Calculus explained through a story
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- Опубликовано: 15 янв 2025
- Here is a look at the essence of calculus through the story of Bob. We use differentiation to find the slope of a curved line and then use 'integration' to find the area of an irregular shape.
Special thanks to the owl and birds in my garden for making so much noise during filming.
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#JoyOfMathematics
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Fun fact: the word calculus comes from the latin word for small pebble
That explains why in portuguese kidney stone is called "kidney calculus"
Wow
I've been watching little pebbly Bob Ross, Jr.; he's discovered your presence. He's shifted his OCD for pebbles and chalky deer toward thoughts about you. He's already been calling you God, I'm afraid to report.
william41017 Who knows, calculus as something tiny that nevertheless l causes a lot of mischief until expelled from the equation might well be behind the original use of the word in this context.
Dustin Perez all of them
Teacher: For this calculus test you can use any calculator you want
Me: *Walks into class with a huge log and a bucket of sand
@Jeemeli - That comment was absolutely hilarious... and am still laughing as I type this!
@@__WJK__ Thanks, although I didnt think it was that funny
lol ..made my day!!
You're nothing without the Pebble...,
that was really funny :D
Bob repairs bridges
Bob cares for the deers
Bob is a good guy
Be like Bob...
Prasath N M i just want to hunt those deers
don't forget.. and Bob is intelligent!!
r sin so a 9yr old is here I guess .Dosent matter pewdiepie and t series both are useless
Omg I follow that Instagram page 🤣🤣🤣
Lol😂😂😆
She’s literally putting Bob Ross in calculus in the same world. My life is complete 😭❤️
*Next up :* bob goes to cern to split some atoms so he can perfectly measure the surface
Bob now is more mature and use God particles to measure areas.
He rearranges the shape into a right angle triangle.
your smile can put a sense of serenity into my stressed up soul
I feel like I was just cured of some weird math disease I’ve had for a decade. Awesome video! Thank you!
Bob: Lays down sand
Windy day: Oh no you don’t
Haha XD
After traveling 50 miles to the beach!
Wow! Story telling is a license to print memories in the minds your audience! Beautifully illustrated and delivered, this lady is inspiring to watch.
Great explanation! As a math minor I know it takes a gift to be able to explain concepts like differentiation and integration in simple terms. You have that gift. Keep it up!
You’re the prettiest and most peaceful math teacher I’ve ever seen.
youtube delivers on occasion
Unbelievably gorgeous
Rick DiClemente INDEED!!
I wish I had her as a Math Teacher as a young boy, instead of the evil angry witch of a teacher I had who ruined Math for me
If I had this young lady as my math teacher, I would have passed Pre-Calc. I certainly wouldn't have missed any classes. I'm subscribing as soon as I'm done typing this sentence.
Loved the story. I wish you had been my calculus teacher many decades ago. Very entertaining and informative. Please don't let anything stop you in life in obtaining, using and helping others with your knowledge, You are and have a great gift.
Oh boy, I'm taking calculus next semester, I'm scared I'll get a teacher who just doesn't care
@schmuck Norris thats an average math and physics teachers in my school
@Late to the Game And you may be ignorant. Most universities will flunk more than 50% of the students who are qualified to take calculus or other professional-track courses. The math departments are very open about wanting to restrict the number of people who are allowed to learn about and have careers that require such knowledge. Not because those students are stupid - they are not - but because that keeps their own industries at higher pay and protected from scrutiny. I worked university advising, from undergrad to PhD level, for 15 years and math/physics as well as engineering/science/medicine & law groups similarly control access to give themselves an insular work force that gives them an edge. And they are completely open about it. My advice: take and re-take courses on the subject area of the discipline you hope to enter. Immerse in it until you know almost the full curriculum from outside sources (RUclips, free online university lectures, tutors, etc. You are ready to start the intro course series only when you are already a course or two above in knowledge. In that way, you have some chance of being in the top 50% of those students who otherwise will be flunked out very quickly to "thin the herd."
she belongs in retail.
