Calculus, a simple explanation…
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- Calculus - a quick explanation of why Calculus is so special.
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![The most beautiful equation in math, explained visually [Euler’s Formula]](/img/n.gif)
I’ll say it as my first calculus teacher told me: calculus makes stupid, overly complicated math simple.
You take a mess of a problem, boil it down, and distill it into something that’s far, far easier (and takes you less time) than the monster you were about to begin.
(Remember, the more steps to a problem, the greater the chance that you’ll make an error somewhere in all that arithmetic.)
This is only one of the sweet benefits /applications of this mathematical dream, but it is a BIG one, if you’re looking for reasons to learn it.
I think the subtitle should be: "Calculus - a quick explanation of why Calculus is so BEAUTIFUL."
TH-cam mathman your videos are awesome and motivating
Without calculus, practically all of the world's progress since the 17th Century would have been impossible.
On the drive home today, I asked myself if there was a dead straight method to understand calculus, by using it where it wasn't needed at all. Like, say, figuring out the area of a right triangle.
So when I saw this video come up in my feed, I thought, damn. Synchronicity baby. Synchronicity.
The curve that you drew in the video is NOT Y=X squared, it is Y=X squared + some Y value. If you calculate the area under the curve of that graph, it will not yield the same value as the area under Y=X squared.
This is why the ACTUAL integral is x^3/3 + c. I was disappointed at the graph used.
Generally, the c is an unknown constant, but in this case c would equal the x times the y intercept.
Y is not x^2. It is Y = x^2 + some y intercept
That example curve goes through the origin.
Your curve is not y=x squared. As you know, it is y=x squared plus a constsnt. A correction is needed.
Shouldn't y=x^2 be sitting at point (0,0)?
Thanks
Area
Darn curves
Very well and easy explanation. You are great. Thank you!
Good analogy with the two problems. Made it easy to understand. Thanks for the video!
I think explaining the logic of the formula helps. So we know that a square or rectangle is LW. And a triangle is really just half of a rectangle, thus the 1/2 in the formula. BH is almost the same as LW, but only the right triangle is easy to see. Getting the height on obtuse and acute triangles changes the width part.
I was depressed until i saw John uploaded the kind of video i was looking for and hearing him naming that shape squiggly made me laugh, thanks a lot John. You really made my day.
Calculus is C👀L!!. There are two general types associated with both a function of (x) and its curve when plotted. They are: (-1-) slope of the graphed line and (-2-) area under that graphed line.
If a weatherman collected data during a rain storm and found the equation that described the rainfall he'd be able to use calculus to (-1-) analyze the slope to know when rainfall was strongest (slope) and (-2-) know the total rainfall (area under the curve.)
If it takes 17+ minutes, it's not simple.
Chain rule?
First 🤸🤸🤸💯💫
Masochists
Stem
Zeno