Also included are 140 exercises with complete solutions in an appendix. Howie has written an outstanding book on complex variables.The readability of the book is improved by more than 80 figures and numerous examples. I'm going to use it the first chance I get. Not only do Howie's selection of topics and their sequence correspond perfectly to what I believe to be the ideal approach to this gorgeous subject, the writing style is (again) wonderful.I think this is a terrific book. I want to use it the next time I teach complex analysis. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided. A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set.

Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers, differentiation, integration, Cauchy's theorem, and its consequences, Laurent series and the residue theorem, applications of contour integration, conformal mappings, and harmonic functions. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective.

Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course.

Complex analysis textbook pdf