Problems in complex variable theory / Jan G. Krzyz

Bibliogr. : p. 277-278. Index

Author's foreword: "This collection of exercises in analytic functions is an enlarged and revised English edition of a Polish version [Państw. Wydawn. Nauk, Warsaw, 1965; RŽMat 1966 2B 146K]. The book is mainly intended for mathematics students who are completing a first course in complex analysis, and its subject matter roughly corresponds to the material covered by L. V. Ahlfors's book [Complex analysis: an introduction to the theory of analytic functions of one complex variable, second edition, McGraw-Hill, New York, 1966; MR0188405 (32 #5844)]. Some chapters, for example, evaluation of residues, determination of conformal mappings, and applications in the two-dimensional field theory may be, however, of interest to engineering students. Most exercises are just examples illustrating basic concepts and theorems, some are standard theorems contained in most textbooks. However, the author does believe that the reconstruction of certain proofs could be instructive and is possible for an average mathematics student. When the subject matter of a particular chapter is not covered by standard textbooks, the numbers in parentheses given in the contents indicate a corresponding bibliography position which may be consulted for further information.
"Some problems are due to the author, and some were adopted by the author from various sources. It was beyond the scope of the author's possibility to trace the original sources and therefore the detailed references are omitted.
"The second part of the book contains solutions of problems. In most cases a complete solution is given; in some cases, where no difficulties could be expected, or when an analogous problem has already been solved in a detailed manner, only a final solution is given. The author is well aware that it was extremely hard to avoid mistakes in a book of this kind. He did his best, however, to reduce their number to a minimum.''
"Table of Contents: Problems: 1. Complex numbers. Linear transformations; 2. Regularity conditions. Elementary functions; 3. Complex integration; 4. Sequences and series of analytic functions; 5. Meromorphic and entire functions; 6. The maximum principle; 7. Analytic continuation. Elliptic functions; 8. The Dirichlet problem; 9. Two-dimensional vector fields; 10. Univalent functions; Solutions. (MathSciNet)