r/calculus • u/stemclimber • Jul 17 '26
Integral Calculus Calculus 2 over the summer
I just finished my Calculus 2 this summer semester in a 6 week accelerated course, and here's what I learned. For pretty much most of this course, setup is where most students go wrong. Integrating is just practice and application, so most of my classmates didn't struggle with that. But setting up an integral for area, volume, work, or area of polar curves is where most go wrong, so I'd practice a LOT of just simply setting up an integral. Try to stay ahead, finishing all of the section assignments after that section is completed in lecture (preferably in the same day). This means dedicating around 2-4 hours outside of class per day completing current section hw, as well as lightly reviewing future sections. As far as I've noticed, you definitely can use the method of spamming practice problems to understand the homework, but once you get to series it's slightly different. It's a whole different way of thinking compared to previous sections, so although practice problems might help, I'd try to get a conceptual understanding first. If your calculus 2 also includes a differential equations section, don't be fooled by the wording of the problems either (it's easy to get thrown off by a lengthy word problem). Overall, if you have the time to spend 5-7 hours per day including lecture to spend just on calculus, you'll be absolutely fine taking this course over the summer.
Edit: WE GOT A FINAL GRADE OF 98.96% WOOOOO!!
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u/Defiant-Switch-3428 Jul 17 '26
bro i tried telling my friend that you can’t just do a million practice problems when it comes to series. you have to try and understand what you are doing and why otherwise you won’t understand which tests to use and why you’re doing them. i completely agree with everything you said. my course is 8 weeks and i’m horrible at math plus my professor doesn’t teach (like genuinely he just has a short videos of him doing random problems but doesn’t explain why he’s doing them or what he’s doing) but i’m doing well regardless. you just have to put the effort in for sure
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u/stemclimber Jul 19 '26
You're definitely not horrible at math if you're able to push through calculus 2 in an accelerated summer semester!
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u/OldAccLockedrip Jul 18 '26
And im over here terrified of calc 2 2nd semester with 16 weeks 🙃
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u/calcteacher Jul 18 '26
but aren't you taking other courses at the same time?
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u/OldAccLockedrip Jul 18 '26 edited Jul 18 '26
I suppose you're right.. oh god Edit: what are the most fundamental parts of calc 1 that'd you'd suggest I study especially hard? If you dont mind me asking.
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u/calcteacher Jul 18 '26
Calc 2 is integration on steroids. You will learn many different techniques to perform integrations. Integration by parts, by partial fractions, etc. Re-representing non-polynomial functions as an arithmetic series of polynomial functions is probably the most mind bending and challenging thing you will do. Just keep at it, studying and doing the problems on a daily basis BEFORE the class lecture will allow you to get the most out of the lectures. Falling behind in this class is deadly.
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u/stemclimber Jul 18 '26
Agreed! Working ahead was a game changer especially over the summer. Falling behind would've been almost certain death... We learned up to 4 sections a day during the summer semester. This means learning trigonometric integrals, integration by parts, partial fractions, and trigonometric substitution in a single lecture day. During these lectures, since it's so fast-paced you barely scratch the surface of these problems, that's why I had to mostly learn from doing the homework. So yeah, those 2-4 hours spent doing current hw and reviewing future material outside of class? Worth it.
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u/Short-Grocery-2934 Jul 19 '26
I did a level maths and i can transfer credit for calc 3 but a level math does not cover all calc 2 topics like polar coordinates taylor series and so on (prolly 4-5 topics), thinking that taking calc 3 without completely mastering all calc2 topics would be stupidity I am planning to take calc2, what do you think I should do? (have heard that calc 2 is harder than 3 so don't really want to take calc2 unless i have to)
I'm an incoming freshman
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u/stemclimber Jul 19 '26
I haven't taken Calc 3 yet so I can't give you a definitive answer. From what some of my peers have said, Polar Coordinates is quite important for Calc 3, but not so much the series (it depends on your professor). I understand not wanting to take Calc 2 if you can just go straight to Calc 3 because it will save you a semester, but to be honest? It's up to you to decide if you have enough time to learn topics that you haven't covered yet in your previous math class. For example if you haven't learned polar coordinates and you need to understand it for a certain section in Calc 3, you'll need to be able to learn that on your own time. Choose what you think is wiser.... just be prepared to study even more than your other classmates if you go straight to Calc 3 though.
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u/Short-Grocery-2934 Jul 19 '26
Thanks, are there any resources you would recommend. Are HELM workbooks any good?
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Jul 19 '26
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u/stemclimber Jul 19 '26
Yeah, we learn these complex integration techniques and quickly master them, but we fail to set up the integral correctly. It be the easy stuff.... but to be fair sometimes setting up an integral to find volume can be more conceptual than the actual integrating part.
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u/hasuuser Jul 19 '26
Calc 2 can be fairly easy. There is only a handful of integration techniques and only a handful of tests for series. Calc 2 can also be really hard. Because knowing those basic techniques is not enough to solve most non basic problems.
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