@@mikeorclem boomer
The deer died 15 years ago...Bob still hasn’t finished counting his sand grains
Turns out there were no deer-Bob lives in an insane asylum...’counting sand’
Okay, I laughed, but she is still good!
@@javapaceable LMFAO
but his legacy continues to live on
Calculus: how to guess really good.
Exactly!
Lol, nice one!
really well
Not really
One of the many things you can learn at the Derek Zoolander School For Kids That Can't Read Good And Want To Do Other Things Good Too.
I have no idea what she's talking about but she's impossibly charming.
haha same :)
@@AlahuSnackbar Charming 100%
Calculus is a topic in Maths mostly taught at Uni...
Same. She is lovely but my brain didn't absorb anything. In my defense it's late at night for me so I'm not super focused but I still listened to the whole thing. Idk how I missed calculus all the way through school. What is calculus? It's math. That is the entire extent of my knowledge. I am 46 and slightly ashamed.
Best comment.
He protecc
He attacc
But most importantly he wants his grass bacc
This is like meditation for me whilst learning something that bored me to tears when I was too young to learn it.
👍 agreed
I never understood the practical uses for differentiation and integration in class until i saw this video. Wish my teachers had told us stories before teaching how to do the calculations. You are doing a great job lady. Keep them coming!
Imagine how peaceful, rational, and lovely the world would be if everyone was like Toby. My new happy place.
How did i get here? Three clicks ago I was listening to Slipknot.
You tube is scrambling right now to avoid congressional action. You're going to get MANY more strange trailing AND recommended for you vids. Join the club...
Funny. One click ago I was learning about buying used cars!
RUclips is trying to divert pissed off white men in the US towards anything that they think might distract or sooth them. For the past few weeks, I've been watching vids on crew served weapons and weapons that have been introduced since I was in the military around 30 years ago, trying to freshen my skills for what is coming. They keep throwing stuff like this and kitten videos up in my recommendations. Figured I would try this one as it might be helpful in land navigation and range estimation. Never messed with calculus, but trig will definitely help put rounds on target.
Betcha y'all watched it to the end though :-)
@@greghuskey7475 - Two clicks and 4 hours from now I'm gonna build a time machine. I understand there were some good used car deals in 1962.
I wish someone cared for me as much as Bob cares for the deer.
Lol 😂
care for someone as much as bob cares for his deer.
Oooooooh, I know !
Jesus cares for you way more than Bob cares about the deer.
i died laughing...
5:00 - She lied to us about not talking math! Five minutes in she brought up logs!
Yes, but the logs in this case have no rhythm. Pay attention!
It’s the classic teacher trick .. I will tell you a story and off he goes straight into ‘open your textbooks’ ..
Oh you are my favourite person, sir.
Good one, mate.
Lmao! That was a good one
She sounded so disappointed when she didn’t know if deer had tails 😂
Wes Wes I noticed that too. She looked sincerely disappointed
Too much maths and not enough observation! A problem in science these days!!!
When Bob finishes counting the grains of sand he discovers the number of deer has changed.
Good Idea, time calculation, ratio of growing number of deer and, his own food supply etc...
That's the mathematical process of multiplication
Bob gets triggered and eats the extra dear, now according to his calculations they 🙂🙂are now equal
Highlander deers
Bob see the entire city is built and no more forest left when he count the last grain.
My six year old granddaughter totally enjoyed this video. She was delighted to see a young woman telling the story. We are still working on addition and subtraction but now she knows that there are more fun things to do in math. Thank you!
The way she talks, its therapeutic, and she does explain these important concepts pretty well, kudos to her
You have a truly wonderful and rare gift for imaginative communication. I hope more people watch your videos and get a sense of what a wonderful world there is in math.
Very innovative, outside the box, and winsome, capturing the simple essence of the amazing thing we call calculus.
