Your Grandmother’s Calculus!

This is a link to a Single Variable Calculus course as taught in 1970 at MIT.

Calculus Revisited: Single Variable Calculus | MIT OpenCourseWare.

Having this course, with videos, transcript and problems is a wonderful resource.

Comparing this course with today’s courses helps us see what it really means, in terms of learning, for faculty to require so much less study effort for their students, as reported by Arum and Roksa.

To give readers (who know a little calculus) an idea of the difference in today’s typical course and yesterday’s course, I will quote one paragraph from a lecture, and state one homework problem.

(To show that this was not just MIT, I will point out,  that, in 1963, I took an “Advanced Math” course in High School in Longview, Texas.  It covered this material, as presented at  MIT, and we had similar homework problems.)

“…Now what I want to do here is scare you a little … The mathematical definition of limit is the following. The limit of ‘f of x’ as ‘x’ approaches ‘a’ equals ‘l’ means, and get this, given epsilon greater than 0, we can find delta greater than 0, such that when the absolute value of ‘x minus a’ is less than delta, but greater than 0, then the absolute value of ‘f of x’ minus ‘l’ is less than epsilon. Now doesn’t that kind of turn you on?…” (From Lecture 4.)

Now, here are some sample problems from this section.  (From the supplementary material on the website.)

 

 

 

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