<p>There are lots of students that take Calc 3 in high-school. Some even take linear algebra, differential equations and mathematical statistics. It’s all a matter of starting early enough and arranging for the courses at a local college or university or via distance learning.</p>
<p>^I actually looked at the exact video you linked before. I think I can understand it just fine, but now that I realize that I really don’t use the notes from the professor’s lecture or understand everything he says the moment he says them. That ain’t bad right? Because now I rely solely on the textbook to learn the concepts. I think this habit developed because of the fact that my professor’s accent is so harsh its so hard to understand him and its so easy to zone out while he’s talking. </p>
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<p>our school offers both calc 1 and 2 and I took both last year so this year I decided to dual enroll. And I personally believe calc 1 is the hardest because thats when you first learn the whole concepts of calculus and you have almost no prior knowledge to help you through it. Plus I remember solving those page long problems where one + or - mistake can cost you the whole problem. urgh.</p>
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<p>I think a lot of this depends on your class and the professor. I’d say Calc 2 actually felt easier than Calc 1 for me, but I still don’t really get stuff like Stoke’s and Green’s Theorems.</p>
<p>Those theorems (of Green & Stokes) are just higher-dimension analogues of the fundamental theorem of integral calculus.</p>
<p>But yeah, I think to really understand them, you’d have to take some upper-level math class where they’d take a step back & generalize things a bit.</p>
<p>I thought that Taylor’s theorem was a lot worse than Green or Stokes or anything in Calc I or Calc III. The first time I saw a Taylor expansion was a huge “***” moment for me. Lo and behold, they are incredibly useful now.</p>
<p>Call me crazy, but I thought Cal I was the hardest. Once you learn that, they’re just teaching you the same thing again worded differently + a couple of applications.</p>
<p>I went through demonstrations of derivatives and integrals for several years with our daughter before she took calculus so that she would have the benefit of a gross overview before actually taking the class. There’s no reason why students with algebra 2 couldn’t do this.</p>
<p>Just my personal opinion…</p>
<p>Once you get pass Calculus I,II & III, you will take math courses that ACTUALLY applies to real life and it makes sense…well except for that Advanced Calculus course which is mostly theory and asks you to prove stuff like A times zero = zero.</p>
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I had this problem in a few of my classes. I’m a senior as well, but I’ve got 7 AP courses… so it’s not too much different than college I would say (and I have looked at college material). I think what would really really help you, because it definitely helped me, was to read your textbook. A lot. I did this for physics class specifically, but for Calculus, when you know a little bit-ish about the lesson before you come to class, the proofs and derivations and all that crazy induction that the professor/teacher may do will come together and just make a whole lot more sense, even if he has some crazy thick Romanian accent, or something.</p>
<p>But really. This helps me so much in Physics… especially now in E&M it’s getting to be a little tougher than mechanics, but spending an hour reading a lesson and checking out how they do those problems really definitely helps. I do believe this is the standard procedure for most engineering students, from what I’ve heard personally. And also, college folk tell me to review the material after class as well. Classic memory techniques like these I think should help you, because they really help me, and a lot of others from what I’ve heard.</p>
<p>Actually, Taylor’s theorem was probably the only thing I enjoyed in Calc 2. It was interesting how you could break up a function into a rather large polynomial and get the same curve. So cool! But, that is the only thing I enjoyed doing in that semester of hell.</p>
<p>I never said it wasn’t interesting/useful, I just said that the first time I saw it, it was mind boggling.</p>
<p>No, I was completely agreeing with you :).</p>
<p>^ It’s pretty cool, Taylor’s theorem, but after doing linear approximations (which you do fairly early in Cal I, at least we did) Taylor’s theorem was a little anticlimactic. I remember several people in my class pointing out that you should be able to use higher-order derivatives to do even better, and the professor said something to the effect of “just wait until the end of Cal II”.</p>
<p>Regardless, I know a lot of people who just dismissed Taylor and forgot all about it after the test and it really came back to bite them in the butt later on. It is incredibly useful in higher level undergrad technical courses and graduate courses.</p>
<p>Let that be a warning to all you CC’ers here! Learn your Taylor expansions!</p>
<p>(That would be me.)</p>