Analytic Functions

Book Details:

• Publisher: Dover

• Author: M.A. Evgrafov

• Language: English

• Edition: Translation

• ISBN: 9780486837604

• Pages: 352

• Cover: Paperback

• Dimensions: 9.0 x 6.0 x 0.7 inches

About The Book:

M.A. Evgrafov's Theory of Functions of a Complex Variable is a rigorous and comprehensive text aimed at advanced undergraduates and graduate students in mathematics. This book is designed to establish a solid foundation in the theory of complex variables, emphasizing modern research aspects and applications.

The author departs from traditional texts by introducing the theory of multiple-valued analytic functions early on, providing a unique perspective on analytic continuation. This approach naturally leads to an introduction to Riemann surfaces and conformal mapping. The book also thoroughly covers residue theory, a crucial aspect of complex analysis, and its practical applications.

The material begins with fundamental concepts of limits, continuity, and integrals, before progressing to more advanced topics such as analytic functions and their properties, singularities, series expansions, Laplace transforms, and harmonic functions. The book's self-contained chapters make it suitable for both classroom use and independent study. Its focus on both theory and application, combined with a modern approach to the subject, makes it a valuable resource for anyone looking to deepen their understanding of complex analysis.