Iterative solution of non‐linear equations using a computer algebra package

Abstract

Much attention has been given recently to problems associated with the application of computers to the teaching of calculus. For some topics, a computer package can easily trivialize the mathematics; other, often more theoretical, topics may be difficult to support computationally, without a careful study. It seems that the integration of computers with calculus ideally should involve a learning process whereby the strengths of the underlying analysis and the numerical features of the package are seen to complement and to reinforce each other. For instance, iterative solution of non‐linear equations can be proved by a contraction mapping principle and the iteration sequences can be implemented on a computer. Since the accuracy of the computer is limited, it is important that appropriate stable schemes are discussed and used when teaching this topic.