Today, computers with the power that could be offered only by large institutions decades ago now sit on the desks of individuals. Methods of analysis
that were only dreamed of decades ago are now used by students to do homework exercises. Entirely new methods of analysis have appeared that take advantage of computers to perform logical and arithmetic operations at great speed.
Unfortunately, with numerical analysis
this has meant that many simply take the tools developed by others and apply them to problems with little knowledge as to the applicability or accuracy of the methods. Numerical algorithms appear as neatly packaged computer programs that are regarded by the user as "black boxes" into which they feed their data and from which come the publishable results. Many of these programs such as MATHCAD
are excellent and provide quick and generally accurate "first looks" at problems. However, the researcher would be well advised to understand the methods used by the "black-boxes" to solve their problems. This effort still provides the basis for many of the operations contained in those commercial packages and it is hoped will provide the researcher with the knowledge of their applicability to his/her particular problem. This book is an attempt to gain that knowledge.
This book is primarily intended for scientists and engineers so while there is a certain familiarity with mathematics that is assumed, the rigor that one expects with a formal mathematical presentation is lacking. Very little is proved in the traditional mathematical sense of the word. Indeed, derivations are resorted to mainly to emphasize the assumptions that underlie the results.