Complex Variables: Introduction and Applications

Cambridge Texts in Applied Mathematics #35

by Mark J. Ablowitz, Athanassios S. Fokas

Complex variables offer very efficient methods for attacking many difficult problems, and it is the aim of this book to offer a thorough review of these methods and their applications. Part I is an introduction to the subject, including residue calculus and transform methods. Part II advances to conformal mappings, and the study of Riemann-Hilbert problems. An extensive array of examples and exercises are included. This new edition has been improved throughout and is ideal for use in introductory undergraduate and graduate level courses in complex variables. First Edition Hb (1997): 0-521-48058-2 First Edition Pb (1997): 0-521-48523-1

Genres: Mathematics, Science

660 pages, Paperback

First published February 13, 1997

Reviews

[Hunter Lybbert · Rating 3 out of 5]

Very tough class but interesting at times. Glad it’s behind me.

[mirela Darau · Rating 5 out of 5]

One of my favourite books along with Bender & Orszag's Mathematical Methods. Accessible language, lots of relevant examples, it's definetely a pleasant read. I had a first look into it when struggling to understand multivalued functions. Examples together with theory always worked best for me, so finding this book was one of the first steps towards my understanding branch cuts and practical ways to redefine them for non-trivial functions.

[Tomáš Ševček · Rating 5 out of 5]

A great book on complex analysis and its many applications throughout mathematics. Standard topics are covered, such as complex and analytic (holomorphic) functions, multivaluedness and Riemann surfaces, complex integration, infinite series and products, singularities, analytic continuation, the residue theorem and more. The applications discussed include the Fourier and Laplace transform, fluid dynamics, ODEs in complex variables, asymptotic analysis and Riemann-Hilbert problems (both scalar and matrix). While the book does not contain as many proofs as some other books on the topic, it is definitely not an easy book and requires active reading. I took a complex analysis course before reading the book, and reading it still gave me a lot. I recommend the book (not only) to anyone who is interested in the ways complex analysis is applied in other parts of mathematics.

[Jovany Agathe · Rating 4 out of 5]

Complex variable, In mathematics, a variable that can take on the value of a complex number. In basic algebra, the variables x and y generally stand for values of real numbers. The algebra of complex numbers (complex analysis) uses the complex variable z to represent a number of the form a + bi...