An Introduction to Nonlinear Partial Differential Equations 2nd Edition by J. David Logan (PDF)

Description

Praise for the First Edition: “This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds.” ―SIAM ReviewA practical introduction to nonlinear PDEs and their real-world applicationsNow in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems.The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include:Additional intermediate-level exercises that facilitate the development of advanced problem-solving skillsNew applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseasesAn expanded bibliography that facilitates further investigation into specialized topicsWith individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.

User’s Reviews

Editorial Reviews: Review “This book is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.” (Mathematical Reviews, 2009c) From the Inside Flap Praise for the First Edition:”This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds.” —SIAM ReviewA practical introduction to nonlinear PDEs and their real-world applicationsNow in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems.The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include:Additional intermediate-level exercises that facilitate the development of advanced problem-solving skillsNew applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseasesAn expanded bibliography that facilitates further investigation into specialized topicsWith individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs. From the Back Cover Praise for the First Edition:”This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds.” —SIAM ReviewA practical introduction to nonlinear PDEs and their real-world applicationsNow in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems.The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include:Additional intermediate-level exercises that facilitate the development of advanced problem-solving skillsNew applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseasesAn expanded bibliography that facilitates further investigation into specialized topicsWith individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs. About the Author J. David Logan, PhD, is Willa Cather Professor of Mathematics at the University of Nebraska–Lincoln. He has authored several texts on elementary differential equations and beginning partial differential equations, including Applied Mathematics, Third Edition, also published by Wiley. Dr. Logan’s research interests include mathematical physics, combustion and detonation, hydrogeology, and mathematical biology. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐There seem to be few textbooks on this particular subject accessible to students; most deal with linear PDE’s, so the book fills a gap. ‘Nonlinear Partial Differential Equations’ assumes the reader is already familiar with differential equations,so is not suitable as an introduction to the subject. It is written at an advanced level, but concepts are very clearly spelled out. Logan takes the reader through all the necessary mathematical steps in explaining a new concept. He does not skip steps in his analysis. Chapter One introduces canonical equations and transformations, but Logan’s treatment is very sparse and there are better texts available for these subjects. Logan’s book concentrates mostly on how PDE’s can be reduced to ordinary differential equations via similarity methods etc. Most standard types of nonlinear systems are dealt with, including reaction diffusion processes, chemically reacting fluids and shock wave development. I like this book and that’s why I bought it from Amazon, but be careful, there are one or two typing errors in the maths.

⭐zwischen der Mathematik und den Anwendungen. Das Buch enthält nur sehr wenig Theorie (dafür einen Punktabzug), dafür aber viele gelungene Plausibilitätsüberlegungen und praktische Beispiele, also etwas, was für Ingenieure wohl gerade richtig ist. Die Auswahl der Gleichungen deckt den Bereich von den Erhaltungsgleichungen bis zu den nichtlinearen Reaktions-Diffusionsgleichungen ab.

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