Visual Complex Functions. Vol.1

This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations, known as phase portraits, which visualize functions as images on their domains. Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings, and Riemann surfaces, it goes somewhat beyond a standard program and leads the reader to more advanced themes. In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations.