Function Theory on Planar Domains: A Second Course in Complex Analysis

If there is one timeless area of mathematics we teach to our undergraduates and graduates alike, it is functions in the plane: This book brings out the beauty of the subject in a delightful way. The plane is where boundary theory is especially attractive and visual. The book is student friendly and includes a very nice selection of exercises. The first three chapters offer background, history, motivations and hints of applications. A great subject supplementing nicely courses in complex function theory, vector calculus, potential theory, mathematical methods in physics, and more. Selected topics: The Greens function, the Dirichlet problem, capacity, uniformization, self-mappings, Hardy spaces, theory of boundaries, Blaschke products, and H^p spaces. Review by Palle Jorgensen, February 2008.