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Session 2265

Mathematics for Scientists and Engineers II at the Colorado School of Mines

Barbara Blake Bath, Robert Underwood, Loren Douglas Poole

Colorado School of Mines (CSM) is in the process of a major curriculum revision as a response to the changing world for today’s science, mathematics, and engineering graduates. An integral part of that revision is the development of new mathematics courses to better prepare students for their studies in science and engineering. Mathematics for Science and Engineering II is a four hour course which addresses the concerns of faculty from other disciplines who comment that students finish their calculus and differential equations courses unprepared or under prepared to do the mathematics in their courses. These same faculty claim that students are unable to translate the calculus they know into new concepts where problems appear to be different. This input led to the idea of developing a set of problems based on the concepts from these various disciplines. By having students work through these problems, students begin to understand the necessity of their mathematics studies, the connections of the mathematics to other subjects, the richness of the other disciplines, and the underlying mathematics beneath the disguises imposed by the variations in terminology in the disciplines.

This course’s development was in response to input from faculty on the CSM campus but it draws from similar projects on other campuses. The National Science Foundation has funded several of these projects such as the ones at Dartmouth, Rensselaer Polytechnic University, and the University of Pennsylvania.i In developing this set of problems, these projects were consulted, but the mission of the Colorado School of Mines, with its emphasis on energy and the environment, has driven the characteristics of this set. Further reasons for developing the course are based on recent calculus reform efforts where an emphasis is put on problem solving with less emphasis of the strict lecture technique which students often find dull and unwelcoming.ii

Course Content The course replaces the traditional second semester of calculus. Instead of the applications of integration and integration techniques which usually inhabit this course, the course starts with vectors, then moves into parametric representations of functions, then lines, curves, and planes in space with an emphasis on the linear algebra requisites, then into multivariate calculus, both differential and integral. The rationale is that these students are concurrently enrolled in physics and they need to understand vectors and multivariate concepts. Topics such as techniques of integration will be pulled in as needed.

Course Design The course is designed to have two classes per week in which the students learn new concepts. Some of these classes are lecture and others are discovery. In the third class period, the students spend two hours working “Real Problems” from the

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Underwood, R., & Poole, L. D., & Bath, B. B. (1997, June), Mathematics For Scientists And Engineers Ii At The Colorado School Of Mines Paper presented at 1997 Annual Conference, Milwaukee, Wisconsin. 10.18260/1-2--6682