Titlebook: Classical Analysis in the Complex Plane; Robert B. Burckel Textbook 2021 Springer Science+Business Media, LLC, part of Springer Nature 202

圆柱

The Index and Some Plane Topology,In this chapter we complete the preliminary investigations of Chapter I on the topology of the plane. The chief tools are the index and deformation and extension techniques.

美丽的写

,Consequences of the Cauchy–Goursat Theorem— Maximum Principles and the Local Theory,Of great utility in the differential calculus of functions on ℝ are . or antiderivatives. The Fundamental Theorem here affirms that integration always produces such primitives.

冒烟

Matrimony

Convergent Sequences of Holomorphic Functions,We have already seen four amazing results on the convergence of sequences of holomorphic functions [5.38(iv), 5.44(ii), 5.45(iii) and 5.74] which have no analog for differentiable functions on the line.

任意

费解

expeditious

Simple and Double Connectivity,We come now to an “enterprise of great pitch and moment,” the climax of much of our previous work. To state the result in its most awesome form we introduce some convenient definitions to supplement those in 4.70 and 9.48.

llibretto

Isolated Singularities,If . is holomorphic in . for some neighborhood . of ., we call . an . of ..

ALLAY

花争吵

Robert B. BurckelCovers the classical theory of functions of a single complex variable with depth, precision, and rigor.Presents the subject from an authoritative historical perspective, containing more than 2,000 ref