Thank you, this is a very important teaching strategy. People like me always struggled in maths because the teacher couldn’t or wouldn’t explain the topic another way. Using stories and analogy’s makes the difference to my style of learning. In teaching we use the term ‘differentiation’, in a non mathematical sense that is used to ensure that each student with a different learning need can be catered for. Some students are very visual in that you show them, sometimes with pictures, or using physical objects to demonstrate the point. Other students learn quickly through audible as in, they understand by hearing an explanation or a fact or series of related facts. Whilst others learn by doing something, applying the principle whether it’s solving a problem by touching, feeling or placing or rearranging component parts or objects.
Thank you for this you are a really good instructor. 😃
Wow, I instantly subscribed when this lovely lady started to speak. I wanted to hear more, just to hear her speak!
Speechless.. You r such an amazing soul with great clarity of topics. Keep up the great work!
Charming and elegant; even Leibniz would have loved it and if deers could sculpt they'd dedicate a statue to Bob.
The first time through I was simply mesmerized by her smile. Then I had to watch it again to notice anything she said.
I wish you were a teacher when I was at school. You sound lovely, there’s kindness to you and you make things simple
I had a teacher in school who, although different, had a lot in common with Tibees...
I never missed any of her classes... But, still, never learned a thing... :-)
You know she really knows her stuff when she can explain calculus in such an understandable way. I could have used her in high school for calculus 😭
You are the only speaker who can smile while speaking....it makes you instantly charming, couple it with your melodious voice, I can listen to you talking math any amount of time....add to that your simple way of explaining complex subjects, your videos have become irresistible!
This is so calming and beautiful, and I learned something! Thank you
"In this Meadow are a couple of deer who are very dear to him."😂
Abhimaneu KJ Deer are dear to Bob but also deer to everyone else 🤔
Oh, dear!
How else are deer supposed to be?
I'm really fawning over your post. Can I offer you a buck for it? I just want to make sure you have some doe. :)
She says "Dee-uh," as if she "fee-uhs" the "lett-uh" "ahh-uh."
Lady, where are you from?
I was going to go to bed, but... This is just a little better than sleeping.
You have this wonderful impish smile... "Sneaking" in the learning. Your teaching is just ARTISTIC! I write training for a living, and I can march information past people and get them to remember it. You get people to take a walk with the concepts, dance with them, mingle with them - and they look down and they've walked through 10 concepts with comfort and ease. BRAVO! Absolutely BRAVO to you for taking higher match from cruel to COOL!!! Just amazing! Thank you!
DEAR AND GLORIOUS EDUCATOR,
You are answering a great calling!
How refreshing it is to see the way you have undertaken the sacred role of the educator... and how learned you have become in so few years! (I am tempted to borrow further from others by stating - "I never knew so young a body with so old a head"). Your delivery and the obvious pleasure the process provides you are worthy of remark. You are a natural teacher... a born enthusiast... and, clearly, you cause a viewer to be all the more attentive due to such attributes.
Furthermore, by offering-up your instructive videos on the worldwide Internet, you are bringing much to average man.
Rather late in his life, I knew an ex Harvard student who left early... and was often described as having brought science, math, complex and critical thought to average man... everywhere and every-when... due to his lifelong worldwide travel for speaking engagements, his extensive writings, and certain films that will live forever. "The Leonardo of our times" - R. Buckminster Fuller - in his youth must have shared much in his nature with you. Ultimately, he was nominated for the Nobel Peace Prize.
I can not help but wonder where your callings will carry you... and how you will serve those who connect with you. This is approximately what I said last year to a man named Bezos at a small gathering in a private home. I framed my comments to him to (hopefully) cause a new type of contemplation about a calling to the role of the humanitarian (because it would be intellectually proper and because his further pursuit of commercial success could not materially advance his human growth nor the welfare of many the way a "Fullerian" redirection of his life would). I asked about what his dreams involved citing the title of a book that his company sold among millions of other titles, Einstein's Dreams. During the depth of night when one's imaginings might reach well beyond what was possible in a typical dream... where might soar the greatest of minds/the possessor of the greatest of tools (e.g. wealth of a scale never before seen)? In the most extreme, evolved form of one's envisionings, what might be accomplished in the future by such a dreamer?
