We Need To Talk About Calculus 2

We talk about Calculus 2 and why it's so hard. Also what can you do to do better in Calculus 2? Do you have advice for people? Please leave any comments below.

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[LaughingManRa]

"If Calculus is so good, how come there's no Calculus 2?" --Gottfried Wilhelm Leibniz

[mrheng]

I got a D in Calc 1 in high school. Then, when I took Calc 1 again in college, my professor made the biggest difference. I plowed throw Calc 1, 2, and 3 with an A because of that one person who took the time to remind me about Algebra 1 and how Calc 1 was mostly Algebra 1 applied to more complicated looking “stuff” is what he called it. :)

[aliasjon]

To use a video game metaphor.
Calc 1 is like a linear storymode game, where your character levels up as you defeat progressively harder bosses and by the end of the game your character is stronger than all the enemies.
Calc 3 is like a sequel to that game. You learn a new mechanic, thinking about functions with multiple variables, and the rest of the difficulty progression is similiar (until you get to stuff like stoke 's theorem which is kinda like DLC).

In contrast, Calc 2 feels like a game made by the same developer in a different genre; an open world game. The game difficulty isnt necessarily linear and it feels like you're going around collecting equipment, until you grind enough mobs to unlock the S-tier enchantment (the intuition necessary for being able to quickly pick the correct and efficient integration techniques and identies to solve any question in a timed exam). Until you get this enchantment, sometimes some of the early game areas even get harder, because you found some cool weapon in a different area (IBP) and you naively tried using it against enemies that are strong against it . And in the endgame, you end up getting introduced to different kinds of enemies as much faster pace. I've seen people try to cover everything from basic diff eqs, error correction, physics and probability applications, all the while trying to wrap up the power series section, during the few weeks between a third (or late second midterm) and the final .

[kevinyonan]

Calc 2 is hard because all the different ways to integrate makes it like playing chess. There's integrating by parts, trig sub, plain u-substitution, partial fraction decomposition, trig integrating by using trigonometric identities, and then having to _apply_ all of these in different contexts like Volumes of Revolution, Surfaces, Arc Length, and then their applications in Physics.

[eitanethan]

Currently in calc 2 with a full time job, studying literally every free second I get, easily getting 4-6 hours in every day, still feels like I’m flying by the seat of my pants

[martinhaub]

I think the reason Calc II is harder is because in Precalc we spend most of the time related more to Calc I. Too often series/sequences are given short shrift in Precalc so the stuff isn't so familiar. Other topics like partial fraction decomposition, polar coordinates are also not given the attention they need.

[hussain]

5:30 man that's so powerful and heart touching! Im sure he'll remember you for all his life

[mgbow-yn]

It was definitely my hardest class. I loved Calc 3 and Diff Equations - but just because I could use the tables to find most integrals. I graduated 20 years ago and have been a professional engineer for the last 10 years. Calculus 2 is very valuable though - it gives you problem solving skills needed for higher level engineering courses. And it helps you gain confidence to do well if you want to pursue professional licenses later on. I have a few textbooks - going to used Book stores is a godsend....I have the Stewart text. And yes, I still like to work problems to keep my problem solving skills up to snuff in general, even though I review plumbing engineering drawings for a living. Mathematics is the Queen of all STEM fields - the language of STEM and thus more invaluable than you will ever know until you get out of college. God Bless you Daniel! And yes - I got a C in Calculus II - it is the time in your life in college that can make things challenging.

[HalfassDIY]

The hardest part for me was the techniques of integration. I could never figure out the best technique to use, but once I learned that any problem could be done using trigonometric substitution, I became an expert at that and used it for everything.

[Megane.Senpai]

Before finding your channel i used to like math, but you made me fall in love with mathematics, thank you math sorcerer!! ❤

[argonwheatbelly]

Calc II was intense (did it over eight weeks, summer '84), but it was also a lot of fun. You build a large toolkit, and spend the time hammering out a lot of interesting solutions to assigned problems. However, then Calc III is a breeze.

At least, that's how it was for me in 1984. I started college in '83 with Pre-calc, and ran from there.

[azimuth]

I do enjoy the Stewart book. Has all the theorems, quite a bit of proofs, and lots of explanations. All kinds of exercises, even a few proofs in the exercises to make sure you understood. Finishing up Calc I and looking foward to Calc II next year 😁

[pressingericrizo]

I love this guy and his videos. Great stuff.

