Complex Variables

This practical textbook offers solid discussions of the mathematics, clear expositions and wide selection of applications for complex variables. It introduces Cauchy's theorems for polynomials and rational functions in the first chapter, allowing students to progress quickly to applications. Providing a variety of exercises labelled according their level of difficulty, this text: furnishes a systematic treatment of applications to potential theory of particular value to science and engineering students; defines exponential and trigonometric functions as infinite series to display their connection with the corresponding real-valued functions of elementary calculus; clarifies the many values of the logarithm by introducing it as an integral early in the book; and examines Laplace transforms, differential equations, conformal mapping, analytic continuations and Riemann surfaces.;Complex Variables is intended for all undergraduate mathematics, science and engineering students in one-semester courses on complex variables.;A solutions manual is available to instructors only. Requests must be made on official school stationery.