000			02061nam a22002057a 4500
003			OSt
005			20241106124926.0
008			190124b ||||| |||| 00| 0 eng d
020			_a978-1-4704-1100-8
040			_cSurya Book Supplier _aICTS-TIFR
050			_aQA300
100			_aSimon Barry
245			_aBasic complex analysis _b: a comprehensive course in analysis, part 2A
260			_aRhode Island: _bAmerican Mathematical Society, _c[c2015]
300			_a641 p
505			_aChapter 1. Preliminaries Chapter 2. The Cauchy integral theorem: Basics Chapter 3. Consequences of the Cauchy integral formula Chapter 4. Chains and the ultimate Cauchy integral theorem Chapter 5. More consequences of the CIT Chapter 6. Spaces of analytic functions Chapter 7. Fractional linear transformations Chapter 8. Conformal maps Chapter 9. Zeros of analytic functions and product formulae Chapter 10. Elliptic functions Chapter 11. Selected additional topics
520			_aPart 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. --- summary provided by publisher
650			_aMathematics
942			_2lcc _cBK
999			_c2192 _d2192