I always had the notion that courses generally become more difficult as they become more advanced. However, as Calculus 1 was coming to an end, my friends told me about how hard Calculus 2 was going to be. “Calculus 2 is harder than Calculus 1 and Calculus 3!” they would tell me.
So, I decided to find out for myself which Calculus class is the hardest. I’m a member of the Facebook group ‘Calculus!!!‘, a group dedicated to teaching and learning Calculus. I made a poll asking 140 people which Calculus class was the hardest.
Which Calculus class is the hardest?
In a poll of 140 past and present calculus students, the overwhelming consensus (72% of pollers) is that Calculus 3 is indeed the hardest Calculus class. This is contrary to the popular belief that Calculus 2 is the hardest Calculus class.
So, Calculus 3 is the hardest Calculus class. That question is answered. However, I feel that it gives rise to further questions. For one; why is it that people think Calculus 2 is the hardest Calculus class? And what is it that actually makes Calculus 3 the hardest Calculus class? Let’s find out.
If you’re struggling with Calculus, I highly recommend Krista King’s courses (shown above). I’ve used them myself in the past when I was having trouble and she explained things way better than my professors. There are quizzes and practice problems in the course so you really master Calculus and walk into class like a boss. The best part? She has a master course for Calculus 1, Calculus 2, and Calculus 3.
Why do people think Calculus 2 is the hardest Calculus class?
Well, the reason I thought it was the hardest Calculus class was that someone told me it was. However, I won’t know for myself until I take it next semester. That said, I was able to find a good explanation for why people think Calculus 2 is the hardest from someone who has already taken the class.
David Vasquez, B.S. Mathematics, commented on the Quora string ‘Is Calculus 2 the Hardest Mathematics Course?‘ According to Vasquez, when students struggle in Calculus 2 more than Calculus 1 or Calculus 3 it’s because of the four following reasons:
1) Integration techniques. Be sure to brush up on your trigonometric identities, partial fraction decomposition, derivatives, and what integration you should know already. Calculus II is integration-heavy, and you’ll realize where you lack mathematically very quickly here.
2) Polar coordinates. You’ve likely worked some with polar coordinates if you’ve taken a proper trigonometry or precalculus class. You’ll apply your new knowledge of integration here.
3) Parametric equations. These are something you’ve likely never worked with before. While not necessarily difficult, they are something new that many of my peers never cared for and will be crucial to the integration involved in calculus III.
-David Vasquez, B.S. in Mathematics
4) Infinite sequences and series. These sections are probably the most prominent outlier of all of calculus. While determining the values of infinite series and sequences is both useful and interesting, it’s an application of, you guessed it: integration.
Essentially, what David is saying is that when people struggle in Calculus 2, it’s typically because of these four topics. If you want to excel in Calculus 2 and get a firm grasp on all the topics covered, you can find a lot of excellent information here:
What makes Calculus 3 the hardest Calculus class?
Calculus 3 is also known as “Multivariate/Multi-variable Calculus” because the curriculum focuses on Integration and Differentiation with multiple variables. This concept, along with the spacial aspect of the course, seems to be at the root of why Calculus 3 is actually the hardest Calculus class.
I’d say Calc III [is the harder class] because of many new concepts and daunting (for some) 3D visualization. However, Calc II is quite the workout of technical skills and techniques.-Larry Santoni
Calculus 3 also requires much more memorization, according to Cridds Laso, also in the Quora string ‘Is Calculus 2 harder than Calculus 3?’:
Calculus 2 is harder for its content. As a class however, Calculus 3 was much more difficult. Why? Because, Calculus II is made up of concepts that you will learn and never unlearn. You begin to learn the purpose of integration and how to apply it in the real world. You finally get to go into series and differentials.
Calculus 3 certainly is filled with a few new concepts with plenty of real world applications– but the class itself however, involves too much memorization. The first month is worse than trigonometric identities from Calculus II. The content itself is as easy to learn as riding a bike, but the work can be a complete chore. In fact, the problems are so tedious that you’ll likely finish the class with a 10:1 ratio of Pre-algebra mistakes to Calculus 3 mistakes.
Disclaimer: In this particular Quora string and in many other forums, there are plenty of people who say that Calculus 2 is the hardest Calculus class. The truth is that it will really depend on the individual, as well as the instructors.
What can I do to succeed in Calculus?
Be it Calculus 1, 2, or 3, Calculus is a tough subject. Part of the reason I’m doing so much research is so that I’m prepared and I’m able to pass without any problems. If you have to take Calculus and want to know how to pass easily, check out:
I wish you the best of luck!