Numerical Mathematics

Numerical Mathematics : A Laboratory Approach

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Description

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.show more

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"For someone wishing to learn the numerical approach to mathematics, this can be a book of genuine value. Recommended for undergraduates at all levels." S. Puckette, Choice "...a unique book that presents rudimentary numerical mathematics in conjunction with computational laboratory assignments."show more

Table of contents

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.show more

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