Synopses & Reviews
This new single-volume edition combines two parts of a renowned mathematician's collection of instructive problems. Vol. I contains more than 300 elementary problems dealing with fundamental concepts, infinite sequences and series, functions of a complex variable, conformal mapping, and more. Vol. II features over 230 problems in advanced theory — singularities, entire and meromorphic functions, periodic functions, analytic continuation, multiple-valued functions and Riemann surfaces, and more. Solution hints are provided, plus complete solutions to all problems.
Synopsis
Single-volume edition of renowned collection of problems. Part 1 contains more than 300 problems dealing with fundamental concepts; part 2 has over 230 problems in advanced theory. Includes hints and full solutions to all problems.
Table of Contents
Chapter I. Fundamental Concepts
1. Numbers and Points. Problems; Answers
2. Point Sets. Paths. Regions
Chapter II. Infinite Sequences and Series
3. Limits of Sequences. Infinite Series with Constant Terms. Problems; Answers
4. Convergence Properties of Power Series. Problems; Answers
Chapter III. Functions of a Complex Variable
5. Limits of Functions. Continuity and Differentiability. Problems; Answers
6. Simple Properties of the Elementary Functions. Problems; Answers
Chapter IV. Integral Theorems
7. Integration in the Complex Domain. Problems; Answers
8. Cauchy's Integral Theorems and Integral Formulas. Problems; Answers
Chapter V. Expansion in Series
9. Series with Variable Terms. Uniform Convergence. Problems; Answers
10. Expansion in Power Series. Problems; Answers
11. Behaviour of Power Series on the Circle of Convergence. Problems; Answers
Chapter V. Conformal Mapping
12. Linear Functions. Stereographic Projection. Problems; Answers
13. Simple Non-Linear Mapping Problems. Problems; Answers