Fundamental Theorem of Calculus Explained | Outlier.org
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- เผยแพร่เมื่อ 20 ก.ค. 2024
- The Fundamental Theorem of Calculus is at the heart of Calculus: it links differentiation and integration with two simple equations. In this lesson, Dr. Hannah Fry shares what this theorem actually means, how it’s calculated, and what it can further allow us to do.
Dr. Hannah Fry (@fryrsquared) is an associate professor in the mathematics of cities at the Centre for Advanced Spatial Analysis at University College London. She works with an interdisciplinary team to study many aspects of human behavior, such as shopping, relationships, transport, and urban crime.
Chapters:
0:00 Definition
3:26 Example
5:24 Differentiation
10:19 Integration
14:22 Summary
This lesson is excerpted from Outlier’s Calculus I course. Learn more about this course and check out our full catalog at www.outlier.org
About @OutlierOrg :
Outlier.org (from the co-founder of MasterClass) has developed the world's best online, university-level courses, taught by some of the most celebrated educators in the world. Our courses employ engaging content and cutting-edge educational technology to create an immersive, student-friendly learning experience complete with transferable credits. Outlier is reimagining higher education as a resource that is accessible, equitable, and affordable for everyone.
#Outlier #Calculus #HannahFry #FundamentalTheoremofCalculus
I'm a 82 yo male self-teaching myself calculus and this presentation was very clearly done and I'm finally getting the theorem! thanks, good job,🙂
Keep on learning!
Where was this video when I was struggling hard to understand this very thing?? I vaguely remember the teacher talking about Darboux's superior and inferior sums and Riemann making an appearance... Oh, and having to memorize a table to primitivations and derivations (my absolute most hated activity in any learning environment)..
Excellently explained.
When I started the journey of Calculus 2, This vid impressed me with 2 approaches towards the area. Now I'm back for a replay after completing the first round of learning. In particular, to address the vagueness in the summation approach. The extended summation formula is pretty interesting.
But frankly, despite that the explanation is silk smooth, the first approach is a certain headache for many and therefore is a weak point from the planning perspective.
Remarkable initiative .....Guys, Could you upload some free series here on precalculus.
Thanks! We hope to post lessons from our newly launched Precalculus course in the future. In the meantime, check out the course page for more info: www.outlier.org/products/precalculus
This is brilliant and very concisely explained. The teacher’s accent is also very relaxing to listen to, like ASMR, so it makes it much easier to focus.
Thanks for the video!
A very ASMR lecture of the fundamental theorem of calculus ✨
fascinating way of summarizing that concept.
Thanks Hannah, and Thanks Outlier
Outstanding!!
Didn't understand a word but would happily listen to the Doctor read the phone book.
Thank you teacher, very helpful video.
Keep up the good work
Thank you so much
This video gives a nice easy example of how to USE the Fundamental Theorem of Calculus. But from the title, I thought it was going to explain why the Fundamental Theorem is true. Why is dA/dx equal to y? When I took calculus, I didn't have much trouble using the theorem, but understanding why it's true is something I never fully grasped. Is there another video in this series that proves the theorem?
It always helped me to rearrange and visualize the same equation as dA = y dx. With y being the vertical length of the small dissecting rectangle and dx being the width. And total AREA equals LENGTH times WIDTH. As is with any rectangle or square. Hope that helps a little.
Brilliant! and LOVE the fountain pens and the lovely handwriting!! Looks like a Cross.....is it??
I got to Green's theorem and realized I was finished with calculus, I aced the class but it was a struggle, that was 46 years ago
I was a little confused until I realized lower case delta was being used instead of capital delta.
The amazing Hannah Fry 🙏🏻
A nice initiative done by teachers but i would like to suggest you that you should try to upload free course on entire calculus and mathematics students will come to know how you teach and a nice exposure for them to clear their concepts it they wanted advance attention so they can refer to paid courses . Actually in INDIA every teacher first available their courses free on youtube then they go for paid .LOVE FROM "INDIA"
Dude, its ok if poor students from third-world developing countries cannot pay for these courses. We are not their target audience anyways.................Remember, people who pay for these also have to earn.
what fountain pen is she using?
1^2 + 2^2 = 5. At 8:13 it says that the sum of squares from 1^2 to n^2 is (n+1)(2n+1)/2. So if n = 2 then (2+1)(4+1)/2 = 3*5/2 = 15/2 which is not the sum of squares to 2. I think a factor of n was left out. I'm finding the sum of squares from 1^2 to n^2 is n(n+1)(2n+1)/2.
Crap she fixed it about 15 seconds on. Grr. It distracts me from learning.
Hannah Fry is a badass. This was a great explanation of the FTC.
Which pens are those?
No one speaks more beautifully of things I don't get, than my lovely Dr. Hannah..
BTW: Sex is like math. I don't get it.
❤❤
Nice video. I enjoyed it a lot.
But I was expecting a formal proof of the fundamental theorem of calculus.
why doesn't (2n+1)/n tend to 3?
Replace n with, say, 10000 and try. You'll see
@@albertorimoldi8713 agree, my question makes no sense, not sure what i was thinking!
"You have some function, y"? I have no clue, either.
Thanks, Professor Fry, and I see there is elegance in calculus. But I STILL don't get it. I might check out the pre-calc course, just because I hate being so frustrated by this. In college (many years ago) I struggled through the 2 calculus courses that were required for my B.S. degree. This despite being an A student in High School for algebra, geometry (loved proofs) and trig. As math builds on itself perhaps I missed a concept leading to calculus. Reminds me of when I was in grade school, 10 or 11 years old, where I was out sick for a couple days when the class was taught the signs/operation for "intersection" and "union" between sets. I was clueless for the following weeks until a friend showed me what they meant.
On the other hand, maybe trig is all my brain was wired to handle. That's ok too. But for anyone with young kids -- I'd say engage those sponge brains on this stuff.
Sometimes the frustrations of learning math are motivating and sometimes they just shut us down. We're sorry your relationship with math is hitting calculus bumps. Some precalculus knowledge is a prerequisite for this Calculus I course so we hope you do check out our Precalculus course, as it's designed to break down concepts visually and it's taught by world-class math communicators. Here's the course page for more info: www.outlier.org/products/precalculus Happy learning!
@@OutlierOrg No, This video explains a complex matter, much, much too fast, if you want to explain the riemann method for the fundamental therom of calculus you can't just chuck it in a video and assume everyone watching it is familiar with the trapezium rule, summing an infinite series and the b-a/n dx substitution and how to calculate F(Xi). A video like this should have at least links or something to help with explaining the aforementioned, as none of this relates to or would show up in pre-calc anyway.
I love how it makes sense to say "naught"
I like Turtles.
🇮🇳
maybe it's just me, but this seemed to introduce way too much material too quickly, and not explain any details of the notation or concepts. (In the first minute, you write the FTC, then seemingly as an afterthought define integrals as limits of Riemann sums.) Then it looks like you're talking about both parts of the FTC, without mentioning that they're different results. (I think?) Not sure if this was meant to be more of an overview as opposed to a typical lesson in the course, but if I were a student I would have a hard time learning from this.
(Also why is the third timestamp called differentiation: both it and the fourth timestamp are integration, just different methods, no?)
No you're not wrong this video is ridiculous for anyone who doesn't already understand it and the timestamps are clearly incorrect
The Emily Blunt of Calculus :D. Yeaaaaaa. Another source added to my list.
Integration as summation is a mess! And time consuming while German notation is easier. I hate Greek Sigma notation.
This girl is a mason
Smart women = So attractive yeah the British accent doesn't hurt either.