ABSTRACT

Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole.

To set the groundwork

chapter 1|86 pages

Preliminaries

chapter 2|34 pages

The classical approach to complex analysis

chapter 4|34 pages

Local properties of holomorphic functions

chapter 5|30 pages

Global properties of holomorphic functions

chapter 6|24 pages

Isolated singularities

chapter 7|22 pages

Homotopy

chapter 8|12 pages

Residue theory

chapter 9|30 pages

Applications of residue calculus

chapter 12|30 pages

Boundary value problems