And, I can assure you that it is not overly melodramatic to ask those questions of you. You have many gifts and a truly great start. I do hope to learn about where you will go... and to what altitudes you will soar!
With sincere compliments,
Gordon
gstubbs@aviajets.com
The slope is *just* flat enough so Bob can walk down the bridge and the area of the grass is *just* big enough to feed the deer. Bob is some risky dude.
Kjoergoe did you *just* come seeing that grammar video?
Bob thinks with his heart
I really enjoyed watching her pretty smile, and I learned about differentiation and integration and everyone in the meadow has enough to eat!
Yay more of these! The attention to detail is just fantastic, just as the calming visuals, the funny words you use and the way you speak so softly. Thank you so much Toby!
I Saw this entire 14:52 Seconds Video With a Smile on my Face cause you had one on your Face for the whole time.And Yesss ThankU for the Concept.❤
Asmr + Calculus = Soothing + mind boggling 👍👍❤️❤️
Bob Ross would be sad if a "happy little tree" falls down.
Then he'd spend 15 minutes explaining how the Happy Little Tree fell to provide more sunlight for the Happy Little Shrubs - which he would paint with some Forest Green and a fan brush in 3.6 seconds and they'd look exactly like real shrubbery...
@@philipbohi983 Bring me a SHRUBBERY... nnnNEE !!!
Bur that wouldn't be a mistake. It would be a happy accident
Barney -😃 I'll bring you a shrubbery, but first you must chop down the largest tree in the forest with....
...a HERRING! Then, we'll place the shrubbery in a little 2-level effect with a path running between them.
(Note: for anyone reading this and wondering wtf we are referencing, it's quotes from "Monty Python and the Holy Grail", one of the most awesomely silly movies ever made. And if you know the movie, I have one question for you: What is the air-speed velocity of an unladen Swallow?)
Best asmr channel.
www.theguardian.com/lifeandstyle/2018/oct/06/sensory-videos-relaxation
LOL IKR?!? This is what i watch for unintentional asmr.
What the hell is asmr????
@@semmugilanv4888 Do you have an internet connection?
True dat. Clearest tingles ever
You are the true beauty with an excellent brain 🌺
@Nim Boo I am sorry your parents did not raise you with the ability to contribute helpfully online. We are poorer for it.
@Nim Boo Yes. Don't meddle with and allow Indian caste system to vanish. We need different breed to survive, especially the uniquely excellent different Indian types.
perhaps you were the real reason for Bob to come down to the meadow, and to hell with the deer.
@Nim Boo see above
You are so worderfull, your energy raises me everytime!
Thank you, Toby. This was a perfect way to explain Calculus. I love Calculus and Mathematics in general very much and this little fun story is EXACTLY the essence of Calculus! 💖
Toby, this series are really successful and enjoyable to watch. As a physics lover i must say, continue that series.
Buğrahan İbicek thanks!
Fantastic video! I learned so much. Just love how the story weaves in central ideas of calculus. Thank you very much for posting this!
Jeez! My face hurts because I was smiling like an idiot throughout the entire video just seeing you smile continously and listening to the story.
Instant sub!
I'm with you with the smiling 😁😁
Now as I've read it, I realized that I did the same :-))))))
@f1fanforever
- LMAO - THANKS for sending me over the edge with that comment!! I'm grinning and laughing so hard, my cheeks hurt, I'm crying and can barely type out my reply....!...
I learned calculus (on a “this is how you do it” basis) in school sixty-five years ago. At last I’m beginning to understand. Thank you - you’re a superb teacher.
I understand. If teachers are not committed, lazy and ignorant, they do a poor job of teaching. This causes students to lose interest in studies and this is especially true for subjects such as math. Biology and chemistry can be understood bcoz we know d applications of d concepts involved which is self evident. Whereas math is not so. I hope all math teachers make a note of this...
