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Antia H.M. Numerical Methods for Scientists and Engineers

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Antia H.M. Numerical Methods for Scientists and Engineers
McGraw-Hill, 1995. — 993 p.
This book has evolved out of lecture courses delivered to Research Scholars at the Tata Institute of Fundamental Research during the period 1978-88. It attempts to provide a practical guide for numerical solutions to mathematical problems on digital computers. It is intended for both students and research workers in science and engineering. Readers are expected to have a reasonable background in mathematics as well as computer programming.
The enormous variety of problems that can be encountered in practice makes numerical computation an art to some extent, and as such the best way of learning it is to practice it. Attempting to learn numerical methods by simply attending lectures or by just reading a book is like trying to learn how to play football by the same method. All students are therefore urged to try out the methods themselves on any problem that they may dfancy, not necessarily the ones given in this book. In fact, the reader will probably not appreciate the contents unless he makes a serious attempt to use numerical methods for solving problems on computers. There is at wide difference between numerical methods for computers and those for desk calculators. The enormous increase in speed enables us to solve much larger problems on computers and frequently such problems are more sensitive to various errors during calculations. Apart from the t'remendotis increase in speed, the main qualitative difference is that in computation
with desk calculators the intermediate results are always available whether we want them or not. Hence, in most cases, it is rather straightforward to detect the numerical errors creeping into the computation, and corrective action can be taken easily. Further, any unexpected result can also be tackled appropriately. But in computation with modern computers, the intermediate results are usually not available and consequently all
possibilities have to be considered while writing the programs. Error propagation in the computation should also be estimated beforehand. Otherwise, the error accumulation could render a plausible set of results absolutely meaningless, and there may be no indication of this difficulty in the final results. This makes the task of computation conceptually more difficult, even though the process itself is far more efficient. In particular, error estimation is far more important with digital computers than it was with desk calculators. As a result, a detailed discussion of errors and pitfalls in numerical calculations has been included in this book, even though rigorous proofs have not always been given. An attempt has also been made to illustrate the effect of errors in numerical computations by giving appropriate examples, rather than treating the theory of error propagation in detail.
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