In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things in calculus also changed with the advantage of technology. Similarly in linear algebra, there was a linear algebra curriculum study group that produced some really good ways of teaching linear algebra and highlighted curriculum changes. This was produced in the January 1993 College Mathematics Journal. Has any similar work been covered in (Further) Engineering Mathematics? I am looking for what are important topics to cover and any work or research on the teaching of Engineering Mathematics. I am looking for some sort of framework.
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1$\begingroup$ I don't know any reference that is reasonably relevant to suggest, but probably the place to look would be in journals/magazines for engineers that correspond to Notices of the AMS and MAA journals for math, and Physics Today for physics, and Journal of Chemical Education for chemistry. I don't know any such journals off-hand, but most any college engineering teacher should know of several such journals. $\endgroup$– Dave L RenfroCommented Feb 15, 2022 at 15:28
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1$\begingroup$ You may also find matheducators.stackexchange.com/questions/6124/… of interest. $\endgroup$– J WCommented Feb 15, 2022 at 16:30
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1$\begingroup$ I've taught for about 20 years in engineering programs. The curricula are quite standard, and second year courses generally include ODEs, numerical methods and probability/statistics (when these aren't taught in the first year). Most engineering degrees teach vector calculus and linear algebra in the first year. Outside the US many (most?) also teach ODEs, numerical methods and probability/statistics in the first year. In the US these subjects are usually left for the second year. $\endgroup$– Dan FoxCommented Feb 17, 2022 at 7:33
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I'm unaware of a major reform in engine math. If you look at the major selling textbooks, for instance, they remain pretty traditional. The most popular, Kreyszig, is one that I had in the mid-80s (and fifth edition already then). Granted there can be innovation (these author name texts become brands like Grey's Anatomy), but scanning the book I don't see much difference, now.
I did a Google Scholar search and there's pretty little out there.
https://scholar.google.com/scholar?hl=en&as_sdt=0%2C47&q=reform+%22engineering+mathematics%22&btnG=
Several of the top hits are actually papers on reforming all math that engineers take, with an emphasis really on calculus. See for instance the several paper on Wright State University, but if you read them, you see the issue was engineers failing first year calculus. Probably reflecting a general issue of sending a lot of kids to college and then weeder courses inevitably (and easily) culling many of them. But in any case, it's not really about "engine math" or what physicists call a "math methods" course.
I would even caution you that in calculus, the reform movement (funded by NSF in the 90s) has pretty much crested, past, and increasingly been forgotten. Can argue if this was the intransigence of the teachers or the drawbacks of the reform. I grant the former, but think the latter applies also. But in any case, even if it rocked, it didn't "win", not like flat TVs killed CRTs. Thomas sells more than Hughes Hallet. Stewart is pretty commercial and tries to be all things, but I wouldn't really consider it a reform text. My point is that even if you find some article (or text) on reformed engine math, I wouldn't assume that it was tested and successful in the market place. At least look at it carefully yourself, before pushing it, to see what you like...not just because it is labeled "reform".
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2$\begingroup$ While someone else might be able to point to something marginally useful and specific for @matqkks, I agree (so +1) that math reform efforts have had little effect on upper level engineering mathematics, at least aside from the obvious increasing use of CAS's. In fact, my observation (based on personal knowledge of a dozen or so large public U.S. universities) is that "calculus for engineers" (when available), and higher level math primarily for engineers, are far more traditional than those for other majors, including math majors. $\endgroup$ Commented Feb 15, 2022 at 15:24