torquetum

Dray, T. & Manogue, C.A. (1999). The vector calculus gap: mathematics ≠ physics. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 9(1), 21-28.

Here we have another paper lamenting (justifiably) the difference in the way vector calculus is taught in maths and physics. The authors emphasise how practical applications and situational geometry are far more important in physics (or engineering) than in maths. For example, they discuss how vectors are defined as ordered triples in maths while as arrows in space in physics. Also, div and curl are defined as differential operations on vector fields in maths but in physics are defined first in terms of their physical meaning as represented by Stokes’ Theorem and Divergence Theorem. The coordinates used in maths are almost invariably rectangular coordinates, the authors argue, while physics situations frequently have circular or spherical symmetry and hence use spherical coordinates to simplify the maths. (Some of the paper’s criticisms could apply to my local course, but not all, I think.) The value of the mathematical methods lies in their general applicability, however in physics the types of cases are few and there is an argument for loss of generality in favour of simplification of the common cases. The authors close with an insistence that the relevant departments collaborate closely.

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.