Introduction to complex variables and applications
- New York : Cambridge University Press, 2021
- viii, 411 p. ; ill., 25 cm.
Includes bibliographical references and index.
The study of complex variables is both 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 the generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can either be included in the syllabus or form the basis for challenging student projects
9781108959728
Complex Analysis Analytic continuation Bilinear transformation Branch point Cauchy-Riemann conditions Conformal mapping Essential singular point Laplace transform Laurent series Multivalued function Taylor series Unit circle Z-plane