Synopses & Reviews
"An exceptionally complete overview. 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. This reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel." ---Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership. Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition is an exceptionally complete and accessible text/reference for graduate students, researchers, and professionals in mathematics, physics, and engineering. It may be used in graduate-level courses, as a self-study resource, or as a research reference.
Review
From the reviews of the first and second editions: "Nonlinear partial differential equations is an old and vast area of research. There is a big and well-developed theory as well as a huge variety of applications. It seems to be impossible to embrace this subject in a single monograph. The book of Lokenath Debnath is a quite successful attempt. It is a second edition of the book, considerably extended and revised. The author is trying to balance the deep and rigorous theory and a variety of approaches and often seminal examples. To examples, he gives the leading, more than just an illustrative, role.... The book could serve as a good selection of choices for a kernel of a graduate or even undergraduate module in Applied Mathematics or Engineering Sciences. For more fundamental courses the book is also useful, since it contains a lot of motivations and well elaborated exercises.... 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) "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... The style is clear and to the point... This is a very useful book for all scientists dealing with nonlinear phenomena. This reviewer feels that it is a very hard act to follow, and recommends it strongly for individual students, practitioners, and libraries alike. The reviewer seldom gets so enthusiastic about the books he is asked to review, but [this book] is a jewel."--Applied Mechanics Review (Review of First Edition) "This book provides a valuable survey of...nonlinear partial differential equations and their methods of solutions...at the end of each chapter [there are] exercises that help build an understanding of the subject matter, ...and in many cases [these exercises] provide an extension of material found in the main body of the text...the style of writing is clear and concise and the choice of topics is comprehensive."--Zentralblatt Math (Review of First Edition) "The book is written in a lucid, no-nonsense style that will be a pleasure for any serious reader. The author's emphasis is on the physical significance of the solutions and less on such mathematical subtleties as existence and uniqueness properties. ...The text is designed and organized primarily for classroom use. It can be used selectively, or the whole book can be used for a two-semester course. It can also serve as a reference and as a starting point for further study. Each chapter contains numerous, well-chosen exercises, and selected solutions are provided at the end of the book, making it suitable for self-study. ...I hope this book will succeed in bringing new developments in PDEs to those classrooms in which students have so far been limited to the classical results."--Computing Reviews (Review of First Edition) "In an effort to make the book useful for a diverse readership, 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."--Booknews (Review of First Edition) "Debnath's book comprehensively surveys methods for solving partial differential equations as well as a complete and thorough analysis of their solutions. The book is well designed for graduate students in physics, engineering, and applied mathematics sequences, and scientists and engineers whose projects require the solution of partial differential equations. It provides an excellent introduction to linear partial differential equations, together with a rigorous treatment of well-selected, real-world examples and methods of solution of nonlinear partial differential equations and their significance. Problems and exercises well suited for use in graduate classes, for example, are completely solved to illustrate the various methods presented. Debnath's book will certainly be an invaluable resource for self-study as well as a reference text for scientists, engineers, and applied mathematicians. Exceptionally well written. Highly recommended." --Choice (Review of First Edition) "This monograph represents a systematic and complex treatment of linear and nonlinear PDE. The book offers not only a rich material for a graduated level course for mathematics, science and engineering students, but also a reference work for a serious and advanced study and research in PDE. ... contains a wide spectrum of exercises, carefully chosen, included at the end of each chapter. ... We recommend this book as an example of how to do the mathematics more accessible and applicable to the physical reality." (Liliana Popa, Iasi Polytechnic Magazine, Vol. 18 (1/4), 2006)
Synopsis
This expanded, revised edition is a thorough and systematic treatment of linear and nonlinear partial differential equations and their varied applications. It contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, make the book useful for a diverse readership including graduates, researchers, and professionals in mathematics, physics and engineering.
Table of Contents
Preface to the Second Edition Preface to the First Edition 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