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 07-26-2012, 09:24 AM #1 New Member   Join Date: Jan 2012 Posts: 13 Multivariable Calculus--AP Calc AB & BC Hello, I will be a college freshman beginning in this upcoming August, and I'm deciding what I should do as a preparation for Multivariable Calculus, which I plan to take in my first semester. I took AP Calculus AB in my Sophomore year and AP Calculus BC in my Junior year, and achieved 5 on both AP exams, but I cannot say that I remember everything I have learned from those classes. It has been more than a year since I touched my Barrons AP Calculus book (I took AP Stats in my senior year), and I'm very worried that I might be having troubles in real college calculus class. How much in depth do I need to understand AP Calc AB&BC to be successful in Multivariable Calculus? I heard fundamental concepts, along with some advanced knowledge of application, will do enough to learn about Multivariable Calculus, because the sequence of AP Calc BC and Multivariable is not like that of AP Calc AB and BC, the latter being the advanced continuation of the former, but rather separate two different calculus sharing some fundamental concepts like limit, integration, derivative, and etc. I plan to review my Barrons book, but I don't plan to re-solve every single questions.. will I be trouble if I do not have sufficient AP Calc AB&BC knowledge I had back in my junior year, or will I be good with fairly good&decent understanding of the overall topics of AB&BC (like by reviewing Barrons). I'd appreciate any answer my fellow CC users want to provide. Thank you, Reply
 07-26-2012, 11:52 AM #2 Senior Member   Join Date: Jan 2010 Location: California-> Socorro, New Mexico Posts: 1,057 Watch the lectures on MIT OCW. Get yourself a textbook too; start doing problems. Reply
 07-26-2012, 12:53 PM #3 Senior Member   Join Date: Dec 2010 Posts: 25,619 Since you took freshman calculus over two years (AB and BC), you should be aware that a true college math course will cover material at a much faster pace than you saw it in high school. Here is a free calculus and multivariable calculus book: Free Online Course Materials | Textbook | MIT OpenCourseWare What you may also want to do is check your college for old final exams for its freshman calculus courses (that you are skipping). Put "[course number] final exam" in the search box of the college web site and see what comes up. Then try the final exams to check your knowledge of what the college's freshman calculus courses cover. Reply
 07-26-2012, 08:06 PM #4 Junior Member   Join Date: Dec 2009 Posts: 264 Calc BC is almost irrelevant for calc iii, so study calc AB more. Reply
 07-27-2012, 03:58 AM #5 New Member   Join Date: Jan 2012 Posts: 13 Thanks guys, ^ucbalumnus, so do you think I need to ace the freshman calculus final exam, in order to be successful in Multivariable calculus? The sole purpose of reviewing the old calculus ab&bc materials is to make sure that I will not have trouble taking Multivariable calculus due to lack of knowledge in calc ab&bc. Reply
 07-27-2012, 11:02 AM #6 Member   Join Date: Dec 2011 Location: Silver Spring, MD Posts: 336 It's not so much that you have to ace calc I/II material in order to understand or succeed in Calc III. Most of Calc III will be new material with usually basic calcI/II methods required (use the chain rule, integrate by u-substitution). What you have to realize is pacing and format of any college math class vs what you're used to in high school. Yes you do need to know a few methods of integration to evaluate integrals, single variable or iterated multivariable. If you were comfortable with concepts like area under a curve and figuring out limits, you'll probably be comfortable with those topics expanded in calc III. The real question you should be asking is how quickly you can pick up new material and how quickly you can successfully apply procedural methods to problems you're given. Anecdotal evidence: There were a handful of guys in my fraternity rush class freshmen year who went into multivariable straight out of high school, 1 got an A, 1 got a B, 3 got C's and one dropped before the final. Now I don't know how they did in their high school calc classes, but the school required 5's on the BC AP exam to skip calc I and II. The guy who had the A was pretty smart but also did practice problems constantly, the one who got a B wasn't as smart but also did practice problems constantly. The group who got C's spent more time partying/playing video games than doing practice problems, only cramming right before tests. The one who dropped almost never went to class, used the solutions manual to do the homework, and only did problems from practice exams to study for tests. Which category of student would you place yourself in? Reply
 07-27-2012, 01:15 PM #7 Senior Member   Join Date: Dec 2010 Posts: 25,619 You should try the college's freshman calculus final exams in order to see which parts of the material you need to review the most (from the college's point of view). In some cases, the college's freshman calculus includes some material not present in the AP syllabus. This is usually not a large amount of material, so motivated students can often self-study it, but you need to be aware of that before going on to more advanced math courses. Reply

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