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

Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics)

Science & Math

Ablowitz, Mark J.

Fokas, Athanassios S.

Mathematics

Cambridge University Press

In addition to being mathematically elegant, complex variables provide a powerful tool for solving problems that are either very difficult or virtually impossible to solve in any other way. Part I of this text provides an introduction to the subject, including analytic functions, integration, series, and residue calculus and also includes transform methods, ODEs in the complex plane, numerical methods and more. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann-Hilbert problems. The authors also provide an extensive array of applications, illustrative examples and homework exercises. This book is ideal for use in introductory undergraduate and graduate level courses in complex variables.

Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics, Series Number 16)

Fokas, Athanssios S.

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

Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics, Series Number 35)

A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. 
A soliton is a localized pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation. For such exactly solvable problems, the inverse scattering transform provides the general solution of their initial value problems. It is equally surprising that some of these exactly solvable problems arise naturally as models of physical phenomena. 
Simply put, the inverse scattering transform is a nonlinear analog of the Fourier transform used for linear problems. Its value lies in the fact that it allows certain nonlinear problems to be treated by what are essentially linear methods. 
Chapters 1 and 2 of the book describe in detail the theory of the inverse scattering transform. Chapter 3 discusses alternate methods for these exactly solvable problems and the interconnections among them. Physical applications are described in Chapter 4, where, for example, similarities between deep water waves and nonlinear optics become evident. Because of the fundamental role of linear theory, there is an extensive appendix that addresses the linear problems and their solutions.

Solitons and the Inverse Scattering Transform (SIAM Studies in Applied Mathematics, No. 4)

Segur, Harvey

Society for Industrial & Applied

A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.

Solitons and Inverse Scattering Transform (SIAM Studies in Applied Mathematics, No. 4)

Society for Industrial and Applied Mathematics

Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons (Cambridge Texts in Applied Mathematics, Series Number 47)

The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg-de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.

Introduction to Complex Variables and Applications (Cambridge Texts in Applied Mathematics, Series Number 63)

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.

See the best price to sell, buy, or rent books by Ablowitz, Mark J.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Ablowitz, Mark J.

See the best price to sell, buy, or rent books by Ablowitz, Mark J.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics)

Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics, Series Number 16)

Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics)

Complex Variables: Introduction and Applications (Cambridge Texts in Applied Mathematics, Series Number 35)

Solitons and the Inverse Scattering Transform (SIAM Studies in Applied Mathematics, No. 4)

Solitons and Inverse Scattering Transform (SIAM Studies in Applied Mathematics, No. 4)

Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons (Cambridge Texts in Applied Mathematics, Series Number 47)

Introduction to Complex Variables and Applications (Cambridge Texts in Applied Mathematics, Series Number 63)

Introduction to Complex Variables and Applications (Cambridge Texts in Applied Mathematics, Series Number 63)