Introduction to the foundations of applied mathematics / Mark H. Holmes

One of the primary objectives of the book is to use mathematics to derive a fundamental understanding of the derivation, analysis and interpretation of mathematical models. A large spectrum of methods for solving the resulting problem is discussed, from Fourier and Laplace transforms to perturbation approximations, similarity solutions, as well as model tailored methods relying on both the mathematical and physical characteristics of the problem.
The mathematical ideas underlying model development are introduced in the context of particular applications, with emphasis on their potential application to other real-life phenomena.
The first two chapters, 1. Dimensional Analysis and 2. Perturbation Methods, establish some of the basic methods needed later in the text. Spatial motion is introduced in the next two chapters, 3. Kinetics, which describes how to model interacting populations, and 4. Diffusion. Chapters 6–9 deal with specific problems in continuum mechanics, from elastic and viscoelastic materials to ideal and Newtonian flows, vorticity and boundary layers.
The book contains a wide spectrum of exercises and detailed illustrations. It addresses students and researchers interested in mathematical modeling in physics, engineering and applied sciences. It can also be recommended as a textbook at the graduate student level. (MathSciNet)