'Written by a skillful teacher and grand master of complex analysis, this complex analysis graduate level textbook stands out from other texts through the clarity and elegance of the arguments, the efficiency of the presentation, and the selection of advanced topics. Each of the 16 chapters ends with a carefully selected set of exercises ranging from routine to challenging, making it an excellent textbook and ideal for a first-year graduate course. Marshall's choice of beginning with power series (following Weierstrass) has the advantage of a very fast and direct approach to some of the highlights of the theory. The connection to Cauchy's integral calculus, which is the starting point of most texts, is then made through partial fractions and Runge's theorem. This makes the book an invaluable addition to the complex analysis literature.' Steffen Rohde, University of Washington
Preface; Prerequisites; Part I: 1. Preliminaries; 2. Analytic functions; 3. The maximum principle; 4. Integration and approximation; 5. Cauchy's theorem; 6. Elementary maps; Part II: 7. Harmonic functions; 8. Conformal maps and harmonic functions; 9. Calculus of residues; 10. Normal families; 11. Series and products; Part III: 12. Conformal maps to Jordan regions; 13. The Dirichlet problem; 14. Riemann surfaces; 15. The uniformization theorem; 16. Meromorphic functions on a Riemann surface; Appendix; Bibliography; Index.
