Now that powerful PCs and Macs are everywhere available, when solving a numerical problem, we should no longer be content with an indefinite answer, that is, an answer where the error bound is either unknown or a vague guess. This book’s software allows you to obtain your numerical answers to a prescribed number of correct decimal places. For instance, one can compute a definite integral to a wide choice of correct decimal places.
The problems treated in this book are standard problems of elementary numerical analysis, including a variety of problems from the field of ordinary differential equations and one standard problem from the field of partial differential equations. Most programs allow you to choose the number of correct decimal places for a problem’s solution, with the understanding that more correct decimals require more computer time.
Besides the availability of powerful computers, two other advances permit the easy generation of accurate numerical answers. One is the development of efficient methods for accurately bounding computation errors, stemming from Ramon Moore’s invention of interval arithmetic in 1962. The other is the development of methods for analyzing computation tasks, stemming from Alan Turing’s groundbreaking work in the 1930s.
The CD that comes with this book contains a set of demonstration programs that will run on any PC using the Microsoft Windows XP operating system. Page 248 explains how to load the demonstration programs onto your PC’s hard disk. After you follow those directions and read the short first chapter, you are ready to use any program. A beginning numerical analysis student can use this software to solve numerical problems that arise in the student’s other science or engineering courses.