Your voice is just so pleasant I could listen to you nag and still find it relaxing
Good story telling always has a real lesson in it. Interesting approach to teaching a complex subject
You've introduced me to Bob Ross and I have so much gratitude for you for this!!! Thank you so much.
I have never seen you not smiling. You are great 💞
WOW! Beauty and smart .. Normally, these two don't go together :-) ... I don't know how I got to this video, but I couldn't interrupt watching .. not sure her voice or her smile or both ... Very great teaching skills ... and patience .. so young and so smart and patient ....
Bravo to you and bravo to the birds. The outdoor setting in your vids is important and very welcoming.
If my calc teacher would have started class on day one with a story like this, I would have enjoyed the class more lol
yeah... after that ... you need to read one, only one pdf of Miles Mathis on Calculus ...
Loved this! Are you a highly visual thinker/learner too? Your explanations are excellent for people like myself who sometimes have trouble grasping abstract concepts unless we can visualise them.
i always get so happy to watch your videos :) thank you for making these!!!!
Very Charming Story told in a very simplistic but detailed manner.
This is so sweet .. thank you ….. one thing to note which still requires integration is that the cumulative area of the gaps between sand grains may be bigger compared to the area of the gaps between the big stones, this is known as porosity. In short porosity is a ratio measure (in %) of the material to the volume of its container
I though I was having a hard day until I found out about Bob!
lmao
Hahaha I love the little tidbits of humor in these videos...lays down individual pebbles of sand to the point that "it's no longer day, it turns to night, then it turns to day.."
Brandon Ulloa I don’t get it, how’s that humorous?
I get it
Anyone who can talk while smiling, gets a like from me.
We can do that?-😂😂😂
Edit:
oh wait- I can-
Welcome to being women. Our training starts very early.
gorgeous setting
I did Differentiation and Integration in school decades ago and I never knew what they were supposed to do! Thanks for this. Some teachers are not good, but you are great.
She could talk about anything, and i'd listen!
*She could
She's = contraction of "she is/has"
alvallac21 I’m very aware chief. Just a typo
When will you be getting your own TV Show, because I AM READY!
I second this
Neptunee I second your second
@@shanewilson1160
I second your seconds second
@@stardust4001 I second your second's second's second
@@saaanchii
I second your seconds seconds seconds second.
Ok thats enough lol
honestly i dont watch a single one of your videos for the knowledge just to used ur voice as gentle calming asmr XD
I don't particularly enjoy this topic but Toby's presentation is so lovely
The smile and joy is the only reason I watched all the way. interesting, wish I would have had teachers like you. :)
Bob is one clever mountain man. If you’re going to survive the harsh conditions on the somewhat vertical side of land, you will definitely need an available food source at the ready.
Differentiation and Integration.
A few days later his friend George (Green) came to visit and Bob recounted the tale of how many days he spent counting grains of sand. George broke out in a hearty laugh, "Why didn't you talk to me first. You know I've been working on line integrals around closed curves. In fact I've got this tremendous theorem . We could have built a large planimeter and saved you days and days".
Peter Brough haha!
Teaching crazy calculus: "I dont know if deer have a tail.." hehe
Well, well done! Beautifully presented...Keep going...The world needs you...
Thank you very much indeed. I am an English teacher in Italy, but I really enjoyed my maths lessons at school back in London, even though I was not good at maths. However, I suppose the reason I enjoyed it was due to my brilliant and enthusiastic Indian maths teacher, Mr Sharma.
I think that you have a great imagination, and your story is wonderful. It brought me a step closer to understanding the terms ‘differentiation’ and ‘ integration’. I wish you too a splendid mathematical day. All the best.
If you were my calculus teacher, I'd never skip a class,
I should say that I liked your attempt to use a story to link the fundamental ideas of calculus and to help the viewers remember it. I also liked the use of pebbles which is the literal meaning of calculus in Latin (they used them in abacus) and it refers to counting the areas of the infinitesimal rectangles in integration.
