Fonctions d'une variable complexe / Bernard Candelpergher

The book consists of two parts. The first part presents a straightforward and concise introduction to elementary complex analysis. This part has 8 chapters. The chapter headings are as follows: 1. Introduction; 2. Differentiability; 3. Elementary properties (Cauchy integral); 4. Analytic continuation; 5. Curvilinear integral; 6. Homotopy; 7. Residues; 8. Inverse function problem. Each chapter is provided by a large number of exercises. All these exercises are solved at the end of the first part. In every solution, the author gives specific suggestions to students, many of which are moderately challenging. The second part of the book consists of 30 problems. The author have chosen the method of “problem teaching” to help consolidate the reader's understanding and familiarity with complex analysis. Introduction to this part contains the list of the problems and each problem is provided by the references on the corresponding books. As a pattern of the problems we give: Problem 1: Cauchy-Riemann equations and harmonic functions. Problem 9: Orthogonal polynomials; Problem 22: The number of zeros and poles in the disk; Problem 30: the Ramanujan formula. (Zentralblatt)

Bibliogr. p. [275]-276. Index