Calculus - taught at the 8th grade level

Learn basic calculus - this video will explain calculus so anyone with at least middle school math skills can understand.
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[@n6mz]

Ever since freshman year of college (calculus I, II, and III) my mind has gone back and forth as to which is more beautiful: calculus or trigonometry. I've decided in old age that they're equally beautiful. Very nice lesson, I think most of us kids of the Mercury/Gemini/Apollo era who went into careers now called "STEM" would have been able to start calc in sophomore or junior year of high school, assuming it was presented this way, which is what we used to call the analytic geometry approach. Keep up the great work!

[@adonaivictor4493]

Newly hired 8th grade math teacher that’s only certified in 1-6🙁 have no clue where to start, your videos have been helping.

[@Rudraaa77]

U good now?

[@Tim-Kaa]

Love these calculus videos, it's so addictive. Can you please do a video deriving circle, triangle, rectangle, square formulas using calculus from scratch? This will be lots of fun!

[@TheRealHedgehogSonic]

I'm just gonna say it... Calculus is fun! I know a lot of people find it boring, what with all the cryptic symbols and instructions, but when you actually apply it to what you'll use it for in a STEM dream job, it's magical. As a man who's on a quest to be a game designer, learning all the things I can apply to code to make something like an enemy work is half the fun of learning calculus problems. In fact the only reason I dropped my first calculus class is because the professor was a machine hating boomer who worked against my very tech heavy note taking and learning methods I set up. To put it in perspective, the dude didn't even have a Canvas page!

[@leedomin888]

😂

[@mrs.muycoskitchen9562]

This is interesting.

[@IbrahimMerjanah]

Hey, just asking; are there any coding problems you've been able to use calculus for to solve?

[@stanleygabrel1045]

I wish I had a teacher like that in school. Great job.

[@jessixa_143]

this was so fun to follow! thank you :D i just wanted to learn calc for fun and this was a really good start for me! tysm

[@arlliegreen7555]

John, that 8th grade calculus problem seemed much more difficult than many others😢. Love your classes & will soldier on. Thank you so much!

[@benfen8798]

At about the 16:30 mark, you got 1.8517 by finding the areas of the rectangles and then adding them. I got about 5.55 myself, and I'm wondering if I did something wrong

[@BNSF2012]

its amazing how you did this in paint so well i cant even paint a car in regular mouse paint i have to use shapes and im 5th grade so this is helpful thanks alot

[@vivaanchandra25]

Sir I am an 8th grader and i saw your video, I tried a different approach to find approx. answer. I also tried adding area of triangle with the 3 rectangle's areas and got an approx. answer of 2.336233. Also, can you please make a video explaining the function, how this formula was made and the dx thing.

[@FranciscoCastillo-bx3rf]

A function is like a machine that takes in a number, does something to it, and then gives you back a new number. For example, let's say you have a function like this one: "f(x)=3x+1" When you put the number 2 into this function, it multiplies it by 3 and adds 1. So, if you put 2 into the function, it gives you back 7 because f(2)=2(3)+1=7. Functions can do all sorts of transformations. But the key thing is that for every input you give it, a function has a clear rule for turning it into an output. That's what defines a function. The ‘dx’ thing basically means ‘differential of x’. Differentials are the instantaneous rate of change at a specific point on the curve of a function, It's like zooming in really, really close to a point on a curve and seeing how much the slope of that curve is changing right at that spot. When you perform an integral like in the video, you must multiply the function by its differential so that we know with respect to which variable we are integrating. In simpler terms, the ‘dx’ is used to know to which letter of the function we are going to add 1 to its exponent, because there are functions that have more letters than just "x". I hope I've explained myself well.

