Calculus and the Computer. The Interplay of Discrete Numerical Methods and Calculus in the Education of Users of Mathematics: Considerations and Experiences

Summary

NEW POSSIBILITIES

As is written in many places in this book, the computer is a mighty mathematical tool, not only for mathematical research, but even more in the process of applying mathematics, or in the process of teaching and learning mathematics. In the following, we shall mainly concentrate on the new possibilities which the computer presents in the realm of calculus for users and future users of mathematics. By a user we understand somebody who is interested in mathematics merely (or mainly) because he uses mathematical models (in particular calculus models) to solve his (extra-mathematical) problems. Future users of mathematics are, for example, engineering students, but even those learning calculus in schools as part of a general education may be considered under this aspect.

New possibilities for the user

We first describe the changes in the mathematical knowledge and habits of the user of mathematics induced by the availability of sophisticated mathematical software to all who have to rely heavily on mathematical problem-solving such as engineers, natural scientists, etc. Whereas the widespread use of such systems (of hardware and software) may to a certain extent seem doubtful, the continuing decrease of prices and the development of powerful personal computers allows us to predict that they will be available on microcomputers not only in research areas, but also in smaller environments by the time, in three to five years, when our students start their professional careers.