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An Introduction to Partial Differential Equations (Texts in Applied Mathematics), by Michael Renardy, Robert C. Rogers
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Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.
- Sales Rank: #1379560 in Books
- Published on: 2004-01-08
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.06" w x 6.14" l, 1.66 pounds
- Binding: Hardcover
- 434 pages
Review
From the reviews of the second edition:
"This second edition of the book from 1993 is still one of the most modern books about PDEs. … There is a number of … new examples and exercises, or new sections about Sobolev spaces and nonlinear variational problems. The book is written very well and can be strongly recommended as a textbook for a number of PDE courses. The presentation of a number of subjects is the best available in the literature." (G. Schneider, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 84(10-11), 2004)
"An Introduction to Partial Differential Equations (2nd ed.) is a very careful exposition of functional analytic methods applied to PDEs. … a self-contained text that can be used as the basis of an advanced course in PDEs or as an excellent guide for self-study by a motivated reader. … acts and feels like a standard book in a specific area of mathematics. ... The Renardy and Rogers text contains a large number of problems … . For students, these problems will be challenging and interesting. … is a great book." (Ronald B. Guenther, Enrique A. Thomann, SIAM Reviews, Vol. 47(1), 2005)
"The purpose of this book is to put the topic of differential equations on the same footing in the graduate curriculum as algebra and analysis. … the authors describe it as a book for three or four semesters. … they succeed admirably. The book is extremely well-written with lots of examples and motivation for the theory." (Gary M. Lieberman, Zentralblatt MATH, Vol. 1072, 2005)
From the Back Cover
Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. Like algebra, topology, and rational mechanics, PDEs are a core area of mathematics.
This book aims to provide the background necessary to initiate work on a Ph.D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in chapter 10, and the necessary tools from functional analysis are developed within the coarse. The book can be used to teach a variety of different courses.
This new edition features new problems throughout, and the problems have been rearranged in each section from simplest to most difficult. New examples have also been added. The material on Sobolev spaces has been rearranged and expanded. A new section on nonlinear variational problems with "Young-measure" solutions appears. The reference section has also been expanded.
Most helpful customer reviews
1 of 1 people found the following review helpful.
Thorough introduction to partial differential equations, very insightful
By van Leeuwen R
This book gives a very thorough introduction to partial differential equations. As a physicist I often encounter partial
differential equations. As a rule these equations can not be solved by analytic methods and one needs numerical methods
to solve them. This book discusses ways of understanding the existence and the general properties of solutions of partial
differential equations, without actually having to find an analytical solution. This is, however, done with many examples.
I found the sections on the mathematical methods that lead to important proofs about partial differential equations
(distributions, Sobolev spaces and operator theory) very readable for a physicist. This is discussed in a much more
friendly manner than in other books I encountered on this topic. I learned a lot from this book, and I can highly recommend it
to anyone interested in the various mathematical theories concerning partial differential equations.
4 of 10 people found the following review helpful.
Struggle
By Allan Vandyke
This is a good book for postgraduate maths students. Even though my first degree was in maths I still could not follow the notation given in this book. I struggled with following the material and never got to the end of the book. I will have to come back to this book in a few years once I have developed the skills elsewhere.
0 of 17 people found the following review helpful.
Lots of theory; hardly any methods of solution.
By A. I. Haque
This book is apparently written for a 4 semester course in PDEs for grad students in pure mathematics. You will not learn how to solve PDEs from this book. I need to solve PDEs; not explore theory which does not lead to any solution. I recommend Strauss's book instead.
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