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.

中文翻译：

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非笛卡尔坐标的多元微积分教科书表示：多元微积分教科书内容与高阶物理应用之间的不一致

高年级本科物理课程需要牢固掌握和流畅使用数学知识，包括了解非笛卡尔坐标（特别是极坐标、球坐标和柱坐标）以及如何使用它们。对物理学生对坐标系的思考的有限研究表明，即使对于高年级学生来说，对坐标系概念的理解也是新兴的。为了更全面地掌握高年级物理学生对非笛卡尔坐标的理解，我们对七本流行的微积分教科书中非笛卡尔内容的流行情况进行了研究。使用内容分析技术，开发了一种编码方案，以定量和定性地深入了解坐标系内容的表示。初步发现，除了一本书之外，所有书籍中均不存在非笛卡尔基本单位向量。对三本微积分教科书的深入分析表明，笛卡尔坐标占教科书内容的绝大多数，并且定性地提出笛卡尔坐标系作为默认坐标系。定量和定性结果给出了这些结果如何影响中高级物理教学和研究的含义。