Preface to the first edition
Published online by Cambridge University Press: 05 June 2012
Summary
Books – so we are often told – should be born out of a sense of mission, a wish to share knowledge, experience and ideas, a penchant for beauty. This book has been born out of a sense of frustration.
For the last decade or so I have been teaching the numerical analysis of differential equations to mathematicians, in Cambridge and elsewhere. Examining this extensive period of trial and (frequent) error, two main conclusions come to mind and both have guided my choice of material and presentation in this volume.
Firstly, mathematicians are different from other varieties of homo sapiens. It may be observed that people study numerical analysis for various reasons. Scientists and engineers require it as a means to an end, a tool to investigate the subject matter that really interests them. Entirely justifiably, they wish to spend neither time nor intellectual effort on the finer points of mathematical analysis, typically preferring a style that combines a cook-book presentation of numerical methods with a leavening of intuitive and hand-waving explanations. Computer scientists adopt a different, more algorithmic, attitude. Their heart goes after the clever algorithm and its interaction with computer architecture. Differential equations and their likes are abandoned as soon as decency allows (or sooner). They are replaced by discrete models, which in turn are analysed by combinatorial techniques. Mathematicians, though, follow a different mode of reasoning.
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- A First Course in the Numerical Analysis of Differential Equations , pp. xiii - xviiiPublisher: Cambridge University PressPrint publication year: 2008