Get a better mic or talk quieter

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.

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.

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

Bro did a math project for an english class

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.

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.

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.

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!

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.

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

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

its all fun and game until the instructor asks you to pull double and half angle formulas out of your ass on test day

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

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.

THE DESMOS PART IS WHAT WE ARE DOING RN HAHAHA. LMFAOOO

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 .

Bro sounded like he wanted to cry at the end of the rant 💀

Physics professors: "And then you just do the integral" The integral: Partial fraction decomposition

"you probably re-learn it in university anyways." I always taught myself this when I was in high school, and it was a mistake. The lecturers won't bother teaching why things go a certain way because you have learned it in high school anyway. They will go straight to solving problems, skips multiple steps then show you the final answer, leaving you confused.

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.

Honesty is so RARE in discussions about calculus.

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.

I would a rather a “just trust me bro” than a whole ass proof on most of the shit I learned in cal II 😭

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

I did cherish these five minutes and fifty-one seconds of calculus. It was interesting to hear your perspective on the subject, and I liked that you indicated curiousity. I like calculus, and I also would like to understand the relationship between slope and area under the curve. Calculus is genuinely fun and I think that math is just awe inspiring when you consider its long tradition. It's a gift, passed down from generation to generation and added to, traveling with time along the existence of our species. I will continue to learn more and cherish it. Thank you!

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

I took a calculus course in high school for 2 semesters and by the end of it even my teacher was confused. Literally asked me what grade I thought I should get. I got an A.

4:43 I’ve pondered this question for quite some time. And then i heard someone said derivatives is the operation of subtraction and division which corresponds to slope function and integrals is the opposite operation: addition and multiplication which corresponds to the area under the curve.

I'm planning to attend grad school for math next year, and I'll likely be teaching a calc 1 course in the near future. What do you wish you could've learned differently or more of that would've made your experience better? Stuff like rigorous proofs of the limit and Fundamental theorem of calculus are relegated to an introductory real analysis course that builds the fundamentals of calculus from the ground up in a completely rigorous manner. However, only math and maybe CS majors usually take this course.

I'm not sure if anyone has pointed this out yet, but integration IS NOT the inverse of derivatives! Derivatives look at the rate of change of something (i.e., this is why the derivative of a linear equation is a constant = the rate at which the line changes is constant). The second order derivatives are usually called concavity, but they are simply measuring the rate of change of the rate of change, and so on for higher order derivatives. If you look at the limit definition, it is simply taking a slope! lim as h->0, (f(x+h) - f(x))/h, right? But note that h is defined as some distance from x. So, x2 is simply x+h, and x is, well x. Then delta x is (x+h) - x = h, just like in the denominator. The numerator is the function evaluated at x+h (which is x2), making this your y2. Similarly, the function evaluated at x is y1. So, you are simply doing the standard slope formula of (y2-y1)/(x2-x1), as the distance between the x2 and x1 values becomes VERY small. The extra condition of making the distance "very small" is justified because the tangent to a curve gives its rate of change at that point, hence, the limit definition of the derivative is simply finding the slope of the tangent line at the point x! Integration is the area under the graph, which is correct. However, that graph can be shifted up or down by any constant value C (it doesn't have to be at 0). So, if my curve is a sinewave centered at y = 1000, my area covered by the curve would be no different than the area covered by a sinewave centered at 0. If you understand this concept, you will understand that integration gives you a RANGE of possible functions (essentially, it gives you a function that can vary infinitely by a constant). So, if I take the derivative of sin(x) + 1000, I'll get cos(x), just as I would if I had done sin(x) - 100, or sin(x) + 35, etc. When I integrate cos(x), my answer is sin(x) + C, where the C signifies an infinite variation of the sin(x) functions - notice how this is not an inverse?! An inverse is, for example, multiplying 4 by 2, then dividing by 2, returns back 4. So, division is an inverse of multiplication (same with addition and subtraction). Finally, consider integrating a second order derivative twice: suppose our second order derivative gave us sin(x). Then, integrating it once will give us -cos(x) + C. Integrating this again will give us -sin(x) + Cx + C1! That means that not only are we getting an infinite constant shift, but ALSO an infinite linear function shift! Hopefully, this helps you understand derivation and integration better, and why integration IS NOT an inverse of derivation :) Best regards, Your friendly neighbourhood Math teacher ^_^

