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Overview
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, 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.Audience: Applied mathematicians, numerical analysts, and computationally oriented scientists. Appropriate for upper-level undergraduate and graduate students and researchers.
Synopsis
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.
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).