TY  - BOOK
AU  - Simon Barry
TI  - Basic complex analysis: : a comprehensive course in analysis, part 2A
SN  - 978-1-4704-1100-8
AV  - QA300 
PY  - 2015///]
CY  - Rhode Island
PB  - American Mathematical Society
KW  - Mathematics
N1  - Chapter 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

N2  - 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. --- summary provided by publisher
ER  -