Introduction to Complex Variables and Applications

The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus or form the basis for challenging student projects.

'… a stylish, well-written and up to date introduction to complex variable methods for undergraduate (or early graduate) students in applied mathematics, science and engineering … I thoroughly enjoyed reading this book and warmly commend it to anyone seeking a brisk, well-organised account of complex variables with a practical focus on applications and calculational aspects.' Nick Lord, The Mathematical Gazette

Mark J. Ablowitz is Professor of Applied Mathematics at the University of Colorado, Boulder. He is the author of five books, including Nonlinear Dispersive Waves (Cambridge, 2011) and Complex Variables: Introduction and Applications (Cambridge, 2003), now in its second edition. Athanassios S. Fokas is Professor of Nonlinear Mathematical Science in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. He is also Adjunct Professor in the Viterby School of Engineering at the University of Southern California. He is the author of four books, including Complex Variables: Introduction and Applications (Cambridge, 2003) and A Unified Approach to Boundary Value Problems (2008).