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.