Introduction to Complex Variables and Applications

An introduction to complex variables that caters for undergraduate students in applied mathematics, science, and engineering.

Mark J. Ablowitz (Author), Athanassios S. Fokas (Author)

9781108832618, Cambridge University Press

Hardback, published 25 March 2021

420 pages
25 x 17.5 x 2.8 cm, 0.85 kg

'… 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

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.

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.

Subject Areas: Maths for engineers [TBJ], Mathematical modelling [PBWH], Complex analysis, complex variables [PBKD]