This text emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. The authors provide an introduction to various appropriate approximation techniques; they show students why the methods work, what type of errors to expect, and when an application might lead to difficulties; and they provide information about the availability of high-quality software for numerical approximation routines. The techniques covered in this text are essentially the same as those covered in the sixth edition of these authors' "Numerical Analysis" text, but the emphasis is much different. In this text, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the student that the method is reasonable both mathematically and computationally.