everything you want to know is covered in the first semester of university calc. an integral is an infinite series of rectangles and a derivative is a secant line between two points "infinitely close together" (x +/- delta). If you take the two points defining your secant line and multiply the distance between them by the height of the function somewhere inside that range of points then you get an approximation of the area contained under the curve between those two points. The approximation gets better as the points you choose (again, x +/- d) get closer together. That's why you get the ftc telling you that the derivative is the inverse of calculus. proving it rigorously is for mathematicians and i promise it won't help you apply it to anything unless you're a mathematician or a theoretical physicist.

Thanks bro, my dad constantly reminds me to start form scratch and this vid really shows me why I've been sinking into a chaotic process in learning. But calc is hard to learn by yourself... I'll try and organise my learning a bit.

Bro, this video actually helped me, I'm watching those chanels you recomended and I think I might be Godlike in near future

Very good content . I did AP Calc AB and it was pretty comprehensive

you legit just explained calculus to me better then any of my lecturers ever did

Currently at midterms. Going to take my first calculus class next semester. Shits looks scary af. My highschool was as shitty as it could be in terms of math.

As someone who has taken Calc I and is currently taking Calc II, the biggest thing that can make the difference with actually understanding the subject is definitely the teacher/professor, thankfully I had an amazing professor in Calc I who made sure to explain WHY everything was the way it was instead of just saying "Do this and this, and you get this", him explaining those essential concepts has made my understanding of Calc II so much better. I personally think high schools should give options to kids where they can take classes to better understand Algebra as well, cause if you don't really understand Algebra, then you are going to STRUGGLE in Calculus.

As a 1 off you're hella good at this, just finished 4U functions functions from an incomprehensible "this is how yo do it, can't tell you why" teacher, headfirst into ONLINE calculus class, this has helped me get a much better grasp of the overall paths calculus takes and what I need to really work on

Ive been pounding my head against a wall the last 3 days because I feel like i’m just memorizing and regurgitating rules and formulas without it being clearly explained why they work. I can’t find a source that explains the proofs in a way I can comprehend. I’m glad this problem isn’t exclusive to me.

Wow this is so true. For me it was now over 20 years ago, I had to take calc I two times before actually understanding what a derivative was in an intuitive sense. Literally after getting through twice, while mid way into calc 2 I finally got it. And it was because I talked to my uncle who was an engineer and he gave me real world usage of what integrals and derivatives are used for, and it suddenly made intuitive sense. And now I realize I wasn't bad at math, I did poorly because of how I was taught.

This guy needs a 3b1b's essence of calculus dose asap 🗿

I'm happy I took AP calculus courses at my high school. Having a full year for what is typically a semester course really let us go through more material and actually build on everything from precalc.

I loved calculus in high school, it always made sense to me and I think they explained pretty well why e.g. the integral is the area of a function

During middle and high school, I always followed formulas, saw a polynomial and thought "Oh I'll just plug it in a formula" and I get the answer a lot of the time. I never understood what those formulas meant. Come my first year of college, I took a remedial math course, and my professor summed up all 4 years of highscool math in a few months, not only that but he explained EVERYTHING perfectly, he explained how formulas were derived, explained why operations worked the way they work, etc. So now when I come accross a polynomial or anything, I don't blindly plug them in a formula anymore, I actually do the long math to make sure I get everything right,

My fist calculus class in highschool (grade 11, for 16-17 year old students) actually started with epsilon-delta, and we had quite a few advanced integrals at the end of it. Even at uni level I could use most of that.

I've found out your channel by youtube's recommendation. Very high-quality contents. I've sub your channels. Hope to see more of your videos.

I had all this in Uni. Thanks for reminding me that 10 years later I remember absolutely nothing.

The mic quality the production I fucking loved this bro thank you for making my day (currently in differential equations and linear algebra)

It's been about a year now, and the only concepts I remember are the ones that were explicitly talked about in 3blue1brown's calculus series. I feel like I've learned NOTHING from those classes, and rather were helpful at nailing down the topics I learned in those videos.

