Complex Made Simple (Graduate Studies in Mathematics)

David C. Ullrich

ISBN 10: 0821844792 / ISBN 13: 9780821844793

Published by American Mathematical Society, 2008

About this Item

This book is in acceptable condition and may have highlighting and or writing throughout. The actual cover image may not match the stock photo, dust jacket may be damaged or missing. Book may show internal and or external wear on spine or cover and may be slightly skewed or have creased pages. This is a used book so codes may be invalid or accompanying media may be missing. May be an Ex library book with stickers and stamps.

Seller Inventory # GBV.0821844792.A

Bibliographic Details

• Title: Complex Made Simple (Graduate Studies in Mathematics)
• Publisher: American Mathematical Society
• Publication Date: 2008
• Language: English
• ISBN 10: 0821844792
• ISBN 13: 9780821844793
• Binding: Hardcover
• Condition: acceptable

About this title

Synopsis

Perhaps uniquely among mathematical topics, complex analysis presents the student with the opportunity to learn a thoroughly developed subject that is rich in both theory and applications. Even in an introductory course, the theorems and techniques can have elegant formulations. But for any of these profound results, the student is often left asking: What does it really mean? Where does it come from? In Complex Made Simple, David Ullrich shows the student how to think like an analyst. In many cases, results are discovered or derived, with an explanation of how the students might have found the theorem on their own. Ullrich explains why a proof works. He will also, sometimes, explain why a tempting idea does not work. Complex Made Simple looks at the Dirichlet problem for harmonic functions twice: once using the Poisson integral for the unit disk and again in an informal section on Brownian motion, where the reader can understand intuitively how the Dirichlet problem works for general domains. Ullrich also takes considerable care to discuss the modular group, modular function, and covering maps, which become important ingredients in his modern treatment of the often-overlooked original proof of the Big Picard Theorem. This book is suitable for a first-year course in complex analysis. The exposition is aimed directly at the students, with plenty of details included. The prerequisite is a good course in advanced calculus or undergraduate analysis.

Review

Altogether, the current book offers a nearly irresistible invitation to the fascinating subject of complex analysis. --Zentralblatt