A Collection of Problems on Complex Analysis (Dover Books on Mathematics) by L. I. Volkovyskii (PDF)

Description

This comprehensive collection contains over 1,500 problems on the theory of functions of the complex variable and covers nearly every branch of classical function theory. It will be of special interest to practicing engineers and researchers in the physical sciences, for considerable attention is given to those problems which illustrate the application of the theory of functions of a complex variable to problems dealing with the mechanics of continuous media and electrical engineering. The problems themselves range in difficulty from elementary to those encountered only in more advanced treatments.The first four chapters involve complex numbers and functions of a complex variable; conformal mappings connected with elementary functions; supplementary geometrical questions and generalized analytic functions; and integrals and power series.Chapters V through VIII cover the Launrent series, singularities of single-valued functions, and integral functions; various series of functions, parametric integrals, and infinite products; residues and their applications; integrals of the Cauchy type; and integral functions of Poisson and Schwarz.The final three chapters discuss analytic continuation, singularities of many-valued character, and Riemann Surfaces; conformal mappings; and applications to mechanic and physics. Answers and solutions are grouped at the end of the text.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I believe you learn math by doing math. When I studied calculus I worked every problem in the book and then some. Same for complex analysis. This is a translation from Russian and was a companion volume to the Russian author Markushevich’s book Short Course of the Theory of Analytic Functions. You can buy the long version Theory of Analytic Functions if you want. There are a lot of problems with solutions. The new book Complex Analysis by Kevin Huston would be a good idea if you want to learn how to do computational exercises. The more problems you do the better you will understand the theory.

⭐This is a very interesting collection of problems for anyone is interested in complex analysis. About 1500 exercixes that need a good preparation to be solved.

⭐Good product. Good deal.

⭐This nice little book by Volkovyskii et al (translated from Russian) is a collection of exercises, and it covers the central aspects of and themes in complex function theory, elementary geometry, harmonic and analytic functions. It contains graphics and illustrations, and the last third of the book consists of answers and solutions. The central topics are (in this order) complex numbers, calculus and geometry of the plane, conformal mappings, harmonic functions, power series and analytic functions, and the standard Cauchy-and residue theorems, symmetry, Laurent series, infinite products, ending with a brief chapter on Riemann surfaces, and applications to hydrodynamics and electrostatics. All the material is presented in the form of exercises. The book was published first in 1965, but reprinted since by Dover. It is suitable and recommended as a supplement in a standard course in complex function theory, late undergraduate level, or beginning graduate.Of other Dover titles on the same subject we recommend the books by Flanigan, Schwerdtfeger, and Silverman. Review by Palle Jorgensen, August 5, 2006.

⭐It’s a wonderful book. Not only an exercises’ recipient. But a valid aid as theory book too.

⭐É uma excelente coleção de problemas sobre funções de uma variável complexa. Isso se deve tanto ao número de problemas quanto à abrangência e ao nível de dificuldade. Para aqueles mais desafiadores há respostas no final do livro.I am using this book as a companion to the book “Complex Variables and Applications”, 3rd edition, by Ruel V. Churchill et al. It greatly help my self study of this fascinating subject of complex variable theory.

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