An Introduction to Numerical Methods and Analysis, Revised Edition

The objective of this book is for the reader to learn where approximation methods come from, why they work, why they sometimes don't work, and when to use which of many techniques that are available, and to do all this in a way that emphasizes readability and usefulness to the numerical methods novice. Each chapter and each section begins with the basic, elementary material and gradually builds up to more advanced topics.  The text begins with a review of the important calculus results, and why and where these ideas play an important role throughout the book.  Some of the concepts required for the study of computational mathematics are introduced, and simple approximations using Taylor's Theorem are treated in some depth. The exposition is intended to be lively and "student friendly".  Exercises run the gamut from simple hand computations that might be characterized as "starter exercises", to challenging derivations and minor proofs, to programming exercises.