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I Session 2265 .— ..

Integrating Integration

Lynn Kiaer Rose-Hulman Institute of Technology

Abstract

Rose-Hulman’s Integrated First Year Curriculum in Science, Engineering and Mathematics consists of a sequence of three one-quarter twelve-credit courses, which incorporate all the traditional technical courses of the first year: differential, integral and multivariate calculus, mechanics, electricity and magnetism, two quarters of general chemistry, engineering statics, graphical communication, computer science and engineering design. It has served approximately one fourth of the entering class of first year students for the last six years. From the inception of the program, many of the synchronicities between mechanics and differential calculus have been well-exploited. In the past two years, additional opportunities to coordinate the treatment of chemical kinetics, electricity and magnetism, and integral calculus have been identified, and a number of classroom, laboratory and homework experiences have been designed to assist students in understanding the relationships between these topics. A number of these activities are described.

Introduction

Students are often presented with similar problems in different surroundings, and it is not uncommon to find a student who can solve a problem easily in a physics class but is completely stymied when presented with the same problem in calculus class. Most students eventually make the connection between calculus and mechanics, but other connections are harder. Making those connections is vitally important to the student’s ability to learn rather than merely be taught. Rose-Hulman’s Integrated First Year Curriculum in Science, Engineering and Mathematics’ was developed in part to assist students in learning by making those connections explicit.

Integration can be a difficult subject to integrate. Techniques of integration appear to be essentially unrelated to the traditional applications of integration, and the introduction of computer algebra systems can make them seem essentially unmotivated. Over the last two years motivating examples have been collected and explicit connections have been made to other disciplines in the areas of

q rates (orders) of chemical reactions and separable differential equations, q work and other traditional applications of integration and Riemann sums, and

q electric field and trigonometric substitution.

{~xij 1996 ASEE Annual Conference Proceedings ‘.,+,yyHll’.’

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Kiaer, L. (1996, June), Integrating Integration Paper presented at 1996 Annual Conference, Washington, District of Columbia. 10.18260/1-2--6123