This book is an introduction to numerical analysis: the solution of mathematical problems using numerical algorithms. Typically these algorithms are implemented with computers. To solve numerically a problem in science or engineering one is typically faced with four concerns:

1. How can the science/engineering problem be posed as a mathematical problem?

2. How can the mathematical problem be solved at all, using a computer?

3. How can it be solved accurately?

4. How can it be solved quickly?

The first concern comes from the science and engineering disciplines, and is outside the scope of this book. However, there are many practical examples and problems drawn from engineering, chemistry, and economics applications.

The focus of most introductory texts on numerical methods is, appropriately, concern #2, and that is also the main emphasis here. Accordingly, a number of different subjects are described that facilitate solution of a wide array of science and engineering problems.

Accuracy, concern #3, deals with numerical error and approximation error. There is a brief introductory chapter on error that presents the main ideas. Throughout the remainder of this book, algorithm choices and implementation details that affect accuracy are described. For the most part, where a claim of accuracy is made an example is given to illuminate the point, and to show how such claims can be tested.