An Introduction to Partial Differential Equations [Hardcover]

Michael Renardy (Author), Robert C. Rogers (Author)

Book Description

ISBN-10: 0387004440 | ISBN-13: 978-0387004440 | Publication Date: January 8, 2004 | Edition: 2nd

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.

Editorial Reviews

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.

Product Details

• Hardcover: 448 pages
• Publisher: Springer; 2nd edition (January 8, 2004)
• Language: English
• ISBN-10: 0387004440
• ISBN-13: 978-0387004440
• Product Dimensions: 9.3 x 6.6 x 1.2 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 3.8 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #935,184 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

13 of 14 people found the following review helpful:

5.0 out of 5 stars A very good book to learn about partial differential eqn's., March 30, 2000

By A Customer

This review is from: An Introduction to Partial Differential Equations (Texts in Applied Mathematics) (v. 13) (Hardcover)

I found what I was looking for in this book to know enough about this huge theory of Partial Differential Equations. Contents of each chapter is clearly developed and no essential point is missed. If you are someone who seriously wants to learn more and apply PDE theory in your research, this book is worth picking. Although the title alludes to an introductory book bearing a simple approach, this book is far more than an introduction, and I would say some little background in PDE's would help.

13 of 15 people found the following review helpful:

5.0 out of 5 stars An extremely well written introduction to PDEs, September 5, 2003

By A Customer

This review is from: An Introduction to Partial Differential Equations (Texts in Applied Mathematics) (v. 13) (Hardcover)

An Introduction to Partial Differential Equations by Renardy and Rogers is a very well written introduction to the huge and important area of PDEs. It covers both the classical and modern PDE theory on, compared with other expositions, a relatively low number of pages. Nevertheless, Renardy and Rogers succeed in introducing the most important concepts and explaining their interrelations, so that alltogether, the book provides the reader with the background necessary for diving safely into the more advanced literature on the subject.

It was a pleasure for me to read the book, and after nearly four years of work in PDEs, it is still my reference of choice. I would highly recommend it for students of mathematics and for mathematically inclined engineering students.

8 of 11 people found the following review helpful:

5.0 out of 5 stars The Best, May 23, 2000

By 

Francisco Coutinho (Sao Paulo, Sao Paulo Brazil) - See all my reviews
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This review is from: An Introduction to Partial Differential Equations (Texts in Applied Mathematics) (v. 13) (Hardcover)

This book is the best book on advanced partial differential equations i know. It is almost self contained. Every definition is motivated. Examples are given. Buy it and enjoy