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Partial Differential Equations: Sources and Solutions

Arthur D. Snider
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Fernando Q. Gouvêa
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This is a Dover reprint of a textbook first published by Prentice-Hall in 1999. It retains its large "standard textbook" format, but is now printed on normal paper and without color. In exchange, it probably costs a lot less than it did in its original incarnation.

Snider writes as an applied mathematician, thinking especially of engineering students. A few quotes from the introduction give a good idea of his point of view:

Most engineering readers have no stomach for the bulky "n-times-continuously-differentiable" type of hypothesis modifiers which ensure complete mathematical generality, particularly when the delimiting counterexamples are unlikely to occur in a lifetime of engineering practice. But there are practical physical situations where such oddities as limited differentiability inhibit accuracy — as, for example, flows with reentrant corners.

Thus, mathematical niceties are introduced only when they are genuinely important in practice. On the other hand, the applied point of view sometimes leades Snider to add technical material that other authors might prefer to exclude:

A classic case in point is the problem of heat flow in a cylindrical wedge. Most texts only treat the situation where the cylindrical side is heated externally — it leads to an orderly Fourier series expansion. This author is aware of no other textbook in the English language which analyzes the configuration where the flat sides are heated (entailing the obscure Lebedev expansions). What is an engineering reader to think when an "applied mathematics" author sidesteps issues because they are not mathematically tidy?

That's a very good point, and the intended readers of this book, though they may hate the Lebedev expansions themselves, will recognize that an effort is being made to address their concerns.

Despite being retired, the author maintains an errata sheet at his home page.

Overall, this is a rather traditional textbook that seems well designed to serve its intended audience.

Fernando Q. Gouvêa is the editor of MAA Reviews. He is Carter Professor of Mathematics at Colby College in Waterville, ME.
The table of contents is not available.