Calculus explained through a story 

Fun fact: the word calculus comes from the latin word for small pebble

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

I have no idea what she's talking about but she's impossibly charming.

She’s literally putting Bob Ross in calculus in the same world. My life is complete 😭❤️

Bob repairs bridges Bob cares for the deers Bob is a good guy Be like Bob...

I feel like I was just cured of some weird math disease I’ve had for a decade. Awesome video! Thank you!

*Next up :* bob goes to cern to split some atoms so he can perfectly measure the surface

Calculus: how to guess really good.

You’re the prettiest and most peaceful math teacher I’ve ever seen.

Bob: Lays down sand Windy day: Oh no you don’t

He protecc He attacc But most importantly he wants his grass bacc

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!

your smile can put a sense of serenity into my stressed up soul

The deer died 15 years ago...Bob still hasn’t finished counting his sand grains

This is like meditation for me whilst learning something that bored me to tears when I was too young to learn it.

How did i get here? Three clicks ago I was listening to Slipknot.

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.

She sounded so disappointed when she didn’t know if deer had tails 😂

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.

5:00 - She lied to us about not talking math! Five minutes in she brought up logs!

I wish someone cared for me as much as Bob cares for the deer.

Imagine how peaceful, rational, and lovely the world would be if everyone was like Toby. My new happy place.

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 😭

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!

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. 😃

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 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

Wow, I instantly subscribed when this lovely lady started to speak. I wanted to hear more, just to hear her speak!

The way she talks, its therapeutic, and she does explain these important concepts pretty well, kudos to her

"In this Meadow are a couple of deer who are very dear to him."😂

Bob Ross would be sad if a "happy little tree" falls down.

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!

Speechless.. You r such an amazing soul with great clarity of topics. Keep up the great work!

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.

Best asmr channel.

Fantastic video! I learned so much. Just love how the story weaves in central ideas of calculus. Thank you very much for posting this!

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! 💖

You are the true beauty with an excellent brain 🌺

Charming and elegant; even Leibniz would have loved it and if deers could sculpt they'd dedicate a statue to Bob.

I really enjoyed watching her pretty smile, and I learned about differentiation and integration and everyone in the meadow has enough to eat!

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 was going to go to bed, but... This is just a little better than sleeping.

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

Asmr + Calculus = Soothing + mind boggling 👍👍❤️❤️

Toby, this series are really successful and enjoyable to watch. As a physics lover i must say, continue that series.

If my calc teacher would have started class on day one with a story like this, I would have enjoyed the class more lol

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!

Your voice is just so pleasant I could listen to you nag and still find it relaxing

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".

This is so calming and beautiful, and I learned something! 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.

You've introduced me to Bob Ross and I have so much gratitude for you for this!!! Thank you so much.

honestly i dont watch a single one of your videos for the knowledge just to used ur voice as gentle calming asmr XD

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.

I really love your videos and its contents and how its presented in a calming and soothing way

I though I was having a hard day until I found out about Bob!

Teaching crazy calculus: "I dont know if deer have a tail.." hehe

I have never seen you not smiling. You are great 💞

I can't think of a better way to refresh what I didn't learn at school but should have. Great stuff!

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

She could talk about anything, and i'd listen!

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!

Bravo to you and bravo to the birds. The outdoor setting in your vids is important and very welcoming.

You are so worderfull, your energy raises me everytime!

After laying down all those grains of sand... bob discovers - he lost count.

When will you be getting your own TV Show, because I AM READY!

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 !

The smile and joy is the only reason I watched all the way. interesting, wish I would have had teachers like you. :)

Wish Toby was around to teach me calculus like this 14 years ago when i cried tears of blood thru calculus classes.

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.

This was fascinating! Thank you for your hard work!

Well, well done! Beautifully presented...Keep going...The world needs you...

She's got a serious mathematical Daenerys Targaryen vibe going

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.."

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

Anyone who can talk while smiling, gets a like from me.

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!

Lovely story, amazing analogies. Remind me of what I was taught in painting , to use the pencil as a measure with the eye. Differentiation and integration , lovely.

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.

I was learning how to fix my Garage door opener, RU-vid decides I need calculus lessons!?

I guess at the end of life, someone like her came to guide you to heaven.

This calmed me down so much, thanks❤️

Simply enchanting. Thanks for sharing!

If you were my calculus teacher, I'd never skip a class,

"Don't stress too much about trying to turn your brain on". Now that's my kind of girl.

Awesome! This is probably the most progress I've made in understanding advanced math. And to think that Bob did all that without eating!

You are a GIFT. Please keep it coming.tx.♥

I wonder, if he is Bob the Builder...

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.

You're really wondrous. Thanks so much for all you do.

thanks for your persistence with us and enthusiasm

Where were you when I was in high school? 😆 Great explanation btw, love your story.

You are a math angel, thank you!! That was really interesting to watch!

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.❤

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! :)