Introduction to the Foundations of Applied Mathematics (Texts in Applied Mathematics, 56)

I took a one-semester upper-level undergraduate / graduate course in mathematical modeling that used this textbook. We covered the material in chapters 1 (dimensional analysis), 2 (perturbation methods), 3 (kinetics), and 4 (diffusion) and we talked a wee bit about chapter 5 (traffic flows). In general, this is a well-written, well-structured textbook with clear examples. The author uses direct and plain language to communicate ideas. To use this textbook, a student really must have the prerequisite knowledge listed in the introduction written by Holmes (that is, a solid understanding of Taylor's theorem, ordinary differential equations, and linear algebra). Parts of the example problems leave out steps that a student with that background would know how to perform. I think this is a good thing because it forced me to work the examples through myself and keep a pencil in hand while reading, but I really did need to rely on knowledge I acquired earlier. Also, like most first-edition textbooks, this book had some minor typos (some incorrect kinetic equations in chapter 3, for example) -- the kind of stuff that you just have to keep an eye out for as a reader of a new textbook. Overall, a solid effort, well-written, one of the better textbooks I've read.

This book worth it.

Excellent overview of many topics in applied mathematics. A few typos, but the author has nearly all of them on his webpage and they are by in large minor. A true introduction: students of mathematics or the natural sciences should be able to tackle the material with little to no background beyond basic 1st or 2nd year undergraduate mathematics.

The book is brand new and in good condition.