However, Gauss once said that the story of the apple falling on Newton's head was a myth that Newton made up to explain gravity because he couldn't explain its deep mathematical formulations to the public. In my opinion, what makes calculus or in general mathematics, one of the most difficult subjects are its high level of abstractness and the concept of infinity. Infinity is a concept, not an amount, and from the largest possible amount to infinity, we need an intuitive leap that doesn't happen in the physical world. That's what your narration needed to convey the essence of calculus.
Another example would be teaching the index form. We can easily say that 2 cubed is 2 multiplied by itself three times. If we don't facilitate students (or in general learners) with the smooth transition to more abstract ideas, they can hardly understand 2^0. What does it even mean? 2 multiplied by itself 0 times? Then should it be 2 or 0? That's why when you ask students what do they think about 2^0 their first answer would be 2 or 0. Because they don't know 2^0 represents a form of writing 1 which helps us extend the application of the index form to, say, to invent the standard form.
The problem with these kinds of stories is that it might even stop people to dig more deeply. Milan Kundera once said that since people didn't understand the deep ideas of communism, the communist leaders had to simplify it for the mass, so they reduced them to some slogans which people could repeat without understanding. This is, more or less, my criticism about your video, though I really liked you and appreciated your effort to educate the public about calculus.
I guess at the end of life, someone like her came to guide you to heaven.
This was hilarious! Thank you! Hopefully your guide to heaven doesn't require you pass Calculus!
She's the fit version of Walkyries
@@Kobe29261 heaven requires you to believe in Jesus Christ and to repent of your sins and that’s it :)
@@citrus4419 k
I like the trees drawn by the ma'am its sooo cute.
Thank you
Tibees - how absolutely delightful. Thoroughly enjoyable as a story of Bob in the mountains, and literally a wonderful illustration of the application of calculus. It's impossible not to smile watching this, in the same way as it's impossible to find the derivative of a vertical line.
After laying down all those grains of sand... bob discovers - he lost count.
I wonder, if he is Bob the Builder...
It's actually Sideshow Bob, doing community service.
Bob is islamic who care about muslim in china
Bobs you're uncle.
It’s actually Bob Lazar
It's BOB ROSS GDmmit!!! Happy Tree and friends that are DEER. Plus she is drawing a mountain. I am convinced.
plot twist : it turns out there isnt enough grass left in the meadow to go around for every deer so Bob decides to sacrifice the excess animals in order for the remaining ones to thrive.
Satisfied about how successful this plan was, Bob changes his name to Thanos and decides to go search for the infinity stones.
infinity pebbles*
*plot twist*
bob got hungry while counting sand so he just ate the rest
You have a dark mind.
And Thor arrives to stop Thanos, leaves the bifrost mark on the grass all over and no sign of grass anymore...
thanks for your persistence with us and enthusiasm
I absolutely sure I was forced to subscribe to your channel seeing your adorable smile, listening your charming voice and drowning in your sweetest manner! :)
wow , the idea of mathematics with nature are awesome😊😊😍😍😘 , i am also try with physics and mathematics are connected with a simple e.g of nature but in india mathematics are always connect with important question for exam not for beauty of subject😬
Nature is awesome 👌👌👌🙏
She's got a serious mathematical Daenerys Targaryen vibe going
Like Bob Ross made me feel confident and interested on painting (when in reality I am a disaster painting anything) you made me feel confident and interested on maths (and I'm bad on maths too).
I'm infinitely amazed ❤️
You're really wondrous. Thanks so much for all you do.
I was learning how to fix my Garage door opener, RUclips decides I need calculus lessons!?
Did you watch the video 😉
“Welcome to another episode of “Fun with Flags”!”
😁
Seriously now, this was great! Clearly explained and entertaining. Thank you
It was me. I broke the bridge. Bob’s wife needed a break from that deer loving neglectful husband
😂 And you are Dead..
Great ideas explained very very very well passionately. Kids wanna wanna attend your lectures ... thank you for doing this!
I can't think of a better way to refresh what I didn't learn at school but should have.
Great stuff!