Mathematics, Engineering and Computer Science Undergraduate Theses

Spring 1975

Thesis

Department

Mathematics, Engineering & Computer Science

Alfred Murray

Thomas Stewart

Sam Sperry

Abstract

Many concepts involved In the calculus can be presented in a nore obvious Banner by the use of a computer. So much of the calculus involves many very small values that become tedious for a beginning student to calculate. In doing the calculations he loses sight of his objective in the problem. This paper attempts to explore the various possibilities for use of the computer in teaching a course In elementary calculus. There are three basic areas of calculus where a computer could be used as an aid for teaching. These are the limit, the integral calculus and graphing. The underlying current throughout calculus Involves the limit concept. The mechanics of working several values through a function can become very tedious, bit with a program that is rather easily written, many values can be put into the function and the limit can be printed, along with the intermediate values used to arrive at the actual limit. Using the limit, but incorporating it within another idea, the calculus student looks at the areas under curves when he begins the integral calculus. Various methods can be used to approximate areas under curves with only the integral giving the exact value. Programs can be written to find values for the trapezoidal approximation and Simpson’s rule. These will vary from the actual value, but the error should be rather small, Various other approximating formulas are used In calculus that are readily adaptable to computer methods. One of these is Newton’s Method for Approximating Roots, The third area is graphing, which is not specifically calculus, but a tool used very often in calculus, Although the computer can only produce approximate graphs, they are explicit enough to merit investigation. Ibis paper does not try to give explicit ways to teach calculus, but instead points out areas where the computer could be applied, if the circumstances were right. One must keep in mind that "certain types of problems are easily solved by computer and that other types of problems are best left to people,*^ The reader is asked to keep in mind that this paper is not advocating continual use of the computer in the teaching of every calculus class, but only supplementary use in particular areas, "...students should understand the relation between computers and mathematics. Mathematics is an important and widely used tool - and will continue to be in the future. Computers are an aid to using that tool and will become a greater aid in the future. The combination - mathematics plus computers - is essential to the student who wants to make effective use of mathematics in our technological society,"2

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