Computable Calculus. Incudes Cd-Rom

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.