Complex Analysis

Donald E. Marshall is Professor of Mathematics at the University of Washington. He received his Ph.D. from University of California, Los Angeles in 1976. Professor Marshall is a leading complex analyst with a very strong research record that has been continuously funded throughout his career. He has given invited lectures in over a dozen countries. He is coauthor of the research-level monograph Harmonic Measure (Cambridge, 2005).

• 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.

'Marshall's book covers the basic topics with crystal clarity in a style that is conversational and concrete, and that guides the student into thinking about these topics the way a working mathematician does, especially one with a geometric or computational bent. Moreover, the book includes many results that are vital to modern function theory and its applications to geometry, dynamics and probability, but that are often omitted from introductory texts. I wish I had first learned the subject from this book, and I am delighted that my students can do so.' Christopher Bishop, State University of New York at Stony Brook