#complex-analysis
30. Complex Analysis
This volume studies functions of a complex variable. It develops analyticity, contour integration, and the rich structure that arises from complex differentiability. Part I. Complex Numbers and Functions Chapter 1. Complex Numbers 1.1 Algebra of complex numbers 1.2 Geometry in the complex plane 1.3 Polar form and Euler’s formula 1.4 Roots of unity 1.5 Basic properties Chapter 2. Complex Functions 2.1 Functions of a complex variable 2.2 Limits and continuity...
32. Several Complex Variables and Analytic Spaces
This volume studies functions of several complex variables, complex manifolds, and analytic spaces. It extends complex analysis into higher dimensions, where geometry and sheaf methods become central. Part I. Functions of Several Complex Variables Chapter 1. Complex Euclidean Space 1.1 Coordinates in ℂⁿ 1.2 Domains and open sets 1.3 Holomorphic functions 1.4 Complex differentiability 1.5 Examples Chapter 2. Power Series 2.1 Several-variable power series 2.2 Domains of convergence 2.3 Holomorphic...