I agree fully that calculus is basically only complicated algebra that you have not learnt before

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

Okay this may sound slightly different, but I have to point out just knowing how to do the computations is a big win for when you actually learn the concepts rigorously. For example, I would always try my best to learn and answer questions about limits/derivatives/integrals, why they come together, but no matter what my high school courses only cared that i knew HOW to do them(obv i tried researching beyond the scope of my course) But in uni when you finally learn the rigorous stuff(like epsilon-delta proof) you see how amazingly everything fits together, and at that point you don't have to worry about learning HOW to do stuff, because you already know it, but instead WHY stuff happens. It's the same thing with other stuff in math too, you need to just sometimes grind through it before the puzzle starts to come together. And if you weren't fluent in computation you probably wont be able to give the theory behind it time. Grinding on problems to just get good at computation is underrated Like you got fluent in basic arithmetics (addition/substraction...) before you actually started applying them in word problems right? Same analogy.

i love this audio-visual content

actually explained the epsilon delta def better than any of my professors so far in a fucking meme vid

I took calc 1 during the summer and my teacher spent ample time going through the rigorous proofs for several concepts (including the limit proof you showed) instead of assigning us exercises to practice computations. Needless to say, I ended up dropping calc 2 on the fall and taking it the following spring ‘cause I had no clue what I was doing. Got an A the second time around at least lol

Man I could really feel your anger towards the end Still thoroughly enjoyed it my man

think if they tried getting the students to understand calc in a more rigorous fashion it'd take up the entire school curriculum and the souls of both the teachers and students LOL

This was actually the funniest math video I’ve ever watched.

Your yelling combined with the distorted mic really takes me back lol

One of the best videos I have ever seen... God job

I start a calculus class in 2 days, and now I’m delightfully worried

Jesse we need to cook math

I get your point and I felt the same way. The entirely of Calc 1 made me feel like a complete idiot because of all of my classmates could jump through hoops like monkeys on demand while I still questioned why sin became cos. Almost flunked the class but after college I feel like I’m part of the 1% that still uses calc from my class while my former classmates couldn’t use calc to save their life. But I have to ask, what is the alternative? Is there really much utility in going through the algebraic tricks needed to produce some of the more obscure derivatives? At the end of the day, calculus is a tool to achieve a goal much like algebra. Should we have spent a few more months on the foundations of calculus?

mickpuffi believe you could be one of the best math teachers on youtube if u continued this gen z way of teaching. so please do make more. if you struggle to find where to start, you can do the NSW Stage 6 Math Adv or math ext syllabus

Calculus to me is more about applying concepts that are seemingly left out or forgotten when the class is being taught. Those concepts are the connections between algebra and the next level that you speak of. Like defining an integral to say it is a function that sweeps from left(a) to right(b) within the bounds of the function and the x-axis depending on if the function is above or below the x-axis.

The issue with bring theoretical math all the way to first year is that it'll throw a bunch of students off, particularly for those who just want to use calculus. What's best is for students to be able to choose whether they want the rigorous math treatment right in first year, and know what they'll learn or miss out on. Of course, there are unis that do this already

My brain is expanding but my ears are bleeding

I was frustrated by the rigor in my calc class, but now I'm happy as I've never had the issues you had

the 3blue1brown course is so good it gives a vague idea of the connection between slopes and areas in literally the first video, before using the limit definition of a derivative and still make complete intuitive sense better than any math class i ever had

I enjoyed math in school, but now I'm so glad that I decided to study medicine

I knew I've taken a lot of math and engineering classes after I started to reconnize most of the formula in those "math noise" images

I’m in math analysis rn (10 grader) and my teacher has actually done a really good job explaining the logic behind limits and derivatives so far. Luv you ms Rosenberger you a real one 🫶

Education system: How to get people to hate math speedrun WR

I haven’t built the proper lebesgue integral yet, but we did do Riemann. Basically, the integral from a to b is defined as the area under the curve, and by building it from piece wise functions and then using uniform approximations you can have a generalised integral. Then from that construction you can prove the well known properties such as fundamental theorem of calculus, linearity, substitution, ibp. The thing is it relies on having a mesured space so vector spaces with norms work but more general topological spaces are problematic hence the lebesgue integral which my professor has hinted at many times

Great Video, great explanation. You should definitely make more videos!

