Introduction to Complex Variables and Applications
Introduction to Complex Variables and Applications

Author: Mark J. Ablowitz

Publisher: Cambridge University Press

Published: 2021-03-25

Total Pages: 422

ISBN-13: 110896334X

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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.

Complex Variables
Complex Variables

Author: Mark J. Ablowitz

Publisher: Cambridge University Press

Published: 1997-02-13

Total Pages: 664

ISBN-13: 9780521485234

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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.

Applied Complex Variables
Applied Complex Variables

Author: John W. Dettman

Publisher: Courier Corporation

Published: 2012-05-07

Total Pages: 514

ISBN-13: 0486158284

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Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.

Complex Analysis with Applications
Complex Analysis with Applications

Author: Richard A. Silverman

Publisher: Courier Corporation

Published: 1984-01-01

Total Pages: 308

ISBN-13: 9780486647623

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The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.

Complex Variables and Applications
Complex Variables and Applications

Author: James Ward Brown

Publisher: McGraw-Hill Science, Engineering & Mathematics

Published: 1996

Total Pages: 426

ISBN-13:

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This text, and accompanying disk, provides coverage of complex variables. It uses examples and exercise sets, with clear explanations of problem-solving techniqes and material on the further theory of functions.

Complex Variables with Applications
Complex Variables with Applications

Author: Saminathan Ponnusamy

Publisher: Springer Science & Business Media

Published: 2007-05-26

Total Pages: 521

ISBN-13: 0817645136

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Explores the interrelations between real and complex numbers by adopting both generalization and specialization methods to move between them, while simultaneously examining their analytic and geometric characteristics Engaging exposition with discussions, remarks, questions, and exercises to motivate understanding and critical thinking skills Encludes numerous examples and applications relevant to science and engineering students

An Introduction to Complex Analysis and the Laplace Transform
An Introduction to Complex Analysis and the Laplace Transform

Author: Vladimir Eiderman

Publisher: CRC Press

Published: 2021-12-20

Total Pages: 383

ISBN-13: 100051112X

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The aim of this comparatively short textbook is a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications. Several important applications in physics and engineering are considered in the book. This thorough presentation includes all theorems (with a few exceptions) presented with proofs. No previous exposure to complex numbers is assumed. The textbook can be used in one-semester or two-semester courses. In one respect this book is larger than usual, namely in the number of detailed solutions of typical problems. This, together with various problems, makes the book useful both for self- study and for the instructor as well. A specific point of the book is the inclusion of the Laplace transform. These two topics are closely related. Concepts in complex analysis are needed to formulate and prove basic theorems in Laplace transforms, such as the inverse Laplace transform formula. Methods of complex analysis provide solutions for problems involving Laplace transforms. Complex numbers lend clarity and completion to some areas of classical analysis. These numbers found important applications not only in the mathematical theory, but in the mathematical descriptions of processes in physics and engineering.