torquetum

Robertson, R.L. (2013). Early vector calculus: A path through multivariable calculus. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 23(2), 133-140.

The author argues for an ordering of topics in a multivariable calculus course which brings the three big theorems as early as possible. The textbook he uses is a standard maths text, with the three big theorems coming last. He lists the topics to be covered before Divergence Theorem can be covered, locating it (by my estimate) a bit less than halfway through the course. Thereafter he covers a few more topics and get to Stokes’ Theorem (probably about 2/3 of the way through the course). Green’s Theorem is presented as a special case of Stokes’ Theorem. The benefits of this approach are argued for convincingly and a few drawbacks are also covered (such as parametrised surfaces before parametrised curves). This is the second paper I have read which recommends Schey’s (2005) Div, Grad, Curl and All That: An Informal Text on Vector Calculus, so I really must track that text down. The practical interpretations of div and curl are emphasised as in so many papers I’m reading. I found this paper intriguing and I also greatly appreciated that the author broke the course down into sufficient detail that I, or someone else, could easily structure a course as he has done.

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.