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The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation.
Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition, improves on an already highly complete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide.
List of contents
Preface to the Third Edition.- Preface.- Linear Partial Differential Equations.- Nonlinear Model Equations and Variational Principles.- First-Order, Quasi-Linear Equations and Method of Characteristics.- First-Order Nonlinear Equations and Their Applications.- Conservation Laws and Shock Waves.- Kinematic Waves and Real-World Nonlinear Problems.- Nonlinear Dispersive Waves and Whitham's Equations.- Nonlinear Diffusion-Reaction Phenomena.- Solitons and the Inverse Scattering Transform.- The Nonlinear Schroedinger Equation and Solitary Waves.- Nonlinear Klein--Gordon and Sine-Gordon Equations.- Asymptotic Methods and Nonlinear Evolution Equations.- Tables of Integral Transforms.- Answers and Hints to Selected Exercises.- Bibliography.- Index.
About the author
Lokenath Debnath is Professor of the Department of Mathematics and Professor of Mechanical and Aerospace Engineering at the University of Central Florida in Orlando. He received his M.Sc. and Ph.D. degrees in pure mathematics from the University of Calcutta, and obtained D.I.C. and Ph.D. degrees in applied mathematics from the Imperial College of Science and Technology, University of London. He was a Senior Research Fellow at the University of Cambridge and has had visiting appointments to several universities in the United States and abroad. His many honors and awards include two Senior Fulbright Fellowships and an NSF Scientist award to visit India for lectures and research. Dr. Debnath is author or co-author of several books and research papers in pure and applied mathematics, and serves on several editorial boards for scientific journals. He is the current and founding Managing Editor of theInternational Journal of Mathematics and Mathematical Sciences.
Summary
The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation.
Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition, improves on an already highly complete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide.
Additional text
From the reviews:
"An exceptionally complete overview of the latest developments in the field of PDEs. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here."—Applied Mechanics Review (Review of First Edition)
From the reviews of the third edition:
"Overall, it is a useful book for teaching, a rich source of examples, and I am happy to have it on a shelf of my library."—UK Nonlinear News (Review of Second Edition)
“This book provides an introduction to nonlinear partial differential equations that arise throughout in science and engineering and to the basic methods for finding the solutions for these equations. The book contains thirteen chapters and three appendixes. At the end of the first twelve chapters there are exercises that help to understand the subject matter. … This book is recommended for graduate students in science and engineering.” (Valery V. Karachik, Zentralblatt MATH, Vol. 1242, 2012)
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From the reviews:
"An exceptionally complete overview of the latest developments in the field of PDEs. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here."-Applied Mechanics Review (Review of First Edition)
From the reviews of the third edition:
"Overall, it is a useful book for teaching, a rich source of examples, and I am happy to have it on a shelf of my library."-UK Nonlinear News (Review of Second Edition)
"This book provides an introduction to nonlinear partial differential equations that arise throughout in science and engineering and to the basic methods for finding the solutions for these equations. The book contains thirteen chapters and three appendixes. At the end of the first twelve chapters there are exercises that help to understand the subject matter. ... This book is recommended for graduate students in science and engineering." (Valery V. Karachik, Zentralblatt MATH, Vol. 1242, 2012)
