The book is the second volume of a “miniseries” of four books forming a course of analysis. While the first three volumes contain introductory Fourier analysis, complex analysis and measure and integration theory (with Hilbert space theory), the last one covers some parts of functional analysis, probability theory, etc. The main idea behind the series is to explain these parts in a unified way accenting their mutual interplay. The book under review contains (together with traditional parts, like the Cauchy theorem and its consequences, meromorphic functions, entire functions or conformal mapping) also chapters on zeta functions and the prime number theorem, elliptic functions, and on applications of theta functions. Two appendices deal with asymptotics and simple connectivity and with the Jordan curve theorem. The style of exposition is similar to the classical book by Rudin. The book contains numerous exercises (165) and problems (50) with hints (some of the problems are rather demanding). The authors hope that the book(s) will be accessible to students interested in diverse disciplines (mathematics, physics, engineering, finance), at both the undergraduate and graduate levels.

Reviewer:

jive