Krdytkyu

I've been asked to tutor a soon-to-be college freshman who has taken AP Calculus and successfully earned college credit for first semester calculus. He has been admitted to an Engineering program, and has been advised that there is a "gap" between where single-variable calculus (e.g. AP calculus) leaves off and multivariable calculus begins.

And so, the request to tutor this freshman to make up for "missed material"/the "gap".

My recommendation (while I'll help), is that the student purchase the text to be used in his upcoming Calculus II, obtain a syllabus from the Calc I & II class at the University, and compare what was covered (Calc I) and where Calc II starts, comparing his coverage of calculus in the AP class he was successful in.

It's been a long time since I took a 3-semester, 18-credit university-honors calculus sequence, and I don't recall when multivariable calculus began in that sequence. Even though I successfully completed two semesters of calculus early in high school, I was on an "honor's track" for my BS in math, for which the three semester sequence I referred to was required. (It tackled the typical 3-semester calculus sequence, plus undergraduate real analysis/advanced calculus.) So, though I believe we started quite early with multivariable calc, my experience wasn't typical.

I'm assuming the student received credit for only first semester calc, but I may be wrong.

My questions are, since I do not have the syllabi or text reference for the courses to be taken, nor the text from which the student studied AP calc:

1. for those who are Calc TA's or instructors at the university level, based on your experience, what "gap" might the "advisor" be referring to? Is there any consistent disparity in what AP coursework covers, and what college-equivalent calc covers?



2. If so, what is it that AP students could be covering/might want to cover, prior to beginning (continuing) calculus at the university level.




3. Also, any AP-students who received college credit for their AP studies, please feel free to share what your experience has been/was in terms of adjusting to the courses following the calculus class(es) for which you earned AP-credit.

This question will hopefully help students in a similar situation: those who have earned college credit in Calculus by passing the requisite AP exam, who may be uncertain as to their readiness for, say, Calc II as a 1st semester college student. Certainly, the summer prior to beginning college would be an ideal time to study what they might find they are expected to know, if that can be ascertained.

Thanks for taking the time to read the above. Your input is welcome!