Oliver Aberth Computable Calculus

ISBN 13: 9780120417520

Computable Calculus

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9780120417520: Computable Calculus
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Computable Calculus treats the fundamental topic of calculus in a novel way that is more in tune with today's computer age. Comprising 11 chapters and an accompanying CD-ROM, the book presents mathematical analysis that has been created to deal with constructively defined concepts. The book's "show your work" approach makes it easier to understand the pitfalls of various computations and, more importantly, how to avoid these pitfalls.

The accompanying CD-ROM has self-contained programs that interact with the text, providing for easy grasp of the new concepts and enabling readers to write their own demonstration programs.

Contains software on CD ROM:

  • The accompanying software demonstrates, through simulation and exercises, how each concept of calculus can be associated with a program for the 'ideal computer'
  • Using this software readers will be able to write their own demonstration programs

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From the Back Cover:

What is Computable Calculus?

Despite the power of today's computers, we still do not routinely solve numerical problems precisely, that is, to a specific number of correct decimal places. Computable Calculus is a version of calculus that makes precise computation a central issue.

Here all concepts are defined constructively or executable by finite means. This constructive point of view makes it easier to understand the pitfalls of various computations, and more importantly, how to avoid those pitfalls.

The English mathematician Alan Turing initiated this way of thinking about mathematical concepts in the same groundbreaking paper wherein he defined the machines now known as Turing machines.

In this book all the key mathematical concepts -- the real numbers, sequences, functions, and so on -- are defined in terms of some computation that an ideal computer (or a Turing machine) can perform.

An accompanying CD offers software that simulates an ideal computer on a PC. Many programs are supplied that enable the ideal computer to do a variety of tasks. Readers can compose and execute their own ideal computer programs.

The book is meant for self-teaching or instruction in an undergraduate class.

Oliver Aberth is Professor Emeritus of Mathematics, Texas A & M University. He is also the author of Precise Numerical Methods in C++ (Academic Press).

About the Author:

Oliver Aberth received his B.S. from City College of New York, his M.S. from Massachusetts Institute of Technology, and his Ph.D. from the University of Pennsylvania. He is also the author of Computable Analysis (McGraw-Hill, 1980) and Precise Numerical Methods Using C++ (Academic Press, 1998). He was professor of mathematics at Texas A & M University from 1970 to 1999. He is currently professor emeritus at Texas A & M University.

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