<p>aibarr, GP, you guys {and yes aibarr, I know you’re a female engineer who still knows how to integrate!}, respond so maturely. I can’t handle it. I can’t buy anything from this OP. </p>
<p>f a c a d e , I gave you a constructive post. Please don’t respond with a snooty attitude. I advised to drop to precalculus – the best calc students are those who know their algebra. I’ve notised in my tutoring that it isn’t the calculus that the students have trouble with in basic calculus courses {taking derivatives, integrating} it is the ALGEBRA. I cannot stress how important it is. Students that take math classes they are not prepared for, sometimes, manage receiving A’s {because they are bright students, and I’m sure you are} but often wish they took a math class that would help them with their fundamentals, so they could go about it confidently.</p>
<p>I took BC after only taking Algebra II with a C+. I killed myself working hard, managed an A+, and a 5 on the BC test. After finishing calc1/2 with so much struggle, and so much hard work, I decided to take a few steps back and took an Algebra/Trig/precalc class at local community college in the summer. It made DE, Multi, and Linear run that much more smoothly. You will be taking engineering classes in which a fluent knowledge in the calculus is ASSUMED, and you cannot deprive yourself of those basic skills. Linear has a few tricky proofs, and Multi is damn-right hard. Students with A’s in Calc II many times manage low Bs/Cs in Multi, DE, etc, b.c., A, they were not sufficiently prepared, and B, overestimated their math skills. </p>
<p>There is such thing as a rigorous treatment of pre-calculus, and a true, thorough understanding of calculus demands it. Little things {and giving you the most basic example, I know} can really mess up some students. I was tutoring high school student a few weeks ago, and I asked him d / dx [ sin x ]. Very smartly (and only in 10th grade!) he responded (cos x)x’. I asked him what would he do if he, for some reason, could not remember each individual trigonometric derivative (arctan, arcsin, etc), and so he proceeded to write f’(x) = lim h -> 0, f(x+deltax)-f(x)/deltax. However, he could not derive it. He had trouble FACTORING. </p>
<p>He understands all his derivative rules, but doesn’t know his reduction formulas, sum and difference formulas, double-angle formulas, power-reducing formulas, sum-to-product formulas, etc. I’ve been trying hard {and heck, his parents pay me $40/hr, he does live in an affluent part of NYC}, to teach him his trig/algebra, since he seems to theoretically understand calculus, but he is just not ready! I’ve advised them to let him drop to a pre-calc course, or take trig/analytic geometry at a college. He has received mid-70s in his tests after studying hard. He is bright, and I do think that when he’s older he’ll be able to ace calc, but because his parents want him so badly to go to Harvard, Cooper, MIT, etc, he was pressured into taking this harder class which he is not prepared for! Do not deprive yourself, and do not pressure yourself into taking classes you aren’t ready for. Calc can be easy, but an ill-prepared calculus student will, even if they manage passing, heck, even if they manage a B, retain little from the course.</p>