Complex Made Simple

Ullrich, David C.

ISBN 10: 0821844792 / ISBN 13: 9780821844793

Edité par Amer Mathematical Society, 2008

illustrated edition. 489 pages. 10.30x7.40x1.20 inches. In Stock. N° de réf. du vendeur 0821844792

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.

Détails bibliographiques

Titre : Complex Made Simple
Éditeur : Amer Mathematical Society
Date d'édition : 2008
Reliure : Hardcover
Etat : Brand New