A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics) [Paperback]

Arieh Iserles (Author)

Book Description

ISBN-10: 0521556554 | ISBN-13: 978-0521556552 | Publication Date: January 26, 1996

This book presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; and methods for parabolic and hyperbolic differential equations and techniques of their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics.

Editorial Reviews

Review

"As a mathematician who developed an interest in numerical analysis in the middle of his professional career, I thoroughly enjoyed reading this text. I wish this book had been available when I first began to take a serious interest in computation. The author's style is comfortable...This book would be my choice for a text to 'modernize' such courses and bring them closer to the current practice of applied mathematics." John Guckenheimer, American Journal of Physics

"...this book succeeds. It provides an excellent introduction to the numerical analysis of differential equations and would serve perfectly as a textbook for a fourth-year undergraduate course in the mathematics curriculum." J. Varah, Computing Reviews

"The overall structure and the clarity of the exposition make this book an excellent introductory textbook for mathematics students. It seems also useful for engineers and scientists who have a practical knowledge of numerical methods and wish to acquire a better understanding of the subject." Mathematical Reviews

"I bel;ieve this book succeeds. It provides an excellent introduction to the numerical analysis of differential equations..." J. Varah, Computing Reviews

Book Description

This text presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject.

See all Editorial Reviews

Product Details

• Paperback: 378 pages
• Publisher: Cambridge University Press (January 26, 1996)
• Language: English
• ISBN-10: 0521556554
• ISBN-13: 978-0521556552
• Product Dimensions: 9.7 x 6.9 x 0.8 inches
• Shipping Weight: 1.2 pounds
• Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #683,776 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

8 of 8 people found the following review helpful:

4.0 out of 5 stars Payback in longrun; not a Cookbook., January 7, 2009

By 

Muthiah Annamalai "gradstudent" (BibleBelt, TX, USA) - See all my reviews
(REAL NAME)   

This review is from: A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics) (Paperback)

In the graduate school, a Math professor used this book, as it talked about a bit of everything. Everything as in initial value problems (IVP) in ODE, 2 point boundary value problems ( BVP ) for ODE, finite difference schemes for boundary value elliptic PDE's and initial-boundary type hypebolic PDE's.

However, the book is written for a mathematician in mind, as the author clearly mentions in the preface. It is not for the light hearted. Book would serve as a
starting point for rigourous foundations in numerical analysis methods for solving
ODE/PDE. Excellent book over all, with numerical examples, watertight arguments,
and crisp prose, without being boring.

6 of 6 people found the following review helpful:

5.0 out of 5 stars Excellent for a graduate course on numerical DE, March 1, 2004

By 

Dennis Pence (Kalamazoo, MI USA) - See all my reviews

This review is from: A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics) (Paperback)

This is an excellent reference and textbook for someone hoping to go beyond the introduction to numerical DE found in any of the standard numerical analysis textbooks. It is not a research monograph, but is also not easy reading. It has already become a fairly standard reference in the literature because of its complete coverage and further references to more specialized sources. I have used it as the textbook for a graduate course on numerical differential equations. I highly recommend it for that purpose and as a reference for someone doing independent reading.

8 of 9 people found the following review helpful:

4.0 out of 5 stars Informal, nice text, April 12, 2006

By 

Stephen Becker - See all my reviews
(REAL NAME)   

This review is from: A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics) (Paperback)

A very informal style of writing with lots of explanation. He doesn't skip large steps like in the old-fashioned terse style of math texts, which makes it very readable, though some readers may not like it. Not very rigorous, but he's upfront about it.

The original version from 1996 has quite a few errors, and the author maintains information on errata on his website. The most recent reprinting has corrected most of these errors. So, even though there is only a single edition, some versions have errors and some don't. So, BEWARE BUYING USED EDITIONS because they will most likely be from an earlier printing and thus have more errors. I assume the new version on amazon is the corrected version.