Calculus explained through a story
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- Äas pĆidĂĄn 5. 10. 2018
- 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 - VÄda a technologie
Fun fact: the word calculus comes from the latin word for small pebble
Tibees
Iâm sorry but...
Kidney stones.
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.
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
*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.
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.
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 đ€Łđ€Łđ€Ł
Lolđđđ
I feel like I was just cured of some weird math disease Iâve had for a decade. Awesome video! Thank you!
I have no idea what she's talking about but she's impossibly charming.
haha same :)
@@lotsofhairbutnomoney3705 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.
Sheâs literally putting Bob Ross in calculus in the same world. My life is complete đâ€ïž
Youâre the prettiest and most peaceful math teacher Iâve 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.
Bob: Lays down sand
Windy day: Oh no you donât
Haha XD
After traveling 50 miles to the beach!
He protecc
He attacc
But most importantly he wants his grass bacc
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!
Itâs the classic teacher trick .. I will tell you a story and off he goes straight into âopen your textbooksâ ..
Oh you are my favourite person, sir.
Good one, mate.
Lmao! That was a good one
your smile can put a sense of serenity into my stressed up soul
The deer died 15 years ago...Bob still hasnât finished counting his sand grains
Turns out there were no deer-Bob lives in an insane asylum...âcounting sandâ
Okay, I laughed, but she is still good!
@@javapaceable LMFAO
but his legacy continues to live on
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!
Imagine how peaceful, rational, and lovely the world would be if everyone was like Toby. My new happy place.
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 (CZcams, 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
She sounded so disappointed when she didnât know if deer had tails đ
Wes Wes I noticed that too. She looked sincerely disappointed
Too much maths and not enough observation! A problem in science these days!!!
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!
CZcams 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.
This is like meditation for me whilst learning something that bored me to tears when I was too young to learn it.
đ agreed
I wish someone cared for me as much as Bob cares for the deer.
Lol đ
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...
Wow! Story telling is a license to print memories in the minds your audience! Beautifully illustrated and delivered, this lady is inspiring to watch.
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 đđare now equal
Highlander deers
Bob see the entire city is built and no more forest left when he count the last grain.
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 đ
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!
"In this Meadow are a couple of deer who are very dear to him."đ
Abhimaneu KJ Deer are dear to Bob but also deer to everyone else đ€
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?
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.
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!
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
I was going to go to bed, but... This is just a little better than sleeping.
Asmr + Calculus = Soothing + mind boggling đđâ€ïžâ€ïž
Speechless.. You r such an amazing soul with great clarity of topics. Keep up the great work!
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 -đ 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?)
Charming and elegant; even Leibniz would have loved it and if deers could sculpt they'd dedicate a statue to Bob.
Thank you, this is a very important teaching strategy. People like me always struggled in maths because the teacher couldnât or wouldnât explain the topic another way. Using stories and analogyâs makes the difference to my style of learning. In teaching we use the term âdifferentiationâ, 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 itâs solving a problem by touching, feeling or placing or rearranging component parts or objects.
Thank you for this you are a really good instructor. đ
Fantastic video! I learned so much. Just love how the story weaves in central ideas of calculus. Thank you very much for posting this!
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 wish you were a teacher when I was at school. You sound lovely, thereâs 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... :-)
Wow, I instantly subscribed when this lovely lady started to speak. I wanted to hear more, just to hear her speak!
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! đ
The first time through I was simply mesmerized by her smile. Then I had to watch it again to notice anything she said.
The way she talks, its therapeutic, and she does explain these important concepts pretty well, kudos to her
i always get so happy to watch your videos :) thank you for making these!!!!
Good story telling always has a real lesson in it. Interesting approach to teaching a complex subject
You are the true beauty with an excellent brain đș
@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
I really enjoyed watching her pretty smile, and I learned about differentiation and integration and everyone in the meadow has enough to eat!
Your voice is just so pleasant I could listen to you nag and still find it relaxing
Well, well done! Beautifully presented...Keep going...The world needs you...
This is so calming and beautiful, and I learned something! Thank you
Anyone who can talk while smiling, gets a like from me.
We can do that?-đđđ
Edit:
oh wait- I can-
Welcome to being women. Our training starts very early.
Very Charming Story told in a very simplistic but detailed manner.
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
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!
Toby, this series are really successful and enjoyable to watch. As a physics lover i must say, continue that series.
BuÄrahan Ä°bicek thanks!
You are so worderfull, your energy raises me everytime!
Simply enchanting. Thanks for sharing!
She could talk about anything, and i'd listen!
*She could
She's = contraction of "she is/has"
alvallac21 Iâm very aware chief. Just a typo
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 ...
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!
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!
I though I was having a hard day until I found out about Bob!
lmao
I have never seen you not smiling. You are great đ
I really love your videos and its contents and how its presented in a calming and soothing way
I learned calculus (on a âthis is how you do itâ basis) in school sixty-five years ago. At last Iâm beginning to understand. Thank you - youâre 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...
You've introduced me to Bob Ross and I have so much gratitude for you for this!!! Thank you so much.
If you were my calculus teacher, I'd never skip a class,
Bravo to you and bravo to the birds. The outdoor setting in your vids is important and very welcoming.
This was fascinating! Thank you for your hard work!
After laying down all those grains of sand... bob discovers - he lost count.
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 thatâs it :)
@@citrus4419 k
@@citrus4419 You're one of the reasons people say Christians have no sense of humor.
gorgeous setting
I can't think of a better way to refresh what I didn't learn at school but should have.
Great stuff!
"Don't stress too much about trying to turn your brain on". Now that's my kind of girl.
Bob is one clever mountain man. If youâre 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.
This calmed me down so much, thanksâ€ïž
thanks for your persistence with us and enthusiasm
honestly i dont watch a single one of your videos for the knowledge just to used ur voice as gentle calming asmr XD
She's got a serious mathematical Daenerys Targaryen vibe going
You are a GIFT. Please keep it coming.tx.â„
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.
Wish Toby was around to teach me calculus like this 14 years ago when i cried tears of blood thru calculus classes.
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!
The smile and joy is the only reason I watched all the way. interesting, wish I would have had teachers like you. :)
This is soooo friggin calming
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 đđ
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....!...
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
This is so sweet .. thank you âŠ.. 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
You're really wondrous. Thanks so much for all you do.
Teaching crazy calculus: "I dont know if deer have a tail.." hehe
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 canât get enough of these videos
This is so soothing.
I was learning how to fix my Garage door opener, CZcams decides I need calculus lessons!?
Did you watch the video đ
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 donât get it, howâs that humorous?
I get it
i dont get it
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.
A nice story that leads to "differentiation" and "integration". You just have reminded me the days that I was having so much fun in all three calculus classes. Well done !
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.
Itâs actually Bob Lazar
@paul snor Happy little tree? Absolutely!
You are a math angel, thank you!! That was really interesting to watch!
Thanks for the lesson ,TOBY!ââđđđđ
Excellent, very creative! Good stuff, thank you!