My son is a high school junior and just completed AP Calculus. He would like to take something over the summer to prepare him for Multivariable math in his senior year. Would you recommend any of these online courses for him to use as a study guide. Thanks!
OCW Scholar - Multivariable Calculus
Stacey Warren - Expert brainly.com
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If he took AP Calculus AB or BC (preferably BC) then he will be ready to take Multivariable Calculus right away. I don't think any high schools offer courses at that level for students in high school but he can certainly self-study Professor Denis Auroux's videos and write out the notes from the lecture videos, answer all the practice problems, follow along with recitation videos, and take the Exams in a timed situation as if he were taking the course. He would be ready to take Multivariable Calculus in university in his first semester if he was to do that on his own time, or during a designated class time (take a spare).
Hopefully this helps, good luck and continue to encourage your son in pursuing mathematics! (Hopefully he enjoys it too, never force a subject on a student if they don't like it).
Keep in mind that many universities don't take high school credits past certain levels of math and even physics. Even if he might find something in his school that is multivariable, they probably won't take it.. As noted above, Denis Auroux's videos are excellent and if he goes through all the online course has to offer, I am sure he will get an easy A when he gets into the university courses.
I would recommend reading Morris Kline's book on caclulus. It's outstanding and should provide a much greater depth of understanding. Linear Algebra could also be worthwhile.
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Where do I find the recitation videos for Multivariable calculus, please??
I would suggest using the single-variable calculus notes and examples on ocw or just borrowing a bc calc book from his school and teaching himself. There really isnt much different b/w ab and bc, except some further integration work, and differentials--easy stuff
What does he want to study in college? If he wants to go on to engineering, economics or physics, he would be best served by multi variate calculus 18.02 or linear algebra 18.06. If he wants math perhaps intoductory topology or set theory in order to get background for honors calc or analysis.
Let the kid have some fun, lest he burns out so young.