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A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics), by Arieh Iserles
Download A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics), by Arieh Iserles
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Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.
- Sales Rank: #857917 in Books
- Published on: 2008-12-29
- Released on: 2008-11-27
- Original language: English
- Number of items: 1
- Dimensions: 9.72" h x .98" w x 6.85" l, 1.85 pounds
- Binding: Paperback
- 480 pages
Most helpful customer reviews
8 of 9 people found the following review helpful.
Informal, nice text
By Stephen Becker
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.
9 of 9 people found the following review helpful.
Payback in longrun; not a Cookbook.
By Muthiah Annamalai
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.
7 of 7 people found the following review helpful.
Excellent for a graduate course on numerical DE
By Dennis Pence
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.
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