Basic Complex Analysis A Comprehensive Course in Analysis Part 2A is popular PDF and ePub book, written by Barry Simon in 2015-11-02, it is a fantastic choice for those who relish reading online the Mathematical analysis genre. Let's immerse ourselves in this engaging Mathematical analysis book by exploring the summary and details provided below. Remember, Basic Complex Analysis A Comprehensive Course in Analysis Part 2A can be Read Online from any device for your convenience.
Basic Complex Analysis A Comprehensive Course in Analysis Part 2A Book PDF Summary
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.
Detail Book of Basic Complex Analysis A Comprehensive Course in Analysis Part 2A PDF
- Author : Barry Simon
- Release : 02 November 2015
- Publisher : American Mathematical Soc.
- ISBN : 9781470411008
- Genre : Mathematical analysis
- Total Page : 641 pages
- Language : English
- PDF File Size : 7,9 Mb
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