Partial Differential Equations: Theory and Completely Solved Problems 1st Edition by Thomas Hillen (PDF)

Description

Uniquely provides fully solved problems for linear partialdifferential equations and boundary value problemsPartial Differential Equations: Theory and Completely SolvedProblems utilizes real-world physical models alongsideessential theoretical concepts. With extensive examples, the bookguides readers through the use of Partial Differential Equations(PDEs) for successfully solving and modeling phenomena inengineering, biology, and the applied sciences.The book focuses exclusively on linear PDEs and how they can besolved using the separation of variables technique. The authorsbegin by describing functions and their partial derivatives whilealso defining the concepts of elliptic, parabolic, and hyperbolicPDEs. Following an introduction to basic theory, subsequentchapters explore key topics including:• Classification of second-order linear PDEs• Derivation of heat, wave, and Laplace’sequations• Fourier series• Separation of variables• Sturm-Liouville theory• Fourier transformsEach chapter concludes with summaries that outline key concepts.Readers are provided the opportunity to test their comprehension ofthe presented material through numerous problems, ranked by theirlevel of complexity, and a related website features supplementaldata and resources.Extensively class-tested to ensure an accessible presentation,Partial Differential Equations is an excellent book forengineering, mathematics, and applied science courses on the topicat the upper-undergraduate and graduate levels.

User’s Reviews

Editorial Reviews: Review “The book gives a vivid description of the theory forsolving linear PDEs. The excellent method, the expensive use ofexamples, and the overview of the existing solutions make the bookvery useful for students and for researchers. It is highlyrecommended.” (Zamm, 1 November 2014)“Summing Up: Recommended. Upper-division undergraduates,graduate students, and faculty.” (Choice, 1August 2013) From the Back Cover Uniquely provides fully solved problems for both linear partial differential equations and boundary value problemsPartial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences.The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including:Classification of second-order linear PDEsDerivation of heat, wave, and Laplace’s equationsFourier seriesSeparation of variablesSturm-Liouville theoryFourier transformsEach chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources.Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels. About the Author T. HILLEN, PhD, is Professor and Associate Chair(Graduate Program) in the Department of Mathematical andStatistical Sciences at the University of Alberta, Canada. Dr.Hillen is a world-leading expert in PDEs applied to mathematicalbiology and has also published extensively in the area of generalapplied mathematics.I. E. LEONARD, PhD, is Lecturer in the Department ofMathematical and Statistical Sciences at the University of Alberta,Canada. Dr. Leonard works in the areas of real analysis anddiscrete mathematics.H. VAN ROESSEL, PhD, is Associate Professor in theDepartment of Mathematical and Statistical Sciences at theUniversity of Alberta, Canada. Dr. Van Roessel works on theapplication of PDEs to coagulation-fragmentation problems andrelated mathematical models. Read more

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

⭐This is the best book on Partial Differential Equations I have come across. In terms of its contents it covers all the main topics for a course on PDE. This book and the book by Debnath (another good book for scientists and engineers) are the only books I have seen that go over how to solve nonhomogenous PDE.The explanations in this book are clear and don’t leave out many steps related to the material. With this being said there is NOT an appendix reviewing prerequisite material. It is assumed you know at the very least Calculus I-II, and Ordinary Differential Equations. If you would like to understand absolutely everything in this book you should learn some elementary Linear Algebra and Multi-variable Calculus.The first half of the book contains theory with worked out examples while the second half has explicitly solved problems with clear solutions. The problems ranged from simple (similar to the examples) to more complex theoretical problems.This text can get somewhat intense at certain parts, but if you are looking for a rigorous introduction then you might want to look somewhere else. This book is aimed at students of Applied Mathematics, science, and engineering. This is odd however, there does not appear to be a lot of applications to the sciences or how PDE are modeled like in other books (Debnath or Logan in particular). This doesn’t bother me much because I was looking for a great first exposure to the subject and my expectation was met.This book luckily isn’t encumbered with a chapter on Finite Difference Methods, but at the same time it doesn’t contain a section on Green’s Function. Not a big deal, however because the book is still a gem.Overall this book is really good. I’ve gone through about 10 books on PDE and this is at the top, with Asmar and Debnath coming in second and third.If this is your first exposure to PDE and you are looking to self study using this book I recommend the following chapters:Chapter 1: Introduction: (a quick skim will suffice. This section was rather boring for me, personally)Chapter 2: Fourier Series (take many notes, this method is used in the following chapter)Chapter 3: Separation of Variable (popular method for finding solutions to PDE)Chapter 8: Fourier Transforms: (used for solving PDE with infinite domains)Chapter 9: Fourier Transforms (using methods in the previous chapter to solve PDE)(These are the topics we covered when I took a course on PDE.)

⭐Don’t have the time I used for writing reviews… However, I had to write one real quick for this great book on PDEs (since no one else has.) I originally purchased this book to supplement another that was terrible. I have since used it repeatedly as a reference/refresher. This is how all text book should be.

⭐The worked-out examples are a great feature, but they do not follow the methods my instructor uses in class.

⭐ok

⭐I wasn’t familiar with the notation but found some appendices that helped to explain a lot of the notation. Now I am looking forward to reading the rest of the book.

⭐useful reference but you can’t really learn the material from this book. you have to have an experienced instructor teach you

⭐Recieved. Thanks.

⭐This book is a joy to read.

⭐Good

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