Presents 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. This book is suitable for a first-year course in complex analysis. Series: Graduate Studies in Mathematics. Num Pages: 489 pages, Illustrations. BIC Classification: PBKD. Category: (P) Professional & Vocational. Dimension: 255 x 184 x 32. Weight in Grams: 1048. . 2008. Hardcover. . . . . Books ship from the US and Ireland.

Codice articolo V9780821844793

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Titolo: Complex Made Simple (Graduate Studies in Mathematics)
Editore: American Mathematical Society
Data di pubblicazione: 2008
Lingua: Inglese
ISBN 10: 0821844792
ISBN 13: 9780821844793
Rilegatura: Rilegato
Condizione: New

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Riassunto

Ullrich teaches readers how to think like analysts long before they get to the "Big Picard Theorem," explaining why proofs do and do not work. He starts with Cauchy-Riemann equations in the introduction, then proceeds to power series, results on holomorphic functions, logarithms, winding numbers, Couchy's theorem, counting zeros and the open mapping theorem, Eulers formula for sin(z), inverses of holomorphic maps, conformal mappings, normal families and the Riemann mapping theorem, harmonic functions, simply connected open sets, Runge's theorem and the Mittag-Leffler theorem, the Weierstrass factorization theorem, Carath�odory's theorem, analytic continuation, orientation, the modular function, and the promised Picard theorems. He continues with Abel's theorem, the gamma function, universal covering spaces, Cauchy's theorem for non-holomorphic functions and harmonic conjugates. The result is suitable for a course in complex analysis for students with experience in advanced calculus. Annotation �2008 Book News, Inc., Portland, OR (booknews.com)

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Book by David C Ullrich

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