Complex Analysis (Springer Undergraduate Mathematics Series) Howie, John M.

Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. 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. 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. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.

From the reviews:

Howie's book is a gem. I want to use it the next time I teach complex analysis. 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'm going to use it the first chance I get. And I recommend it very, very highly.

MAA Online

Howie has written an outstanding book on complex variables...The readability of the book is improved by more than 80 figures and numerous examples. Also included are 140 exercises with complete solutions in an appendix. All this makes the book ideal for self-study. Summing up: Highly recommended.

CHOICE

"This book provides a self-study text for students in mathematics, science and engineering. It covers all the topics likely to feature in a first course in complex analysis up to Laurent series, the residue theorem and conformal mappings. ... Many carefully worked examples and more than 100 exercises with solutions make the book a valuable contribution to the extensive literature on complex analysis." (F.Haslinger, Monatshefte für Mathematik, Vol. 143 (2), 2004)

"This is a superbly well-written, balanced introduction to complex analysis that will meet the needs of a wide range of undergraduates. ... Here, page after page, I found myself nodding in agreement with the choices that the author has made ... . ‘Of all the many introductions to complex analysis, Howie’s is arguably the most attractive’." (Nick Lord, The Mathematical Gazette, Vol. 88 (512), 2004)

"This book takes account of the varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. ... Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 49 (3-4), 2003)

"Howie ... has written an outstanding book on complex variables. ... The readability of the book is improved by more than 80 figures and numerous examples. Also included are 140 exercises with complete solutions in an appendix. All this make the book ideal for self-study. Summing Up: Highly recommended." (D.P.Turner, CHOICE, December, 2003)