I just finished teaching Calculus I this semester at my university, and I have several students that failed the course despite working hard. The culprit in all of the cases was inadequate background knowledge coming into the course. My university does not offer any lower level courses, so I'd like to come up with helpful suggestions for them, so that they can adequately prepare this summer to be able to retake Calculus I in the fall with a good chance of being able to pass the course.

Obviously, one option would be to take a college algebra or pre-calculus course at a local college near their hometown. But if that option is not available to the students, can you recommend any resources for self-study that the students can use? These students have a weak background, so they will need a lot of specific guidance on what topics to study, as well as explanations for all of the concepts they are studying.

Thank you in advance for any suggestions you can offer.

  • $\begingroup$ Take a peek at William Chen's lecture notes, he covers much of beginning undergraduate math well. In general, you might be able to find lecture notes/class web pages for many courses, a selection of those (homework, exams, ...) could fit the bill at little cost. $\endgroup$
    – vonbrand
    May 6, 2014 at 19:50

1 Answer 1


YouTube is a good source of tutorial videos, particularly PatrickJMT's channel. I would not steer the student toward Khan Academy, though that name might be the first one to come to mind when you think about math videos -- too much cookbook, not enough conceptual understanding that a student who failed Calc 1 needs.

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    $\begingroup$ Interesting viewpoint on Khan Academy, a viewpoint I suspect I would agree with (I haven't listened to any of the Khan videos; maybe I'll listen to a few during lunch today), but a viewpoint I also find surprisingly rare in math stackexchange, where Khan Academy videos are almost universally praised. $\endgroup$ May 7, 2014 at 13:58
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    $\begingroup$ When my previous university department was looking into calculus videos, we came to the same conclusion -- that the Khan Academy videos leaned too far toward "getting the answer" as the primary goal. To be clear, I don't think they are bad -- just that they are more suited to high school mathematics. $\endgroup$ May 8, 2014 at 14:38
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    $\begingroup$ @Chris Cunningham and Robert: I just listened to parts of several videos from the "Differential Calculus" selection. They were better than I expected. While listening, I was trying to find neat alternate methods that may have been overlooked and for "not entirely correct" statements, but I didn't find any. The few times I've listened to U-Tube videos on math (high school teachers, mostly) this has not been the case. Still, the Khan videos strike me as more of the recitation sections in calculus (typically conducted by graduate students in the U.S.) than the actual course content. $\endgroup$ May 9, 2014 at 18:03

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