Numerical mathematics : a laboratory approach
著者
書誌事項
Numerical mathematics : a laboratory approach
Cambridge University Press, 1993
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注記
Includes index
内容説明・目次
内容説明
Numerical Mathematics is a unique textbook which presents rudimentary numerical mathematics in conjunction with computational laboratory assignments. No previous knowledge of calculus or linear algebra is presupposed, and thus the book is tailor-made for undergraduate students, as well as prospective mathematics teachers. The material in the book emphasises algorithmic aspects of mathematics, which are made viable through numerical assignments, in which the traditional 'chalk-and-talk' lecturer turns, in part, into a laboratory instructor. The book is not a numerical methods book, containing ready-made computational recipes. Rather, it guides the student to create the algorithm required for any given assignment - expressed in whichever programming language is used - on the basis of the underlying mathematics. The computational assignments cover iterative processes, area approximations, solution of linear systems, acceleration of series summation, interpolative approximations, and construction of computer-library functions. Throughout the book, strong emphasis is being put upon vital concepts such as error bounds, precision control, numerical efficiency, computational complexity, as well as round off errors and numerical stability. It is the authors' belief that the material presented in this book is part and parcel of the mathematical foundations that should be acquired by a student in the microcomputer era.
目次
- Preface
- 1. Mathematics in a numerical laboratory
- 2. Iterations for root extraction
- 3. Area approximation
- 4. Linear systems - an algorithmic approach
- 5. Algorithmic computations of p and e
- 6. Convergence acceleration
- 7. Interpolative approximation
- 8. Computer library functions
- Solutions to selected exercises
- Index.
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