Applied Partial Differential Equations (Undergraduate Texts in Mathematics) [Paperback]

J. David Logan (Author)

Book Description

ISBN-10: 0387984399 | ISBN-13: 978-0387984391 | Publication Date: May 1998

This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the physical sciences. The topics include derivations of some of the standard models of mathematical physics (e.g., the heat equation, the wave equation, and Laplaces equation) and methods for solving those equations on unbounded and bounded domains (transform methods and eigenfunction expansions). Prerequisites include multivariable calculus and elementary differential equations. The text differs from other texts in that it is a brief treatment (about 200 pages); yet it provides coverage of the main topics usually studied in the standard course as well as an introduction to using computer algebra packages to solve and understand partial differential equations. The many exercises help students sharpen their computational skills by encouraging them to think about concepts and derivations. The student who reads this book carefully and solves most of the problems will have a sound knowledge base for a second-year partial differential equations course where careful proofs are constructed or upper division courses in science and in engineering where detailed applications of partial differential equations are introduced.

Editorial Reviews

Review

From the reviews of the second edition: "This second edition of the short undergraduate text provides a fist course in PDE aimed at students in mathematics, engineering and the sciences. The material is standard … . Strong emphasis is put on modeling and applications throughout; the main text is supplied with many examples and exercises." (R. Steinbauer, Monatshefte für Mathematik, Vol. 150 (4), 2007) "This book contains an elementary introduction of partial differential equations to undergraduate students in mathematics, engineering, and physical sciences. … This is a unique book in the sense that it provides a coverage of the main topics of the subject in a concise style which is accessible to science and engineering students. … Reading this book and solving the problems, the students will have a solid base for a course in partial differential equations … ." (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 74, 2008) --This text refers to the Hardcover edition.

From the Back Cover

This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of the exercises will have a sound knowledge base for upper division mathematics, science, and engineering courses where detailed models and applications are introduced. J. David Logan is Professor of Mathematics at University of Nebraska, Lincoln. He is also the author of numerous books, including Transport Modeling in Hydrogeochemical Systems (Springer 2001). --This text refers to the Hardcover edition.

Product Details

• Paperback: 181 pages
• Publisher: Springer-Verlag (May 1998)
• Language: English
• ISBN-10: 0387984399
• ISBN-13: 978-0387984391
• Product Dimensions: 9.2 x 6.2 x 0.4 inches
• Shipping Weight: 10.2 ounces
• Average Customer Review: 3.2 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #3,397,250 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

13 of 14 people found the following review helpful:

3.0 out of 5 stars Nice idea, May 6, 2006

By 

Bruce Nourish "bjan" (Phoenix, Arizona, USA) - See all my reviews
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This review is from: Applied Partial Differential Equations (Undergraduate Texts in Mathematics) (Paperback)

This book has two flaws. The first is the classic pitfall of mathematicians trying to reach an audience who are interested in mathematics largely as a tool rather than an end in itself. The author or instructor teaches a pure math course and inserts "application chapters," or pauses between boardfuls of algebra to mumble, "...and this represents a vibrating drumhead." The second is that the book is just too thin. The explanations are very brief, the material is arguably not complete, and there aren't enough examples or problems. While I share the author's taste for minimalism, PDE's are a big subject, and you need a bigger book than this to do them justice.

A general problem with applied PDE courses and books (including this one) is that they fail to give adequate consideration to finite difference methods. Any course in the 21st century should give at least parity to these methods, as they are immeasurably more useful in the real world than eigenfunction expansions or Duhamel's principle. I give the book three stars because the author has succeeded to the extent possible given the constraints he placed upon himself, but I can't recommend it to someone who actually wants to learn applied PDE's; instead, I would recommend DuChateau and Zachmann for a comprehensive and understandable treatment for $20 less.

On the other hand, if you want physical intuition and running code, pick up Garcia, "Numerical Methods for Physics." If you are a mathematician trying to figure out how to write an applied book, drop everything and buy H.M. Schey's "Div, Grad, Curl and All That."

4 of 4 people found the following review helpful:

4.0 out of 5 stars Worth a look as a possible text for a course in partial differential equations, June 12, 2007

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Applied Partial Differential Equations (Undergraduate Texts in Mathematics) (Paperback)

In my opinion, courses in partial differential equations should be offered more often in undergraduate curricula. Many of the problems encountered in the world are solved using partial differential equations rather than ordinary differential equations. This book would be a good text for a course in partial differential equations; it begins with a chapter on the physical origins of partial differential equations and contains descriptions of the mathematical models of the physical events. The sections of the chapter are:

*) Mathematical models
*) Conservation laws
*) Diffusion
*) PDEs in biology
*) Vibrations and acoustics
*) Quantum mechanics
*) Heat flow in three dimensions
*) Laplace's equation
*) Classification of PDEs

A small set of exercises are included at the end of each section, although no solutions are included. The level of discourse is rigorous, yet well within the bounds of the advanced undergraduate with calculus and a course in ordinary differential equations behind them. If you are scheduled to teach or are pondering a course in partial differential equations, then this is a book you should consider as a possible text.

1 of 3 people found the following review helpful:

5.0 out of 5 stars It is really an APPLIED approach to PDE, March 9, 2009

By 

John smith12 - See all my reviews

This review is from: Applied Partial Differential Equations (Undergraduate Texts in Mathematics) (Paperback)

well even if it doesn't cover all the methods of solving PDE. it still a great book, it explains the origin of each problem and the way to attack it.
i think this book is goo for someone who is seeking to understand PDE but not used a course book (other books are better for courses).