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This book is intended to be an intermediate treatment of the theory and applications of numerical methods. Much of the material has been presented at the University of Michigan in a course for senior and graduate engineering students. The main feature of this volume is that the various numerical methods are not only discussed in the text but are also illustrated by completely documented computer programs. Many of these programs relate to problems in engineering and applied mathematics. The reader should gain an appreciation of what to expect during the implementation of particular numerical techniques on a digital computer.
Although the emphasis here is on numerical methods (in contrast to numerical analysis), short proofs or their outlines are given throughout the text. The more important numerical methods are illustrated by worked computer examples. The appendix explains the general manner in which the computer examples are presented, and also describes the flow-diagram convention that is adopted. In addition to the computer examples, which are numbered, there are several much shorter examples appearing throughout the text. These shorter examples are not numbered, and usually illustrate a particular point by means of a short hand-calculation. The computer programs are written in the FORTRAN-IV language and have been run on an IBM 360/67 computer. We assume that the reader is already moderately familiar with the FORTRAN-IV language.