Developing Intuition
|
Walter
G. Spunde
Dept. of Mathematics & Computing University of Southern Queensland spunde@ usq.edu.au |
 |
| Richard
D. Neidinger
Department of Mathematics Davidson College rineidinger@davidson.edu |
 |
Developing Intuition
|
Walter
G. Spunde
Dept. of Mathematics & Computing University of Southern Queensland spunde@ usq.edu.au |
|
| Richard
D. Neidinger
Department of Mathematics Davidson College rineidinger@davidson.edu |
|
 The
paper "Sample Calculus", appearing in The
Mathematics Magazine, Vol.
72, No.3. (June,'99) pps 171-182 , describes how to use lists of variable
values to demonstrate the basic operations of calculus. The use of adequate
samples of values is common in plotting functional relationships, but can
also be used to compute (and plot) arithmetic combinations of functions
and their approximate derivatives and integrals. Lists can be used to plot
functions defined by line integrals along curves given parametrically and
to demonstrate the truth of the rules for symbolic differentiation and
integration, the Fundamental Theorem, Green's Theorem and most other procedures
in the calculus of functions of a single variable
without demanding
a high level of skill in symbolic manipulation.
The basic tools required to implement these computations on a computer are the functions, sample, mids, d, sum, S and plot. More detailed discussion of the use of these functions is given in the paper. The implementations, referred to on the Mathematics Magazine's Supplements page, can be accessed through the links below and provide the tools for the practical testing of the discussion in the paper. |
| Each computing environment requires
its own syntax to implement the required functions.
Links to pages showing possible function definitions are given below. |
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| J | Matlab | Mathematica | Maple | APL | HP48G | TI85 | TI89 |