Over the last decade, there has been an increasing, widespread pedagogical interest in developing various types of integrated curricula for science and engineering programs. Over the last three years, a year-long Integrated Math/Physics course has been developed at Union College. This paper will focus on a model for a one-quarter integrated course organized around a traditional set of electricity and magnetism (E&M) physics topics, integrated with appropriate mathematical topics. Traditional, nonintegrated E&M physics students often struggle with challenging vector calculus ideas which may have been forgotten, not yet encountered, or introduced with different notation in different contexts. Likewise, traditional vector calculus mathematics students are often unable to gain intuitive insight, or fail to grasp the physical significance of many of the vector calculus ideas they are learning. Many of these frustrations are due to the fact that at many schools, the physics and calculus teachers teaching separate courses probably have little or no idea what their fellow educators are actually doing in these courses. Substantial differences in context, notation, and philosophy can cause breakdowns in the transfer of knowledge between mathematics and physics courses. We will discuss the methods, philosophy, and implementation of our course, and then go on to present what we feel were the substantial strengths and insights gained from a thoughtful integration of the two subjects. In addition, some problem areas and recommendations for probable student difficulties will be addressed.

## REFERENCES

*Integrated Physics and Calculus*(Addison–Wesley, Reading, MA, 1999).

*Physics for Scientists and Engineers*(Saunders College Publishing, Philadelphia, PA, 1996).

*Calculus*(Wiley, New York, 1999).

*Integrated Introduction to Mathematics and Physical Science (IMPS)*course at Dartmouth is presently under development; see the internet web site at http://www.dartmouth.edu/∼matc/IMPS/IMPSpage.html.

*Div, Grad, Curl and All That*(Norton, New York, 1973), pp. 36–39.

*Introduction to Electrodynamics*(Prentice–Hall, Englewood Cliffs, NJ, 1989), 2nd ed., p. 20.

*Dy*or $y\u2032),$ or between unit vectors and ordered triples. These examples are also less severe than those we will mention concerning integrals, as these notation differences focus on separate preferences favored by one group or another, while the integral notation differences concern nearly identical notation which is much easier to confuse.

*American Journal of Physics*and

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