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Students in physics courses are often asked to compute integrals that are both similar and different compared to the integrals from Calculus courses. We interviewed three students at a mid-sized midwestern university, and asked them to work on integral problems from math and physics contexts and talk through their thinking. We identified five conceptual resources that students activated throughout and across the interviews. Here, we highlight two of the five resources through an example of a student reasoning through a volume integral problem, and their thought process as they attempt to connect different conceptions of integration. We argue that this case study excerpt is representative of some of the hurdles that certain conceptions of integrals may lead to when solving different integral problems in physics despite students’ prior success in math courses. 

Abstract Upper-division undergraduate physics coursework necessitates a firm grasp on and fluid use of mathematical knowledge, including an understanding of non-cartesian (specifically polar, spherical and cylindrical) coordinates and how to use them. A limited body of research into physics students’ thinking about coordinate systems suggests that even for upper-division students, understanding of coordinate system concepts is emergent. To more fully grasp upper-division physics students’ incoming understanding of non-cartesian coordinates, the prevalence of non-cartesian content in seven popular Calculus textbooks was studied. Using content analysis techniques, a coding scheme was developed to gain insight into the presentation of coordinate system content both quantitatively and qualitatively. An initial finding was that non-cartesian basis unit vectors were absent in all but one book. A deeper analysis of three of the calculus textbooks showed that cartesian coordinates comprise an overwhelming proportion of the textbooks’ content and that qualitatively the cartesian coordinate system is presented as the default coordinate system. Quantitative and qualitative results are presented with implications for how these results might impact physics teaching and research at the middle and upper-division.