I really feel bad for y’all who got introduced to calculus this way. I didn’t take it until college after taking years away from math courses and they went through a lot and had us construct a lot of proofs which helped establish the theoretical foundations of the work we were doing (epsilon delta proofs of limits, riemann sums, fundamental theorem, etc). This was even in courses mainly for science and engineering students and not just the math majors. It was actually interesting and it really felt like I was taking a peak at just how vast and deep mathematics can really be by being taught some fundamentals tools of analysis. I used to hate math but college (along with good youtube math communicators and me getting farther in my science education) really helped me change that view

I could not be more greatful to have a good AP calc teacher. I'm comming up on the exam now and evryone in the class actually understands everything bc he taught it well enough

Dude… THANK YOU❤

This was a nice video, I was about to subscribe but then I saw everything else are just Valorant videos xd I think you could build a cool math channel lol 👍

all this video did was make me appreciate how my own cal a class was structured, starting with limits and then going from limits into the idea of a tangent line to a curve representing the “slope” of the whole curve at that point, which then led into derivatives. Then, anti derivatives were introduced before integrals, shortly followed by the indefinite integral, which was explained as representing the set of all antiderivatives of the integrand function. From there, we briefly covered finite sums and sigma notation and then Riemann sums, which served as the basis for definite integrals. (Most of the other methods for solving integrals were also gone over before the Fundamental Theorem was introduced). So, yeah. Thanks Dr. Bossaller

3:12 me: it's not that difficult, I just learned it two weeks ago! 3:16 always me: HOLY SHIT, WTF IS THIS !!!

3b1b and Khan academy fr carried my junior and senior years that shit was my life support

I took calc 1-3, diff eq and linear algebra before Covid then dropped out, came back to finish engineering degree this year and remember nothing. I want to go back and relearn the proper way (I never did proofs besides in Lin alg) but don’t have time between work and classes. Great video

At least you guys play with desmos, all we did in my goofy ass country is write shit down 💀

In Israel (I'm personally in the most accelerated "normal" course (technoscientific reserve (amat))), the teacher shortly explained limits and then we did the power rule and most of the other rules, except the chain rule for some reason? It's currently been half a year and the most advanced derivative we've done is fractions with square roots, so I don't know how that compares to somewhere like the US.

Bro's channel consists of Valorant gameplay. And there is just this. And I just realized I gotta do this shit in grade 12. I have no idea how agebra works, I just use recognition. And my teacher barely teaches it. 💀

yes, you go years on confused about anything, but it slowly adds up together

Calc 3 is a reward for the first two, and I am exceptionally disappointed you didn't take it

Took up to calc 4 and many engi courses and all I can say is "it is what it is"

Couldn't have been a better time.

getting this reccomended by yt the same day i jsut gave my calculus 2 exam lmao i wanna cry

My pre calc class was nothing but trig. Calculus 1 was taught by a guy getting in his Ph.D. In animal genetics. Calculus 2 was taught by a high school teacher getting his Ed.D. I switched majors after limping through these classes. To this day, I still have not used calculus.

The fact i understand every single thing that you say is unbelievable

this channel is tonal W and it's been only two videos

i am learning calc 1 right now in university and this made me feel so understood, thank you.

I liked the end of the video because I literally got an A in calculus just to be able to say I got an A in calculus and look smart in front of my friends. In truth I learned VERY little and can absolutely NOT do any calculus equations because I have no fucking idea whats happening.

I took the advanced first-year calculus course at my uni this semester and it spent the first 5 or so weeks defining sets, the notation, then going into sequences and limits (rigorously proving everything along the way), and then finally went into derivatives, integrals (using the riemann definition with partitions and so forth), and finally we are now onto series. It definitely isnt introductory since it assumes you did well in the advanced maths at high school which include a lot of calculus

The Mic really adds to this experience. I had this conversation over the pandemic on discord all the time. Your mic is exactly what they sounded like when we’d open an assignment & it was just a page of math proofs 😭😭😭😭

Nice to see the basics again after being stuck in the world of Calc 2 for what seems like forever