Complex made simple.9780821844793 Complex made simple. Ullrich, David C. American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards to mathematicians. 2008 489 pages $75.00 Hardcover Graduate studies in mathematics; v.97 QA331 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 In mathematics, there are two theorems with the name "open mapping theorem". In both cases, they give conditions under which certain maps are open maps, i.e. they map open sets to open sets. , Eulers formula for sin(z), inverses of holomorphic maps, conformal con·for·mal adj. 1. Mathematics Designating or specifying a mapping of a surface or region upon another surface so that all angles between intersecting curves remain unchanged. 2. mappings, normal families and the Riemann mapping theorem In complex analysis, the Riemann mapping theorem states that if  is a simply connected open subset of the complex number plane C which is not all of C , harmonic functions, simply connected open sets,
Runge's theorem and the Mittag-Leffler theorem, the Weierstrass
factorization theorem In mathematics, the Weierstrass factorization theorem in complex analysis, named after Karl Weierstrass, asserts that entire functions can be represented by a product involving their zeroes. , Caratheodory'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.
([c]20082005 Book News, Inc., Portland, OR) |
|
||||||||||||||||
Printer friendly
Cite/link
Email
Feedback
Reader Opinion