VI.1.26b and VI.1.26e have the same answer because the denominators have the same residues, Well how about the numerators? In 26e the z in the numerator implies that the terms of the laurent series of the quotient are not all of even degree anymore, so I claim (check it! I could be wrong too) the correct answer is that all residues in that case are equal to 2, not zero. (This comes from 2= 1/(1/2) the quotient of the coefficient 1 of the z in the top, and the first non zero coefficient 1/2 of the taylor series of 1-sin at '/2.) So without having read any more of this book, even if this is the only error, I say it is almost worthless to someone really wanting to learn the subject. But if you are like someone who cannot exercise without watching a Jane Fonda video, and you do buy this book, please work the problems yourself, and do not just take the author's word for them. I do recommend Lang's book, and the exercises. Probably my favorite complex book is that by Henri Cartan available in a cheap paperback, and the one by Frederick Greenleaf (available used and in libraries) is excellent for beginners, and he gives the answers (but not the solutions) to most of his exercises right in the book if you want that.