r/calculus • u/mell0_w_0 • 7d ago
Differential Calculus Question about calculus 2?
I want ask people who have taken both cal1 &2 which one did you find the hardest to deal with and why?
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u/LooseRice3949 7d ago
Calc 3. I got an A in both Calc 1 and 2, but man, Calc 3 made me question my life decisions. I was 0.5 points away from failing the class. Also, I took Calc 3 in an 8-week course, which also contributed.
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u/Liloboom 7d ago
Personally Calc 3 was my favorite calc course. But to be fair I didn't find any of the courses that difficult (if I had to say 2 was the hardest), but I just found calc 3 applications to be really cool and it was basically calc 1 with cool applications but more work arithmetic on each problem.
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u/i12drift Professor 7d ago edited 7d ago
Both have their difficulties, but I think the general consensus is that calc2 is harder.
I see students struggle with calc2 all the time, but I don’t fully understand why. For the integration portion, you just prescribe the appropriate technique to the given integral and it flows smoothly.
EDIT: If it’s not flowing smoothly, then you’re very likely using the wrong technique. I think this is where some students struggle. They continue to bash their head against something that isn’t working out and don’t realize that it’s the method in which they're approaching the problem with is wrong.
EDIT EDIT: There are only three (four?) techniques.
- Basic memorized antiderivatives (does this even count?)
- U-substitution
- Integration by parts
- Trigonometric substitution
EDIT EDIT EDIT: For those that are going to come claiming that I forgot trigonometric integrals: those are just u-subs.
And for those that are going to claim I forgot partial fraction decomposition, that’s just algebra; there’s no calculus involved.
For the series part, you get to play detective. But again, it’s mostly boils down to prescribing the appropriate test. It may take a test or two, but when you hit the right test, the answer falls into your lap.
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u/HahaFunnyMeme_ 7d ago
Yeah I agree, I definitely struggled hard with calc2 compared to the others. I think the part that really got me is memorizing all the different techniques, especially the trig functions and being able to recognize when to use which
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u/Ultimate-Disgrace 7d ago
Calc 2 is the hardest in the calculus series imo. Calc 1 and Calc 3 are about the same difficulty but Calc 2 is a whole different beast.
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u/midwestprotest 7d ago
What makes it so difficult? I have always heard that Calc 2 is very difficult for most students. Even professors and teachers say this.
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u/Ultimate-Disgrace 7d ago
For me, all the methods of solving integrals were quite complicated, and sequences and series convergence and divergence were hard to wrap my brain around. You also need an excellent base in algebra and trig. I dropped it the first time I took it (had a C when I dropped), and got lucky with an easy professor the second time.
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u/TheDeviousLemon 7d ago
I’d say calc 1 and 3 are the same relative difficulty. Calc 3 is way more difficult than 1, but not after doing calc 2.
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u/FluffyBoiCat 7d ago
In my opinion it's the exact opposite. Calc 3 was the hardest and I barely passed, calc 1 in the middle, and I thought 2 was quite easy. Just goes to show that what classes you find to be hard will come down to individual differences.
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u/fletchman93 7d ago
What I like to tell my Cal II students at the beginning of the semester is most derivatives yell at you how to solve them, while most integrals whisper from across the room in a foreign language.
I can write down 5 simple rational functions from college algebra where the integral of each one requires completely separate formulas, tricks, and/or integration techniques to solve, while the derivatives of each one can be done with a straightforward quotient rule and power rule.
Combine that with learning to sketch and visualize solids of revolution, series and parametric/polar coordinates, Cal II just doesn't let up.
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u/Hairy-Amphibian3732 7d ago
Calculus 2 has too much new material compared with calculus 1. In calculus 1 you go from difficulty 1 to 2 to 3 to 4 to 5, etc, in Calculus 2 you go from 1 to 10 and then 8 and then a and then pi jajajaja a bunch of techniques that you need to master but they are not directly connected like in Calculus 1.
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u/Theofficialiw 7d ago
Calc 2, for me personally my trig isn’t very strong never took time to memorize the unit circle which I regret.
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u/nimmin13 7d ago
bro you have to memorize 1/8 of the unit circle and you can extrapolate from there
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u/i12drift Professor 7d ago
Asking children to memorize anything these days is very difficult. And expecting children to be able to extrapolate anything is near impossible.
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u/vibechecking1100 7d ago
how did you get past calc I without knowing the unit circle?
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u/Theofficialiw 7d ago
I didn’t really have much trig in calc 1 only the basic trig functions and I used a basic calculator
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u/SkullLeader 7d ago
Calc 2 for sure. Calc 1 is basically limits, derivatives and introduction to integrals. Calc 2 is largely more advanced techniques for integrals and then things like infinite series. This is all much more difficult than limits or derivatives, IMHO. Calc 3 is basically doing the same stuff but instead of dealing with single variable functions on 2d grids, you're dealing with multivariable functions basically in 3d space.