[JGonzalezGUS]

I'm old an retired guy learning Calculus on my own. Quite a coincidence that I just finished Calc I using Larson's textbook and in the last few days I've using Stewart's (odd problems only) as a review before starting Calc 2 next week.

[RichardJohnson_dydx]

Calc 2 was regarded by the engineering students as one of the hardest courses. I loved techniques and applications of integration. I still love integrals. Series is what sucked for me. I got my lowest exam score on the series exam. Everything after series was very easy.

Series didn't click with me until after the fact. Similar to looking at an integral and thinking about all the techniques that could work, the same is similar with evaluating a series.

[Mcdude]

In Calc 2 right now, and I absolutely agree it’s the hardest. I’m not personally struggling, but every single minute in this class I’m learning a ton and my math knowledge and intuition is expanding. The amount of content is staggering and it’s not simple. I’m making vast leaps in my understanding and it’s *just* enough to keep up. If I wasn’t making consistent epiphanies about how this stuff works, I’d be falling behind like crazy.

I was the only one who managed the finish the entire first exam, it’s brutal

[danielgross]

I think calc 2 is the most difficult because of the number of new topics introduced. Series and sequences are barely introduced in the precalc, and in calc 2 you go pretty hard on them. Polar coordinates are also introduced for the first time. Last, which I think is the most important, is that you are starting to learn how to set up the problem more than solving the problem itself. In calc 1, it was usually just taking the derivative or integral and you're good to go. In calc 2 you have to think a bit harder on how to set up the disk and shell method. Setting up the sequence is also difficult because you can have multiple right answers.

[caseyfergus]

Currently in Calc 2, returning to college 13 years after dropping out. The reason it’s so hard for me is because of the amount of precalc and trig stuff that comes up that you need to be able to both see and do. I’m looking at problems, unsure where to go, and it’s like, oh, as the very first step you need to complete the square of the denominator or factor the difference of two cubes. Not necessarily hard, but I don’t remember and it so it doesn’t occur to me. I spend a lot of time struggling to solve something after missing a crucial early step. I get nowhere, get frustrated, and waste a lot of time.

Then it’s similar with the trig stuff. Something like sin(arcsec(5)) will come up and I’ll be drawing triangles and chanting Sohcahtoa because my trig stuff is super rusty and the rest of the class just did it and moved on. I’m pretty good at unit circle stuff but some of the identities just don’t pop out to me the way they need to.

Anyway, it could just be me, because I’m so far removed from the years of doing math on a regular basis, but to me it feels like you really need all your algebra, trig, and precalc to be super solid for Calc 2, and so instead of just learning whatever is in the current lesson, I also need to relearn several things on the fly as we go.

[dtonysun]

Thanks and hello agin for this set of videos on calculus - I'm starting my math master's journey this year by auditing Cal 1, 2, 3 simulataneously now, and so far it went well and I agree that Cal 2's area/volume calculations are a challenge hurdle for many students.

[aliasjon]

I think for most people calc 2 is the first class where just plugging in a formula or algorithm doesnt automatically give you the right answer. You learn a lot of identities and technique, but getting the correct answer is contingent on developing the intuition to use the correct tools. And sadly, even if you are working towards a "correct" solution, having bad intuition can cause you to take a very lengthy route to get there, which is horrible for timed exams .

It begins as early as people incorrectly visualizing or inefficiently setting up integrals for solids of revolution, spikes exponentially once you get to integration techniques (for some of the integrals you can create entire trees of possible mistakes and lengthy routes you can take) and by the time people get to power series or error approximation it almost feels like a whole other class.

In contrast Calc 1 is intrinsically a lot more straightforward ( you derive derivatives, and derivative rules, get used to using them and then just learn a bunch of plug and play applications) .

Even calc 3 is better as a lot of it is just extending familiar material from calc 1 and 2 to multiple dimensions and generally ending with some applications (unless you go down the vector calculus stuff ). While the issues with calc 2 can still technically hurt you here, the amount of material seems to generally for professors fo test you on concepts introduced in calc 3, rather than trying to trip you up with a tricky integral from the previous course.