I’m still confused as to what cal 3 is. Is it truly just cal 1 in 3D?
Is Cal 3 harder than cal 2? I’m struggling with Cal 2. I’ve heard Cal 3 is easier than Cal 2 but harder than cal 1. What do you think?
@JoseWhat A lot of calculus 3 generalizes what you have already seen in calculus 1 and 2 but to higher dimensions. In calculus 1 and 2 you learned how to compute limits and differentiate and integrate functions of a single variable. Multivariate calculus extends many of those notions to functions of more than one variable, and use that to compute surface areas and volumes, and other things.
Different universities have different calculus sequences. Calc 3 for some universities is a different topic than calc 3 for others. For most universities, this is multivariable calculus. Can you link or copy/paste the course description of calc 2 and calc 3 at your university?
Personally I found Calc III slightly harder than Calc II (wasn’t good at 3D visualization). Both are generally easier than Calc I.
Multivariable calc is generally pretty easy if you understand the concepts from regular calc. You’ll also be dealing with matrices and vectors for the first time but they’re not that hard to understand.
I found Calc III to be slightly harder, but maybe it’s because I am not fabulous at visualizing three-dimensional shapes.
Calc III is way harder. Then again, I learned it in 5 weeks so.
Calc 3 was a bit rougher than 1 & 2, at least for me. The first reason was because you have to have a very keen ability to visualize things in 3 Dimensions, especially when first learning about iterated integration (multiple integrals)
The second thing was (and I believe it is this way for many) vector calculus is typically covered at the end of Calc 3 and is usually a bit more conceptually difficult in terms of knowing exactly what is going on (the calculations are tedious as well).
Calc III was way easier than the other ones. Calc II was the hardest.
How does calc 1 compare to calc 2 and 3?
I thought 1 (differentiation, and at my HS some integration) was easier than 2 (integration, sequences and series) and merely simpler than 3 (1 in multiple dimensions).
Calc I is mainly differentiation/integration introduction/techniques. It’s hard in that it’s a new type of math for many people, but once you get the concepts down it’s not bad.
Calc II is an introduction to more complex differentation/integration techniques (partial fraction decomposition, integration by parts etc) as well as series. I didn’t find Calc II to be hard (although I took it in high school and had a full year to learn it, compared to the 3 months colleges offer for you to cram the same material).
Once you master I and II, most topics in Calc III are easy: partial derivatives, line integrals, scalar line integrals etc. I’d say the three main hard topics are parametrizing surfaces, double integrals and triple integrals. I also found polar coordinates hard in Calc II, so it was somewhat hard to now have more advanced polar coordinate mappings in Calc III. But honestly, if you’re good at learning how to find constraints for the bounds of integrals, most of your problems in Calc III are solved.