William F. Ames - Numerical Methods for Partial Differential Equations

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Review:
Ames' textbook is a second edition or, more accurately, an expansion of its highly reputable predecessor published by Barnes and Noble in 1969. Apparently the author's principle in producing this new edition was "If it ain't broke, don't fix it," for he has left all of the material in the first edition virtually unchanged, both in text and in problems.
For those unfamiliar with his earlier book, Ames presented the expected coverage in five chapters: "Fundamentals," "Parabolic equations," "Elliptic equations," "Hyperbolic equations," and "special topics." In the new edition he has added some more recent methods: hopscotch and explicit-implicit schemes for conservation laws in Chapter 4; "Monte Carlo methods," the method of lines, the fast Fourier transform, and the method of fractional steps in Chapter 5; and a new Chapter 6, "Weighted residuals and finite elements." These additions are welcome, and they keep the book from showing its age, but they create added difficulty in fitting the material into a standard length course.
The numerical methods are, of course, computer-oriented and Ames makes occasional remarks about efficiency, but he does not take up computer coding per se. There are, however, occasional problems which expect computational algorithms to be developed.
This book is not for the mathematically immature students-probably three years of analysis, including some linear algebra, make a reasonable background-but the style is informal and the level of rigor is not excessive, so engineering and science students, as well as applied mathematics students, will find it to their tastes. The problem selection is adequate (nearly 300), though not particularly imaginative, and the problem selection is adequate (nearly bibliography is excellent (over 500 entries).
JOHN M. PERRY
Virginia Polytechnic Institute and State University

Uploader's note: The posted cover was taken from the third edition. Also, the first few pages of the book, including the table of contents, is at the end.



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