[@benfen8798]

I'm planning my high school classes and further education and I need calculus for my cs course so I am watching this

[@argonwheatbelly637]

39 in a little over half a minute in my head. Sorry it took so long, but it's 3:37am, and I'm beat. 😔 Nice video!! Good intro to concepts of integration. Calc is fun! Ok, reality for college: Calc I is a weeder course. Calc II is a litany of memorization of techniques. Calc III is suddenly super easy once you made it through the first two. If you have finished Calc III, then Physics will be a breeze! By then, you will likely have already taken Bio as well as Chem, but once you know the Physics part, Chem will feel far easier. Chem, Quant, then Orgo, PChem, Biochem, etc... Sorry, but I'm rambling about how all of this stuff is interconnected for a chem/physics/biochem student. Enjoy!!!

[@jonathansmith336]

Might have used 4/3 and 5/3 for the x values and then used the squares for the y values and only approximated at the end in décimal form.

[@AngadGautam02]

in india we have this in 11th and 12th grade 11th- Differential and 12th- Integral

[@ugaugauga488]

Shouldn't that final answer of 2.3 be just the triangled area, not the bottom part which is square? Shouldn't we then add the triangled area to the square area? After all, we're not adding triangles in the square area, only in the upper area. No matter how small we make them they'll never include the bottom square area. Confusing!

[@quakers200]

Why f(x) and not just call it y or instead of the y axis call it the f(x) axis.? I found statistics much more valuable and though much of statistics depends on calculus, for me it was more practical . It really depends on your major.

[@cancer9630]

It's because at times it's easier to teach and do coordinates as (x,y) instead of (x,f(x)), and other times it is easier to describe things as functions and not variables. Plus, when writing certain types of equations it would just be confusing since the f(x) parenthesis can confuse people. As you said, it really depends on what you're studying.

[@TheJojoaruba52]

Thanks for the explanation. I made it through college calculus, but it helped hearing your explanation. It would have helped me if I had had a better pre-calculus teacher.

[@matdoesconstruction2182]

Can anyone give the answer to the car problem or provide a link to any videos explaining how to solve for the car’s speed?

[@matdoesconstruction2182]

Is it approx 50.5 mph at 13.82 seconds ?

[@BRNavalgund]

Though I have done integration 100 times..but I listened to it as it is my first time.. Lots of ❤️

[@glvarner]

Brilliant explanation.

[@Shanniddhya]

Wait I manually added the decimals for the rectangles and got 1.8214 not 1.8517 how ?

[@dr.d.45]

The .3 is actually .33333333 to infinity so extend out to the 1000th place

[@cto_plushtubing]

Most of the calculus intro videos go over integration concepts, but very little on differentiation concepts. Why?

[@FranciscoCastillo-bx3rf]

I think it's because the concept of ‘finding the area’ is something much more intuitive than that of a derivative, where you have to find the instantaneous rate of change of a function at a point.

[@butchordenes3812]

You're supposed to perform integration for the limits 2 to 5, yet you change your limits to 1 to 2 during the computation?

[@ricklarsen852]

That was probably just his title page for the presentation/course because clearly he used the limit of 1 to 2 for the lecture calculations

[@jonathansmith336]

Good point!

[@beachman8106]

⭐️⭐️⭐️👍👍👍 from 🇦🇺

[@benquinneyiii7941]

The infinite

[@suhaslatkar9007]

You took lots of time stressing the need for having an infinite number of skinny rectangles inside the curve to get the correct area under the curve but jumped suddenly to the f(x) without warning the readers and then omitted to explain why,how and which (some) rules of calculus have to be followed to get the area under the curve, leaving the poor thread of infinite numbers of the skinny rectangles dangling unattended till the last few closing lines of the video. From point 1 to point 2 how we are covering infinite numbers of the rectangles, is it by some magic,! *This is why so many (non mathematical) people hate maths,if you want to reduce the number of math haters by even one number please make another video including explanations every moment of your narration then possibly at least i ( a non mathematical person) will be out of the maths haters category*!😊🙏

[@marveloussoftware1417]

Good explanation but for me, the long windsdness and constant repeating makes it hard to listen to. 😒