Surprisingly I managed to get through the remaining 14 question on the course challenge this week and only got one wrong! Meaning my final score was 27/30 correct, a.k.a. 90%, a.k.a. the minimum necessary score I gave to myself to move forward, which means I’m FINALLY moving on to Multivariable Calculus!!! 🥳🎉🎊 I started Calc.2 in Week 147 so I’m feeling pretty proud that I made it through, especially considering how much of a struggle it has been at times. There are only a few math courses left to get through on KA which is also part of why I’m so pumped right now. After more than 3.5 years, I’m finally pretty close to finishing this, relatively speaking. There’s still a significant amount of math left to get through, and I’m sure that the remaining courses will be more difficult to understand than what I’ve worked on up to this point, but I can now clearly see the light at the end of the tunnel and I’m SO proud/happy/fired up to have made it here. 😤
Although I was happy with my score on the course challenge and am ok with moving forward, I cheated on two questions. 😔 The very first question of this week asked me to state whether a series would converge or diverge by using the ratio test. I forgot that if the limit using the ratio test was 1 then the test was inconclusive. I thought that if the limit was 1 then the series would diverge. I looked it up and realized I was wrong so I switched my answer. I’m not thrilled that I couldn’t remember the answer but I think in the grand scheme of things, forgetting that the ratio test is inconclusive when the limit equals 1 is a relatively minor detail when compared with all of Calculus 2.
Here are five other notable questions I worked through on the course challenge:
Question 1
I had a hard time remembering exactly how this type of question worked. I remembered a 3Blue1Brown video where Grant (who’s the producer of those videos and – spoiler alert! – is part of an interesting twist at the end of this post!) goes through an example of finding the velocity of a car by taking the derivative of its speed, and how the area under velocity graph was equal to the distance the car travelled. Remembering that video, I was able to work out that the correct solution to this particular question (which is the exact same type of question) was the second answer, 1∫3 v(t) dt.
Question 2
As you can see from the KA solution to this question, the way that KA solved this question was a bit nuts. I got this question correct but used trial and error to figure it out and definitely did not solve it the same way KA did. I started by graphing r = sin2(2θ) on Desmos and then reduced the bounds:
It looked pretty clear that a line perpendicular to the point π/4 would be a line with a slope of –1 and be tangent to the outer most point of the ‘clover’ was in the 1st quadrant. I literally guessed y = –x + √2 on my first attempt and it was correct. I then used a bit of algebra on the first answer to get it into y = mx + b form and realized that it was the correct answer. Boom. (Obviously kind of cheated on this question though. 😔)
Question 3
This was the question I got wrong this week and had no idea what I was looking at as I was working through it. As you can see from KA’s answer, it turns out the given answers are denoting a Riemann Sum. After getting it wrong, I had to go back and watch a video to remember exactly how the notation works and find it relatively easy to understand now. That said, if I didn’t see this type of notation for a few weeks and then it suddenly came up, I think I’d probably forget what I was looking at. Nonetheless, I’m happy knowing that I can completely understand how/why it works by going through the video on it.
Question 4
I was able to work out the solution to this question fairly quickly in the same way that KA did and was pretty proud of myself which is the only reason why I made a note of it. One of the keys for me to work through this question, which I’m very happy about, is that I can switch between Leibniz and Lagrange notation fluidly which makes the calculus much easier in my mind. I find dy/dx much harder to wrap my head around than y’(x) so I’m glad that I can now quickly make the connection between the two and swap them if need be.
Question 5
This was another question I cheated on by using Symbolab. When I saw this question, I tried using the inverse power-rule and inverse chain-rule but couldn’t solve it. I completely forgot about polynomial long division. 🤦🏻♂️ I’m certain I would have got it correct if I had thought of using polynomial division because once I realized that’s what KA’s answer used I was able work through it myself without fully reading through all of the solution. I’m bummed that I cheated to get this question correct but, knowing that I know how to do polynomial long division, I don’t think it’s the end of the world.
I finished the course challenge on Thursday and started the next course, Multivariable Calculus, on Friday. When opening up the course, I realized that the entire first unit, Thinking About Multivariable Functions, has no exercises and therefore no mastery points to earn. The first section, Introduction to Multivariable Calculus, only had one video in it which I watched and was surprised that it wasn’t narrated by Sal. It turned out to be voiced over but by the SAME GUY that runs the YouTube channel 3Blue1Brown, Grant Sanderson! 🤯 For me, this was a small collision of worlds since I’ve watch the 3Blue1Brown “Essence of Calculus” playlist on YouTube many times. After getting through that first video, I moved on to the next section, Vectors and Matrices, which is made up of 7 articles. Here’s a screen shot from the first article which I believe actually incorporates what will be the other 6 articles in the list of concepts shown at the bottom of the last screen shot:
There’s clearly a lot of options for things to review here which I’m surprisingly looking forward to. I’m guessing/hoping that a lot of the topics that I worked through before but had a hard time understanding will become more clear to me now as I work through them again in the next few weeks. It makes me think of the quote I saw on reddit a few years ago where a student said that his professor told him or her that you don’t learn the math you’re working on until you use it in the next course. 🤞🏼
I’m a whopping 2% of the way through Multivariable Calculus (100/4,800 M.P.) but honestly couldn’t be happier about it. For some reason I feel more fired up about getting through Calc.2 than I have about getting through any other unit or course up to this point. As I said at the beginning, I think the reason why I’m this fired up is because I’m SO close to being done. I’m not happy about almost being done because I won’t have to study math once I’m finished – I’ll start on physics right away anyways so it’s not like I’m going to stop studying, in general – but because I’ll have accomplished a goal that I’ll have worked on daily for close to four years. 😤💪🏼