Overview

At almost all academic institutions worldwide, complex variables and analytic functions are utilized in courses on applied mathematics, physics, engineering, and other related subjects. For most students, formulas alone do not provide a sufficient introduction to this widely taught material, yet illustrations of functions are sparse in current books on the topic. This is the first primary introductory textbook on complex variables and analytic functions to make extensive use of functional illustrations. Aiming to reach undergraduate students entering the world of complex variables and analytic functions, this book utilizes graphics to visually build on familiar cases and illustrate how these same functions extend beyond the real axis. It covers several important topics that are omitted in nearly all recent texts, including techniques for analytic continuation and discussions of elliptic functions and of Wiener–Hopf methods. It also presents current advances in research, highlighting the subject’s active and fascinating frontier. The primary audience for this textbook is undergraduate students taking an introductory course on complex variables and analytic functions. It is also geared toward graduate students taking a second semester course on these topics, engineers and physicists who use complex variables in their work, and students and researchers at any level who want a reference book on the subject.

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9781611975970

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Bengt Fornberg has been a professor of applied mathematics at the University of Colorado, Boulder, since 1995. His primary research interests focus on computational methods for solving PDEs and numerical methodologies related to analytic functions. He has held positions at the European Organization for Nuclear Research (CERN), California Institute of Technology, and Exxon Corporate Research. In 2014, he was elected a SIAM Fellow. Cécile Piret is a faculty member in the department of mathematical sciences at Michigan Technological University. A former postdoctoral fellow at Catholic University of Louvain and the National Center for Atmospheric Research (NCAR), her research interests revolve around the development of high order methods for numerically solving differential equations.

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