Is Calculus 2 Harder than Differential Equations?

Is Calculus 2 Harder than Differential Equations?

In this video I give reasons as to why I think which one is harder. Which one do you think is harder?

Please leave any comments or questions in the comment section below. Thank you:)

[justinclark]

Good answer. But, as I've said before, a great professor makes a world of difference. I'm a firm believer that math isn't hard it's just taught wrong.

[joeyGalileoHotto]

Calculus 2 was harder than Differential Equations for me because Calc II was the first class where I was exposed to the rigor needed to succeed in engineering courses

[SoloRenegade]

In my experience, it is the Sequences and Series that causes people to struggle in Calc2. Most students I've seen taking Calc2 had basically no prior exposure to sequences and series. And I've seen calc2 classes that didn't cover sequences and series and those students overall didn't consider it difficult. When all you learn is basic integration, it's very similar to Calc1. I also agree with the fact that Diff Eq is a second round of exposure to things that were brand new in Calc2, so for many people it may be easier for them.

[ricardovergara-puello]

Honestly, I think DE was a lot harder. Maybe it's because my DE professor was extremely demanding. But I also think the subject is hearder because the operational part of the subject is a lot more dense and demonstrating the theorems and solving equations with Laplace transforms, sometimes gets hard. I don't know if it's just me.

[wycked]

Calc 2 no competition, by the time I took DE I was much more prepared to deal with the various integration techniques.

[PhrontDoor]

My biggest piece of advice for any course, math especially, is that every course seems hard when you HAVE to learn the stuff right before the next test. I have always had the luxury of being able to ENJOY math by virtue of the simple fact that I can start something, play with it, wade in gently or jump all the way in and I go at MY pace before I move on. I can do all the example problems, look up more, reflect on the ramifications of a point to my minds content as well.

If you have to learn vectors NOW because there's a test next week, AND because everything from this point onward depends on vectors (and it probably will) then this course is going to suck for you (especially if everything depends on some minor mastery of the material you only just encountered ever-so recently).

My opinion.

[MorbidlyObeseChell]

Both can be easy with the right amount of tutoring, self discipline, study time, and a proffessor that understands not everyone is a technical thinker and needs more then textbook examples and problems (nothing is wrong with the textbooks to me they serve as refreshers and an opening to asking the right questions).

[OleJoe]

I think the answer to which is harder, DE or Calc 2, is, that depends. My first impression of Diff EQ was that it is a bag of "tricks" and "guesses" you had to pull out of your hat to solve the equations. To a certain extent this is true. If you knew the trick, you could solve the problem. If you didn't, you were out of luck. When they got into existence theorems and application derivation it got hard. It wasn't until later that I learned that most Diff Eqs can't be solved in closed form, using elementary techniques! Most are solved using sophisticated numerical techniques on a computer, which is another whole subject in itself. So, Calc 2 is harder, until they get into the existence and uniqueness theorems, in my opinion.

[surrealistidealist]

This is truly encouraging, and inspiring, too! I'm still in the Calc 1 zone, but now I'm even more motivated to keep going!!! 😍🤩😍🤩

[jordancourtemanche]

While the question asks about comparing the *level* of difficulty, it might be helpful to consider another angle on this.

I always told my students that Calculus 2 and Differential Equations have the same *type* of difficulty, or they're difficult for the same reason. I think what makes Calculus 2 and Differential Equations difficult is CHOICE. While you're still getting your bearings, you have so many different possible avenues to take. (Cal2: which series test, which integration method, etc.; DiffEq: which first-order ODE method, what form is this higher-order equation, etc.)

In both disciplines, a given problem might really only have one appropriate method of solution (that they've learned). Or there might be multiple methods that work but one is much better/quicker/smoother than the others.

This very well may be the first time students confront math that isn't purely algorithmic, and it's disorienting. It flies in the face of everything they know about math. Students need to learn not just the mechanics of the methods but also their utility/strengths/purpose in order to look back and make those calls and discern the viable or opportune paths. The benefit of an experienced and organized approach is in making that initial (and formerly paralyzing) decision more routine - in essence, turning the decision-making process itself algorithmic! (I'm a big fan of flowcharts for these decisions.)

[bradlarson]

please make a youtube series or a udemy series on calc 2! that would be so beneficial to a variety of calc students. thanks!

[robertjr]

Differential equations is a lot harder for me than calculus 2 was. There’s a lot of reading involved for my class and we are required to do 50 problems within a week along with studying the new subject and preparing for a test. It’s really difficult to keep up. Might take a course on udemy or something if I pass this class to strengthen my understanding. It just feels like I’m trying to pass and not learn.

[xyzct]

I found the disk/shell stuff clear and simple.

[daviddixon]

DE was much easier for me because I had learned all the different techniques of integration in Calculus II. I enjoyed DE much more than Calculus II.

[thehungarywaffleinc.]

I think calc 2 is harder because it’s the part where you learn the language. Calc 1 seemed really similar to algebra to me

[gustavoturm]

Could you describe what is "calc 2"? In my university, it is multivariable calculus. But in some other universities, even in the same country (I am from Brazil), it seems calc 2 can be something different like series, etc.

[leonardobranco]

What?? D.E is much more hard than Calc 2, for me, in D.E, is very hard to understand the demonstrations or proof of the theorems.

[FerryPatrix]

I dont know, i love integral techniques in calc 2, so DE is harder for me, especially PDE

[xNinjxHD]

agreed for the reasons you've stated!

[AcidicElm]

Hello Math Sorcerer, so I am cruising pretty nicely in my calc 2 class because it is online. But I really don’t think I am learning too much. After integration by parts, I just lost it. Do you think I’ll be able to survive in differential equations next semester? I just need a C