Remember there�s more to life than computers.
From the preface:
The last time I looked, the Java programming language still had +, -, *, /, and % operators to do operations with numbers. It may be hard to believe today, but programming is not only about Web pages, graphics, enterprise software, database systems, and computer games.
I wrote this book to remind today's programmers, especially Java programmers, that computers really are quite good at numerical computing, affectionately known as "number crunching." In fact, some numerical computing underlies most programs -- for example, not too many graphics applications or interactive computer games would get very far without crunching at least a few numbers. Of course, scientific, mathematical, statistical, and financial programs rely heavily on numerical computing.
So it behooves the typical Java programmer, besides knowing the standard API alphabet soup -- JFC, RMI, JSP, EJB, JDBC, and so on -- to know something about how to do good numerical computing. You'll never know when a roundoff error will bite you, or why that "correct" formula you copied right out of your favorite physics textbook into your program somehow computes the wrong answer.
Another reason I wrote this book is that I'm fascinated by the dichotomies of pure mathematics and computer science. On one hand, you have mathematics, a rigorous, abstract world where it is possible to prove, absolutely, that a computation is correct. On the other hand, you have computers, where computations are, well, they're fast. And yet, mathematicians and computer scientists can work together to devise some very clever ways to enable computers to do mathematics and, in the great majority of cases, to compute the right answer.
This book is an introduction to numerical computing. It is not a textbook on numerical methods or numerical analysis, although it certainly shows how to program many key numerical algorithms in Java. We'll examine these algorithms, enough to get a feel for how they work and why they're useful, without formally proving why they work. Because Java is ideal for doing so, we'll also demonstrate many of the algorithms with interactive, graphical programs. After seeing how we can dodge some of the pitfalls of floating-point and integer computations, we'll explore programs that solve equations for x, do interpolation and integration, solve differential equations and systems of linear equations, and more.
Numerical computing is not all work, either. This book also contains several chapters on lighter (but not necessarily less useful) topics, including computing thousands of digits of pi, using different ways to generate random numbers, looking for patterns in the prime numbers, and creating the intricately beautiful fractal images.
I tried hard to keep the math in this book at the freshman calculus level or below -- knowledge of high school algebra should be enough for most of it. All the interactive programs in this book can run either as applets or as standalone programs. My friends and I have tested them with the Netscape 4.7 browser running on Windows, Linux, and Solaris, with Microsoft Internet Explorer 6.0 running on the PC, and Microsoft Internet Explorer 5.1 running on the Macintosh. I've tested the standalone programs on my Windows 98 PC with JDK 1.2, 1.3, and 1.4. Of course, there's no guarantee they'll all work perfectly for you, but the source code for all the programs, along with instructions on how to compile and run them, are available for downloading.
I wrote all the programs strictly as illustrative examples for this book. You're free to use the source code anyway you like, but bear in mind that this is not fully tested, commercial-quality code. Neither Prentice-Hall nor I can be responsible for anything bad that may happen if you use these programs. I had a lot of fun writing this book and its programs, and I hope that comes through in the text. If you're inspired to learn more about any of the topics, then I will be very happy.
Numerical computing is dynamic!
Algorithms are stable or unstable.
They may converge or diverge.
And from their computed values,
Patterns may emerge!