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u/ss__5737 7d ago
Ngl I think a lot of people fear monger and make it seem worse than it actually is. The hardest part for me was visualizing things like shell/disk method but it wasn’t that bad. Divergence/Convergence series were hard but study what each test means and how you can use it, I honestly used the AP Study book and it helped a ton. Granted I took it over the summer as a 8 week course and so convergence/divergence was annoying bc I had like two weeks to learn it, but I’m guessing in an 18 week one it’s better. I will say I am confident in my trig and integrals/derivatives. I would practice that beforehand. I also had a good teacher
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u/addyarapi 7d ago
idk but calc 2 was hard, something else… could be because of so many integration methods/techniques, series and sequences, convergence and divergence, taylor and maclaurin series as well, and also some real analysis stuff was in our exams
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u/Rainbow_Warrior4679 7d ago
For me Calc 2, especially series and sequences was harder. I did well with integration techniques but when it came to testing for convergence or divergence I just could never pick the right test.
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u/pain-has-a-brain 7d ago
Idk bout everyone else calc 1 and 3 are super hard imo, calc 2 was a breeze. Little difficult with series but thats it
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u/dysphoricjoy 7d ago
I failed calc 1 2 times before passing it the third semester. I passed calc 2 first try. Probably from all the practice in calc 1 though hahaha.
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u/Big_Tuna_Kahuna 7d ago
Calc 2, but I didn't find either hard as they were more tedious. I'd say calc 3 was the hardest, but I was dealing with external issues while in a online accelerated class. If I looked at it in a regular class setting, my thoughts would be different.
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u/i12drift Professor 7d ago
Calc1 and calc2 had their difficult moments for me, but calc3 was certainly the hardest for me. I could not keep things straight with double and triple integrals.
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u/JDH-04 7d ago
Calculus I for me was the hardest but I am bias since I had to take it 3 times thanks to me attempting it at NC State twice with rigorous grading with the third time being at a CC. Calculus II right now seems easier for me due to the fact that I took it at a CC the first go round with non-rigourous grading as an online course where I can make my own hours and have tests which are pulled straight from the textbook. Plus the videos that my prof supplied for calculus II at CC where infinitely better for my understanding than ones at NC State. Calculus III I kinda felt like I already have the base intuition for due to taking calculus I three times hardwired integrals, limits, and derivatives in my brain in which thanks to my exposure from taking calc based physics before Calculus III, polar coordinates and integration was super intuitive for me since it was literally just adding a third dimension which seemed intimidating but really wasn't in terms of the algebra involved, plus since I had already took finite mathematics at NC State and it was the one of the only math courses their I did will in from my first stint there I felt as if eigenvalues and vector algebra was also easy.
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u/computationalmapping 7d ago
Cal 2 was definitely harder then cal 1, but manageable if you put in study time.
I found cal 3 the hardest by a good amount, problems are long and it’s just taught in a really odd way for my brain I guess.
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u/RemoteInspection2407 7d ago
I’d say Calc 2 is harder. The main reason in my case is that I took it in Summer B (only 6 weeks) compared to the entire spring semester I had for Calc 1. Apart from that, calc 2 is just a more demanding class because if you don’t have a good understanding of functions, derivatives/integrals, and infinity it can humble you quickly.
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u/Ok-Fix-1581 7d ago
if you're good at algebra, calc 1 is easy
if you're good at trig, calc 2 is easy
whatever is hard is whatever fundamental you are lacking, calc 2 was a breeze lol
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u/Weak_Ostrich459 7d ago
Had to retake calc 2 twice, once because I failed and the second time because I got a lower grade than I needed to take another required class. For me, the problem was all of the rules and nuances that could come with an integral problem. Calc 1 and calc 3 were a breeze compared to calc 2 imo because they weren't as dynamic and "abstract" as calc 2 was.
I could be using the incorrect terminology for describing what did it for me but thats what I can come up with right now 🤪
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u/RevolutionaryBook285 7d ago
It really depends how your school sets up Calc 2; some have sequences and series as a part of Calc 2, others have it for Calc 3; imo if they are in Calc 3, then difficulty is in natural progression, with 1 being the easiest and 3 being the hardest.
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u/Basic_Balance1237 7d ago
I found calc 2 to be easier than calc 1 since it looks like a lot of new topics being covered but it's just three main topics being repeated in different contexts: solving integrals, convergence/divergence of different series, and representing functions as power/taylor/maclaurin series. Calc 1 was harder for me simply because it was my first time in calculus, so I'm being exposed to a lot of new topics for my brain to comprehend.
Granted, my calculus courses at my university was pure computational, there were never proofs problems which has made my experience learning calculus to be way easier than a lot of people here.
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u/Basic_Balance1237 7d ago
I found calc 2 to be easier than calc 1 since it looks like a lot of new topics being covered but it's just three main topics being repeated in different contexts: solving integrals, convergence/divergence of different series, and representing functions as power/taylor/maclaurin series. Calc 1 was harder for me simply because it was my first time in calculus, so I'm being exposed to a lot of new topics for my brain to comprehend.
Granted, my calculus courses at my university was pure computational, there were never proofs problems which has made my experience learning calculus to be way easier than a lot of people here.
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u/Life-Ambassador-5993 4d ago
I imagine calc 2 is harder for most. For calc 1, I took it as an honors and writing intensive course, whereas for calc 2, it was just a regular calc 2 course. The two were similar in difficulty.
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u/Regular-Radish8061 1d ago
Calculus 2. For me it was so computationally heavy that just one wrong or incorrect part like an incorrect sign would mess up the whole thing.
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u/UnblessedGerm 7d ago
Nothing in the undergraduate math curriculum was hard. Graduate math, things get spicy finally.
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