<p>Someone who's taken both told me that today.</p>
<p>Is that true? (I just finished Calc II last semester)</p>
<p>It depends on how you deal with math on an individual level. Calculus II is often centered around series, whereas calculus III teaches vector calculus. They're completely separate, with the former relying more on technique and the latter relying more on conceptualizing. If you're able to conceptualize well, you'll do well in the latter. If you're better at algorithms and techniques in general, you'll do better in the former.</p>
<p>I felt that I actually had to understand Calc I and II to do well in the class, but I survived Calc III by pure memorization. In that sense, yes, Calc III is easier than Calc II. But I thought it was a lot harder to grasp the concepts in Calc III than in Calc I or II.</p>
<p>Calc II just seemed like a different course to me whereas Calc I and III seemed to go somewhat together...not to mention my school likes to add a pesky linear algebra segment into the Calc II curriculum. I found Calc III to be easier</p>
<p>Hi all, I think one interesting point about Calc III is that it's a bit harder to do more than computational problems. The proofs of some of the things you use in Calc III can be pretty hard to give any idea of. I think in Calc II, you can get a really good, hands-dirty sort of experience with infinite series. In other words, I think you're getting closer to the real thing in Calc II, "real" meaning the actual purest and most complete version.</p>
<p>Now, Calc III is harder to visualize and in some areas conceptualize. But there may be something intrinsically difficult about the thoroughness of how you can go through infinite series in Calc II.</p>
<p>Calc III is harder than Calc II. Don't be fooled by the beginning of the semester. The course will probably start as differential calc, then integral calc, and then a combination of the two. The first portion (directional derivatives, paths/curves, lagrange) isn't bad at all. But surface integrals and Gauss/Green/Stokes' Theorems are, in my opinion, way tougher than Calc II. Maybe that's just me though.</p>
<p>I have not taken Calculus yet. I am in advanced Pre-Calculus. We learned a lot of trig. this semester and did polar curves in detail. My teachers Always remind me that most of the stuff we are doing now will eventually return full circle in calculus - they never seem to specify what level of calculus, I mean for real, is it Cal I or Cal III?</p>
<p>Anyway, since you already took Cal. II then you are definetly going above the average folk's knowledge on advanced math. I know that Calculus III is Vector based so be sure to encounter that. I hear you get several theorems from various famous math guys. Basically, what I can tell you is to look at your most recent experiences wtih calculus directly. How was Calculus I in general for you? What about calculus II? If you barely made it through the course or were not too far from borderline, then I suggest taking the course again, probably Calclus II since Calculus I is hopefully by now under your belt. Good luck!</p>
<p>Odd, I always thought thought that Calc 2 was way easier than the others in the series (pun intended). Especially the series part, I had been looking forward to that for a long time. Vectors from Calc 3 was very interesting, so I loved that part. I don't know which is easier, but my calc 3 teacher was very challenging. Vector calc, though, is one of the most beautiful and applicable courses though (oddly enough, I find Green's theorem more beautiful than Stokes', even though Stokes' is more general), so pay very good attentioin, because I believe that this is the course which is the "payoff" for most people (proving that gravity is a conservative field, area of n-gon, efficiency of engines). Look forward to this course, thouhg, cause diff eq is one of the most boring courses you will ever encounter, utterly devoid of any beauty, just application.</p>
<p>And, no, almost none of the stuff you learn from pre-cal will be in calc III, just know the identities well, the derivations can go in the garbage. Calc II does have a bit of trig, but it really is not challenging at all, just remember sin^2+cos^2=1.</p>
<p>When I took Calculus (only I and II), I found integral to be easier than differential. I'm probably strange for that matter.</p>
<p>I wasn't going to be an engineer so it made no sense for me to pursue Calculus III.</p>
<p>The whole topic is essentially ambiguous cause it really depends on the nature of your Calculus III and Calculus II courses. If these are routine computational type courses (i.e. using Stewart's Calculus books), then most likely the difficulty of Calculus III and Calculus II is similar as both require similar techniques and Calculus III might be easier since you've already had dosages of computational calculus from Calculus I and II. However, if these are highly theoretical courses more concern with rigorous proofs, then Calculus III will seem somewhat of an introductory differential geometry course with all the far-reaching theorems such as Green, Divergence, Stokes, Implicit/Inverse Function theorems, etc. is harder to grasp than single variable integral calculus.</p>
<p>"Calculus III will seem somewhat of an introductory differential geometry course with all the far-reaching theorems such as Green, Divergence, Stokes, Implicit/Inverse Function theorems, etc. is harder to grasp than single variable integral calculus."</p>
<p>I think it's kinda uncommon for the class to be like this ;) but yeah, would be cool if it were.
I always thought that lower division math sucks, and they should make honors equivalents that're fascinating, so as to excite the students.</p>
<p>Take a look at Corwin's Calculus in Vector Spaces. And no, it's not cool. Not cool at all...</p>
<p>Now now b@rl!um I think with a good professor whose goal is to really TEACH the material, not to thrust it on students and kill 'em, I think such a class might actually excite them! </p>
<p>Hehhh. Checked out the book. Seriously, I think combining linear algebra and multivariable calculus in this healthy way is a great idea. I never had such an experience, but it would've been cool. I really didn't like multivariable calculus or ODE's without linear algebra.</p>
<p>Did you actually read the text or just skim the table of contents? I am honestly curious. </p>
<p>Maybe linear algebra + multivariable calc = good idea, but linear algebra + multivariable calculus - examples - pictures = bad idea.</p>
<p>(=> bad idea + examples + pictures = good idea... that might come in handy at some point)</p>
<p>Sorry, I honestly barely looked at it. When I said "this healthy way" I was as usual wording things in my strange, ambiguous manner of communication...which is to say I meant I just like the idea of MV calculus + linear algebra. Not minus pictures and examples at all.</p>
<p>Hah, pictures are great even to an advanced abstract mathematician =] and examples are of course crucial. No place in the world for dry math, should be fun!!</p>
<p>The reason I brought the book up was because it is written in a formal definition-theorem-proof style and I think that a course that might go along with it would look much like cp3's description:</p>
<p>
[quote]
However, if these are highly theoretical courses more concern with rigorous proofs, then Calculus III will seem somewhat of an introductory differential geometry course with all the far-reaching theorems such as Green, Divergence, Stokes, Implicit/Inverse Function theorems, etc. is harder to grasp than single variable integral calculus.
[/quote]
</p>
<p>Maybe Multivariable Calculus courses of this sort are rather uncommon, but they definitely do exist.</p>
<p>Well OK to be perfectly honest, some added rigor and clarity in presenting multivariable calculus beyond just stating results would be nice. One doesn't have to prove EVERYTHING. But like, some extent of rigor actually makes one feel more comfortable.</p>
<p>I actually have this experience that once I took lower div courses, I felt like I'd learned several miscellaneous things. While if I take a more theoretical math course, I feel like everything is somehow unified. And this actually helps me get <em>more</em> out of the theoretical ones. I.e., remember them more clearly.</p>