Introduction to Complex Analysis (Translations of Mathematical Monographs) [Hardcover]

Junjiro Noguchi (Author)

Book Description

Publication Date: October 21, 1997 | ISBN-10: 0821803778 | ISBN-13: 978-0821803776

This book describes a classical introductory part of complex analysis for university students in the sciences and engineering and could serve as a text or reference book. It places emphasis on rigorous proofs, presenting the subject as a fundamental mathematical theory. The volume begins with a problem dealing with curves related to Cauchy's integral theorem. To deal with it rigorously, the author gives detailed descriptions of the homotopy of plane curves. Since the residue theorem is important in both pure and applied mathematics, the author gives a fairly detailed explanation of how to apply it to numerical calculations; this should be sufficient for those who are studying complex analysis as a tool.

Editorial Reviews

Language Notes

Text: English (translation)
Original Language: Japanese

Product Details

• Hardcover: 250 pages
• Publisher: American Mathematical Society (October 21, 1997)
• Language: English
• ISBN-10: 0821803778
• ISBN-13: 978-0821803776
• Product Dimensions: 10.2 x 7.1 x 0.8 inches
• Shipping Weight: 1.5 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,101,232 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

1 of 1 people found the following review helpful:

5.0 out of 5 stars A good, if expensive, introduction to functions of a complex variable, November 11, 2009

By 

Alice Taniyama "math fiend" (Houston, Texas United States) - See all my reviews

This review is from: Introduction to Complex Analysis (Paperback)

Suitable for a one year course in complex analysis, at the advanced undergraduate or graduate level, this is a pretty good introduction to the subject, with well-written, detailed proofs and lots of exercises. If you take the time to work the exercises, you will learn the subject, and you will learn it well, and if you have trouble with some of them, you can look in the back for answers, though if you have this as a textbook, your professor will probably assign problems whose solutions are not in the book.

The chapter on Cauchy's integral theorem is particularly good, describing the material in detail and providing a nice illustration of homotopy of curves. Studied dutifully, this can help a student through one of the thornier areas of the subject, often an area that trips those new to complex analysis. That alone could make the book worth the price.

This is, though, only an introduction, and a student hoping to cover more advanced material is urged to consider William Veech's "A Second Course in Complex Analysis" or some other books suitable for that purpose.