to start off, i’d like to say i’m scared ■■■■■■■■ now i’m about to take calc 2 this spring semester. how hard is the class and what exactly makes most people say calc 2 would be the hardest in calc 1-3?
right now, 2 weeks before the semester starts, i’m tried some advance studying. luckily, i found a professor who uploads his classes online (you could look up Professor Leonard on youtube) that lasts around 2 hours each section. so far i’ve spent 4 hours finishing his whole integration by parts and trigonometric integrals video and it has been easy so far (probably since those are the earlier/beginning topics in calc 2).
merely the names of the other sections however, like parametric equations, polar coordinates, etc. absolutely daunt me. obviously i wont be able to finish all his videos because 1) two weeks clearly aint enough time and 2) im not THAT paranoid… i hope
i found calc 1 pretty easy and managed to get an A but i’ve heard multiple accounts of people breezing through calc 1 and suddenly failing calc 2. any tips on how to pass (and hopefully ace) this class? thank you
It depends on the college, but you are right that Calculus 2 is the hardest class in sequence.
For example, Calc 2 at WashU is focused on proofs and deriving the formulas and equations and applying the concepts. Most students aren’t used to proof based math or deriving the equations.
Try to read ahead and learn how to derive/apply equations and concepts. Some students try to do multiple problems without understanding the concepts, which is not a good approach.
If you can find tests from previous years, try to do them as practice, but don’t expect the tests to be same.
It can be tricky to learn integration (lots of types of problems, and you have to remember the steps to solve each type), and different coordinate systems might be confusing at first (can be hard to visualize for some), but I think the main thing that trips people up is sequences and series. It’s different from basically anything else you’ve learned and personally I didn’t find it very intuitive.
If you thought differentiation was easy, you should be fine with integration, and parametric equations / coordinate systems should be pretty doable (with some effort, if required).
There are lots of online math resources. I like Paul’s Math Notes a lot. Also Khan Academy, PatrickJMT, in addition to Professor Leonard, as you’ve already found.
Also, everything sounds scary when you haven’t been introduced to it yet. Don’t let it psych you out!
Calc 2 is hard because there’s no obvious path to follow while integrating, and the key is practice and experience. Knowledge of the general rules and principles will only get you so far. Practice as much as you can, and get ready to use a lot of foundational math (geometry especially) to solve problems.
It’s been 30 years since I’ve studied engineering but from what I remember here is the list from easiest to hardest.
Precalc
Calc-3 (it's called Multivariables now)
Calc-1
Calc-2
Precalc is where you have to start understanding how calculus is different from the rest of your math. It is massive shortcutting steps to get to answers, using formulations that by derivation, use many steps in one. So Precalc is where you start with summation and calculating how graphs and slopes work in space. Basically, it’s the calculation of things that change and how they are demonstrably explained.
Calc-1 has a lot of procedures that need to be memorized. How to use derivations and integrations.
Calc-2 as I remember it, had a lot of new procedures that were extremely complicated. I failed it once because I took it for the first time during summer. A whole semester of calc-2 cut down in the time of summer is not recommended as it is really for people who want to retake it. Calc-2 is where you start to learn about u-substitutions and other very complicated things.
Calc-3 is everything you’ve learned and being implemented into a third axis. Pretty easy and mostly conceptual stuff so you have to see things in 3 dimensional space. Some things may have changed in the past 30 years but that’s basically how I remember it.
It really depends on what’s taught in your school’s calc 2 class. For me, calc 2 is hard because it’s very heavy on pattern recognition and messy algebra. A bulk of calc 2 is getting an integral or series into a form you recognize and going from there - and if you can’t do that quickly you’ll have a hard time. I found the best way to do well is to just keep doing problems. You’ll recognize the patterns by experience.
My ranking from easiest to hardest
Calc 1 = basics concepts. Easy enough if you can understand the concepts of differentiation, integration, and limits.
DiffEr = Pattern recognition heavy, but the patterns are pretty easy to see. Also probably the most used material later on.
Calc 3 = Calc 1 but in 3d. I found it a bit harder because of the algebra and because it’s harder to visualize but it’s still pretty easy.
LinAlg = At my school it’s taught in a very proof-y way which makes it difficult. It’s one of the more abstract courses in the engineering sequence though very useful later on.
Calc 2 = posters are hard to recognize and the algebra is messy.
