Introduction to Complex Variables and Applications

by Mark J. Ablowitz, Athanassios S. Fokas

2021 · Cambridge University Press

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.

Solitons, Nonlinear Evolution Equations and Inverse Scattering

by Mark J. Ablowitz, P. A. Clarkson

1991 · Cambridge University Press

This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.