Introduction to Complex Variables and Applications

1. Complex numbers and elementary functions
2. Analytic functions and integration
3. Sequences, series and singularities of complex functions
4. Residue calculus and applications of contour integration
5. Conformal mappings and applications
Appendix. Answers to selected odd-numbered exercises
References
Index.

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 Fokas has a BS in Aeronautics from Imperial College (1975), a PhD in Applied Mathematics from California Institute of Technology (1979, and an MD from the University of Miami (1986). He also has eight honorary degrees. In 1978 he was appointed a Saul Kaplun Fellow at the Department of Applied Mathematics at Caltech. Over the successive 47 years he has been appointed to a Chair in Applied Mathematics at Imperial College and first holder of the inaugural Chair of Nonlinear Mathematical Science at the University of Cambridge, Adjunct Professor at the University of Southern California, held visiting positions at Stanford and Harvard Universities, and been made a Fellow of Clare Hall College, Cambridge, the Guggenheim Foundation, American Institute for Medical and Biological Engineering, and the American mathematical Society. Professor Fokas received the Naylor Prize of the London Mathematical Society (the previous recipient being Stephen Hawking) in 2000, the Aristos Prize of the Academy of Athens in 2004, the Excellence Prize of the Bodassaki Foundation in 2006, the Senior EPSRC Fellowship in 2015, the Blaise Pascal Medal of the European Academy of Sciences in 2023, and the SIAM Kruskal Award/Lecture in 2024. One of only 11 Honorary Members of the World Academy of Sciences (seven of whom are Nobel Prize Laureates), Professor Fokas was pronounced by Research.com a "UK Mathematics Leader, 2024" as a result of being in the list of the 10 most cited UK mathematicians of all time by H-index and the most cited mathematician of all time from the University of Cambridge, not to mention his being the author or co-author of eight monographs and eight books, and published more than 400 papers across the fields of Mathematics, Physics, Engineering, Biology, Medicine, Philosophy, and the Arts. In 2006 the distinguished mathematician Israel Gelfand wrote that "Fokas is a rare scientist in the style of Renaissance".