Functions of One Complex Variable II [Hardcover]

This is the sequel to my book Functions of One Complex Variable I, and probably a good opportunity to express my appreciation to the mathemat? ical community for its reception of that work. In retrospect, writing that book was a crazy venture. As a graduate student I had had one of the worst learning experiences of my career when I took complex analysis; a truly bad teacher. As a non-tenured assistant professor, the department allowed me to teach the graduate course in complex analysis. They thought I knew the material; I wanted to learn it. I adopted a standard text and shortly after beginning to prepare my lectures I became dissatisfied. All the books in print had virtues; but I was educated as a modern analyst, not a classical one, and they failed to satisfy me. This set a pattern for me in learning new mathematics after I had become a mathematician. Some topics I found satisfactorily treated in some sources; some I read in many books and then recast in my own style. There is also the matter of philosophy and point of view. Going from a certain mathematical vantage point to another is thought by many as being independent of the path; certainly true if your only objective is getting there. But getting there is often half the fun and often there is twice the value in the journey if the path is properly chosen.of Volume II.- 13 Return to Basics.- 1 Regions and Curves.- 2 Derivatives and Other Recollections.- 3 Harmonic Conjugates and Primitives.- 4 Analytic Arcs and the Reflection Principle.- 5 Boundary Values for Bounded Analytic Functions.- 14 Conformal Equivalence for Simply Connected Regions.- 1 Elementary Properties and Examples.- 2 Crosscuts.- 3 Prime Ends.- 4 Impressions of a Prime End.- 5 Boundary Values of Riemann Maps.- 6 The Area Theorem.- 7 Disk Mappings: The Class S.- 15 Conformal Equivalence for Finitely Connected Regions.- 1 Analysis on a Finitely Connected Region.- 2 Conformal Equivalence with an Analytic Jordan Region.- 3 Boundary Values for a ConfolÃ,