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Course Queries Syllabus Queries 2 years ago
Posted on 16 Aug 2022, this text provides information on Syllabus Queries related to Course Queries. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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A colleague of mine in a math department at another university is looking for a textbook on multivariable calculus that discusses applications of higher-dimensional integrals that feel contemporary rather than solidly traditional. In particular, he is looking for a path through the subject that culminates in something other than Stokes' theorem, since that is hard to get majors outside of math and physics excited about. The students who take the course in its current form are willing to work hard to pass the class, but they are not math-oriented (e.g., they major in economics or biology) and they simply don't see an overlap between the standard big integral theorems of vector calculus and their own interests. (I once asked a statistics professor if he ever used Stokes' theorem and he said no.) It's not even necessary that the multivariable calculus be applied to a student's major, but at least to something that looks fresh and modern (computer graphics, forecasting of all kinds) and maybe even exhibits an awareness that the people who use it and don't live in a math department rely on computers.
[Edit: My colleague is looking for a new book as part of faculty discussions to change the syllabus of the department's multivariable calculus course.]
Are there any textbooks on the market that have a genuinely different approach to what multivariable calculus can be good for and present a series of interesting applications of multidimensional integrals?
Perhaps not really an answer to the question, but I believe I understand where this comes from.
In my experience, such calculus courses are among the first ones, long before students have seen enough (make that "anything at all" if you want) of their future field to understand what "realistic" applications of the covered techniques are. Also, such classes are usually a mixture of majors, so a relevant example for, say, chemical engineering will be greek to civil engineers or physicists. This unfortunately leaves geometric examples, or stuff that can be understood with high-school science.
Perhaps the best strategy is to talk with the teachers of the relevant higher courses to suggest problems to discuss, offer their students some "remedial" help as appropiate, or even restructure the curricula for "just in time" teaching of mathematics.
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