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Foundations of Applied Mathematics

Michael D. Greenberg
Dover Publications
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The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
William J. Satzer
, on

This Dover publication is an unabridged reproduction of a classic textbook in applied mathematics first published in 1978. It is intended for advanced undergraduates and first-year graduate students in engineering. For prerequisites the author suggests only single and multivariable calculus, some experience with differential equations and a touch of mathematical maturity.

Although this is a very comprehensive text, the style is crisp and clear and the exposition is tightly organized. The book is divided into five sections: real analysis, complex variables, linear analysis, and then ordinary and partial differential equations. The chapters are all pretty short — only two are longer than thirty pages and most are twenty pages or less. The whole book gives the impression of something carefully crafted — just the right amount for each subject and no more.

The author also chooses to concentrate on only a few of the many possible physical applications from engineering and applied physics. He selects fluid mechanics, heat conduction and Newtonian mechanics and provides self-contained discussions for each one. A key to the success of the author’s approach is how he shows the reader the physical concepts as they intertwine with the mathematics, how mathematical insight clarifies the physics and how physical intuition guides the mathematics.

Although the title refers to “applied mathematics” without qualification, it is clear that this book is about applications in physics and engineering. Obviously much of the material here is relevant in other fields, but mathematical topics that might be more relevant to applications outside engineering (graph theory or probability or group theory, for example) are not even mentioned here.

The author is not reticent about discussing theory, stating theorems precisely, and even giving some proofs, but the emphasis is very definitely on methods and techniques. This is reinforced with excellent exercises, many of them computational, some conceptual, some asking for proofs, and a few introducing new material.

Even more than three decades after its first publication this remains a very relevant resource and would still be a good choice for a text.

Bill Satzer ( is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

The table of contents is not available.