Introductory Calculus Classes in a Nutshell

sending this as my english project (hell naw)

[alexandergayowsky]

Hearing your profs say "trust me bro" a few times during calc 1, 2, and 3 is a small price to pay for deferring real analysis.

[mooredaxon]

I'm actually going through a calc class in high school right now: my teacher ain't even really a math guy, he just got roped into being a math teacher because he originally was going to work on computers, then decided to be a teacher, and since he had taken math for his computer classes, math was what was taught. Anyway, it really plays to his advantage, because he asks the same sort of questions you do about his own material, and so he ends up going over WHY the math works, not just how. Definitely one of my favorite people.

[maverickiwnl]

please never change you're mic, it is fucking hilarious and makes the video 10000x better. This shit was funny as fuck, thank you.

[omegax]

Watching this video made me appreciate my math professor more. He actually spent a significant chunk of time in class going over proofs for limits and derivatives. He was really thorough and had good answers to our questions.

[Lemurai]

I was super disappointed in my first calculus course at uni, there was no time in my life other than this situation where I felt like I had a better grasp of the subject than the teacher. I don’t know if he was new, but the guy glossed over trig functions in a single lesson, didn’t appear knowledgeable on how to use them, couldn’t articulate what Cos or Sin meant, seemed really nervous & confused when someone asked a question & really didn’t understand limits, which is insane because limits are based of the initial function’s people learn in college algebra. It was a complete disaster, the entire class complained at the end of the semester & he was removed (probably fired) because I never saw him again. But he really messed it up for those people who really needed to understand calc 1 before they went on to calc 2, I’m blessed that my dad is a metallurgical engineer so he taught us all these concepts at home when my brothers & I were growing up. But seriously, universities need to do a better job of investigating the backgrounds of the people they hired instead of being greedy for money.

[onlineacc]

Bro did a math project for an english class

[tomtommcjohn]

Real analysis goes into almost all of the theory that builds up to calculus. It's also much harder than calculus. So the teaching order, while seemingly bizarre, makes sense in a way. You effectively memorize the building blocks of higher math, and later learn how they themselves are built. I wish they presented it that way.

[LorxusIsAFox]

Hey, actual Calc prof here. One way to see why derivatives and integrals are opposite to each other is to remember that derivatives always represent slopes of tangent lines. Now look at a definite integral. If you extend the upper bound a *tiny* bit h, the additional tiny rectangle you get is that tiny amount times f(b+h), so that your area changes by about f(b) per unit of h. But that's the derivative of the integral showing up as f(b) again!

[stormy]

I was fortunate enough to take Calc 1 with a professor who absolutely refused to skip the rigorous proofs. It was really freakin' difficult to follow those, but it made the concepts of calculus intelligibly and consistently build on one another. The classes also refused to skip the "this case is stupid messy and requires a ton of algebraic manipulation" topics

[markdave]

Yo dude, I was in the same boat as you because I passed calc 1, 2, 3 but later realized i didn't know wtf i was really doing, just manipulating symbols. I took one summer to relearn calc 1 and 2 and one winter break to relearn calc 3 all on khan academy. It was well worth the time spent because Sal and Grant Sanderson (the guy from 3blue1brown math youtube channel) explain why things are true in the first place. For example, proving all the derivative rules, the connection between area and slope, why antiderivatives give you area, how double, triple, line and surface integrals really work, and other theorems you learn in calc. Of course, I also had to learn why some concepts in algebra, trig, and linear algebra (like the dot and cross products) were also true before I had to relearn calc. Although the information gained isn't really useful to the average joe since you never really use it unless you work in a specialized field.

[MikeHawk-sg]

I was actually taught the rigorous definition of a limit when I took intro to calculus. however, my teacher didn’t really understand it herself and she abandoned the topic after one confusing lecture lol

[amirmatrix]

bro, you hit the spot. You're literally pinpointed each problem with the world and calculus and all the people that are teaching it, are missing a lot of things and themselves need to learn it again .

[marcusmelander]

Here's how I like to think about/justify the fundamental theorem of calculus

Derivative = slope = rise over run = x/y

Integral = area = x*y

I know everyone else is complaining about calc classes but I wanted to throw that out there.

[kratostheinevitable]

dude i'm doing engineering and my professor is speedrunning maths like bro 🤣😭

[Drakonus_]

I'm majoring in Computer Science and Calculus was taught to me in the 2nd semester. The professor pretty much taught it the way you did. He also addressed the same questions that people wonder whenever they take the course. And since I had already learned Linear Algebra in the 1st semester, the behind the scenes stuff with Calculus was kind of a breeze.

[stevematson]

Honesty is so RARE in discussions about calculus.

[pinochet]

3:38 This is very relatable.
As a highschool senior, I am currently taking Accelerated Calculus and AP Physics Mechanics. I have a D in Calc and an A in calc-based physics. My calculus class is incredibly dense and boring, and my physics class is fun and exciting. When my calc teacher speaks, my mind drifts (I've literally fallen asleep multiple times in her class) and my physics class is one of the highlights of my day. My physics teacher teaches more calculus in 15 minutes than my calc teacher does in a week, and I actually remember it.
I really hate introductory calculus class, and I only put up with it because it is a necessary stepping stone towards the engineering degree I hope to pursue.

[parmisiguess]

i was so lucky to have such good professors for both my calc 1 and 2 classes. i’m not pursuing any further math than calc 2 because my major doesn’t need it but even tho i don’t like higher math, these two professors made me appreciate it more and understand what the hell these processes mean

[enozi]

Dude really took 3 calc lessons to make a video. Kudos!

[scrapyarddragon]

Please do more of these, as someone who struggled to get through uni calc this is a great deal of catharsis.